From e6ef405c62f311e087289c354d03dc3e84e84a56 Mon Sep 17 00:00:00 2001 From: Cassandra Heart Date: Sat, 15 Apr 2023 00:05:26 -0400 Subject: [PATCH] Initial commit of CLI client --- basis.json | 65808 ++++++++++++++++++++++++++++++++ bootstrap.go | 251 + ec/bls48581/ARCH.go | 27 + ec/bls48581/BIG.go | 1023 + ec/bls48581/BLS256.go | 155 + ec/bls48581/CONFIG_BIG.go | 34 + ec/bls48581/CONFIG_CURVE.go | 76 + ec/bls48581/CONFIG_FIELD.go | 47 + ec/bls48581/DBIG.go | 298 + ec/bls48581/ECDH.go | 381 + ec/bls48581/ECP.go | 1850 + ec/bls48581/ECP8.go | 1074 + ec/bls48581/FP.go | 760 + ec/bls48581/FP16.go | 616 + ec/bls48581/FP2.go | 505 + ec/bls48581/FP4.go | 759 + ec/bls48581/FP48.go | 1189 + ec/bls48581/FP8.go | 781 + ec/bls48581/HPKE.go | 327 + ec/bls48581/MPIN256.go | 202 + ec/bls48581/PAIR8.go | 978 + ec/bls48581/ROM.go | 74 + ec/bls48581/core/AES.go | 835 + ec/bls48581/core/DILITHIUM.go | 1290 + ec/bls48581/core/GCM.go | 457 + ec/bls48581/core/HASH256.go | 233 + ec/bls48581/core/HASH384.go | 247 + ec/bls48581/core/HASH512.go | 247 + ec/bls48581/core/HMAC.go | 909 + ec/bls48581/core/KYBER.go | 796 + ec/bls48581/core/RAND.go | 178 + ec/bls48581/core/SHA3.go | 302 + ec/bls48581/core/SHARE.go | 164 + feldman/feldman.go | 540 + go.mod | 7 + go.sum | 4 + main.go | 71 + quil_voucher.hex | 1 + 38 files changed, 83496 insertions(+) create mode 100644 basis.json create mode 100644 bootstrap.go create mode 100644 ec/bls48581/ARCH.go create mode 100644 ec/bls48581/BIG.go create mode 100644 ec/bls48581/BLS256.go create mode 100644 ec/bls48581/CONFIG_BIG.go create mode 100644 ec/bls48581/CONFIG_CURVE.go create mode 100644 ec/bls48581/CONFIG_FIELD.go create mode 100644 ec/bls48581/DBIG.go create mode 100644 ec/bls48581/ECDH.go create mode 100644 ec/bls48581/ECP.go create mode 100644 ec/bls48581/ECP8.go create mode 100644 ec/bls48581/FP.go create mode 100644 ec/bls48581/FP16.go create mode 100644 ec/bls48581/FP2.go create mode 100644 ec/bls48581/FP4.go create mode 100644 ec/bls48581/FP48.go create mode 100644 ec/bls48581/FP8.go create mode 100644 ec/bls48581/HPKE.go create mode 100644 ec/bls48581/MPIN256.go create mode 100644 ec/bls48581/PAIR8.go create mode 100644 ec/bls48581/ROM.go create mode 100644 ec/bls48581/core/AES.go create mode 100644 ec/bls48581/core/DILITHIUM.go create mode 100644 ec/bls48581/core/GCM.go create mode 100644 ec/bls48581/core/HASH256.go create mode 100644 ec/bls48581/core/HASH384.go create mode 100644 ec/bls48581/core/HASH512.go create mode 100644 ec/bls48581/core/HMAC.go create mode 100644 ec/bls48581/core/KYBER.go create mode 100644 ec/bls48581/core/RAND.go create mode 100644 ec/bls48581/core/SHA3.go create mode 100644 ec/bls48581/core/SHARE.go create mode 100644 feldman/feldman.go create mode 100644 go.mod create mode 100644 go.sum create mode 100644 main.go create mode 100644 quil_voucher.hex diff --git a/basis.json b/basis.json new file mode 100644 index 0000000..7884850 --- /dev/null +++ b/basis.json @@ -0,0 +1,65808 @@ 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"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" + ] + }, + "potPubkey": "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" + } + ] +} diff --git a/bootstrap.go b/bootstrap.go new file mode 100644 index 0000000..4abf083 --- /dev/null +++ b/bootstrap.go @@ -0,0 +1,251 @@ +package main + +import ( + "bytes" + "crypto" + "crypto/rand" + "encoding/hex" + "encoding/json" + "fmt" + "io" + "net/http" + "os" + "strings" + + "github.com/cloudflare/circl/sign/ed448" + bls48581 "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581" +) + +const SEQUENCER_ACCEPTING = "\"ACCEPTING\"" + +type PowersOfTauJson struct { + G1Affines []string `json:"G1Powers"` + G2Affines []string `json:"G2Powers"` +} + +type ContributionJson struct { + PowersOfTau PowersOfTauJson `json:"powersOfTau"` + PotPubKey string `json:"potPubKey"` + VoucherPubKey string `json:"voucherPubKey"` +} + +type BatchContribution struct { + Contribution Contribution +} + +type PowersOfTau struct { + G1Affines []*bls48581.ECP + G2Affines []*bls48581.ECP8 +} + +type Contribution struct { + NumG1Powers int + NumG2Powers int + PowersOfTau PowersOfTau + PotPubKey *bls48581.ECP8 +} + +var voucherPubKey ed448.PublicKey +var voucher ed448.PrivateKey +var secret *bls48581.BIG +var bcj *ContributionJson = &ContributionJson{} + +func JoinLobby() { + var err error + if voucherPubKey == nil { + voucherPubKey, voucher, err = ed448.GenerateKey(rand.Reader) + if err != nil { + panic(err) + } + } + + sig, err := voucher.Sign(rand.Reader, []byte("JOIN"), ed448.SignerOptions{Hash: crypto.Hash(0), Scheme: ed448.ED448}) + if err != nil { + panic(err) + } + + reqHex := hex.EncodeToString(voucherPubKey) + sigHex := hex.EncodeToString(sig) + + req, err := http.NewRequest("POST", HOST+"join", bytes.NewBuffer([]byte(reqHex))) + if err != nil { + panic(err) + } + + req.Header.Set("Content-Type", "text/plain") + req.Header.Set("Authorization", sigHex) + + client := http.DefaultClient + resp, err := client.Do(req) + fmt.Println("connected") + + if err != nil { + panic(err) + } else { + _, err := io.ReadAll(resp.Body) + if err != nil { + panic(err) + } else { + return + } + } +} + +func GetSequencerState() string { + req, err := http.NewRequest("POST", HOST+"sequencer_state", bytes.NewBuffer([]byte("{}"))) + if err != nil { + panic(err) + } + + req.Header.Set("Content-Type", "application/json") + + client := http.DefaultClient + resp, err := client.Do(req) + if err != nil { + panic(err) + } + + sequencerState, err := io.ReadAll(resp.Body) + if err != nil { + panic(err) + } + return string(sequencerState) +} + +func Bootstrap(batch uint, batchSize uint) { + if batch == 65536/batchSize { + return + } + + if batch == 0 { + secretBytes := make([]byte, (8 * int(bls48581.MODBYTES))) + rand.Read(secretBytes) + secret = bls48581.FromBytes(secretBytes) + + bcjRes, err := http.DefaultClient.Post(HOST+"current_state", "application/json", bytes.NewBufferString("{}")) + if err != nil { + panic(err) + } + + defer bcjRes.Body.Close() + + bcjBytes, err := io.ReadAll(bcjRes.Body) + if err != nil { + panic(err) + } + + if err := json.Unmarshal(bcjBytes, bcj); err != nil { + // message is not conformant, we are in validating phase + panic(err) + } + } + + contributeWithSecrets(batch, batchSize, secret) + + fmt.Printf("Participating... %f%% Complete\n", float32(batch*batchSize)/655.36) +} + +func contributeWithSecrets(batch uint, batchSize uint, secret *bls48581.BIG) error { + updatePowersOfTau(batch, batchSize, secret) + + if batch == 0 { + updateWitness(secret) + } + + return nil +} + +var xi *bls48581.BIG +var xi2 *bls48581.BIG + +func updatePowersOfTau(batch uint, batchSize uint, secret *bls48581.BIG) { + if batch == 0 { + xi = bls48581.NewBIGint(1) + xi2 = bls48581.NewBIGint(1) + } + + for i := batchSize * batch; i < batchSize*(batch+1); i++ { + g1PowersString := strings.TrimPrefix(bcj.PowersOfTau.G1Affines[i], "0x") + g1PowersHex, _ := hex.DecodeString(g1PowersString) + g1Power := bls48581.ECP_fromBytes(g1PowersHex) + + if g1Power.Equals(bls48581.NewECP()) { + panic("invalid g1Power") + } + + g1Power = g1Power.Mul(xi) + g1Power.ToBytes(g1PowersHex, true) + bcj.PowersOfTau.G1Affines[i] = "0x" + hex.EncodeToString(g1PowersHex) + + if (i%batchSize == 0) && i < uint(257*batchSize) { + g2PowersString := strings.TrimPrefix(bcj.PowersOfTau.G2Affines[i/batchSize], "0x") + g2PowersHex, _ := hex.DecodeString(g2PowersString) + g2Power := bls48581.ECP8_fromBytes(g2PowersHex) + + if g2Power.Equals(bls48581.NewECP8()) { + panic("invalid g1Power") + } + + g2Power = g2Power.Mul(xi2) + g2Power.ToBytes(g2PowersHex, true) + bcj.PowersOfTau.G2Affines[i/batchSize] = "0x" + hex.EncodeToString(g2PowersHex) + xi2 = bls48581.Modmul(xi2, secret, bls48581.NewBIGints(bls48581.Modulus)) + } + xi = bls48581.Modmul(xi, secret, bls48581.NewBIGints(bls48581.Modulus)) + } +} + +func updateWitness(secret *bls48581.BIG) { + g2PowersString := strings.TrimPrefix(bcj.PotPubKey, "0x") + g2PowersHex, _ := hex.DecodeString(g2PowersString) + g2Power := bls48581.ECP8_fromBytes(g2PowersHex) + + if g2Power.Equals(bls48581.NewECP8()) { + panic("invalid g2Power") + } + + newPotPubKey := g2Power.Mul(secret) + newPotPubKey.ToBytes(g2PowersHex, true) + bcj.PotPubKey = "0x" + hex.EncodeToString(g2PowersHex) + bcj.VoucherPubKey = "0x" + hex.EncodeToString(voucherPubKey) +} + +func ContributeAndGetVoucher() { + sendBytes, err := json.Marshal(bcj) + if err != nil { + panic(err) + } + + req, err := http.NewRequest("POST", HOST+"contribute", bytes.NewBuffer(sendBytes)) + if err != nil { + panic(err) + } + + req.Header.Set("Content-Type", "application/json") + sig, err := voucher.Sign(rand.Reader, []byte(bcj.PotPubKey), ed448.SignerOptions{Hash: crypto.Hash(0), Scheme: ed448.ED448}) + if err != nil { + panic(err) + } + + sigHex := hex.EncodeToString(sig) + req.Header.Set("Authorization", sigHex) + + client := http.DefaultClient + resp, err := client.Do(req) + if err != nil { + panic(err) + } + + defer resp.Body.Close() + filename := "quil_voucher.hex" + if len(os.Args) > 1 { + filename = os.Args[1] + } else { + fmt.Println("Voucher file name not provided, writing to quil_voucher.hex") + } + + if err := os.WriteFile(filename, []byte(hex.EncodeToString(voucher)), 0644); err != nil { + fmt.Println("Could not write voucher to file, voucher hex string below:") + fmt.Println(hex.EncodeToString(voucher)) + } +} diff --git a/ec/bls48581/ARCH.go b/ec/bls48581/ARCH.go new file mode 100644 index 0000000..ac0c2e7 --- /dev/null +++ b/ec/bls48581/ARCH.go @@ -0,0 +1,27 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* core BIG number class */ + +package bls48581 + +type Chunk int32 +type DChunk int64 + +const CHUNK int = 32 /* Set word size */ diff --git a/ec/bls48581/BIG.go b/ec/bls48581/BIG.go new file mode 100644 index 0000000..6d30432 --- /dev/null +++ b/ec/bls48581/BIG.go @@ -0,0 +1,1023 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* core BIG number class */ + +package bls48581 + +import ( + "strconv" + + "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" +) + +//import "fmt" + +type BIG struct { + w [NLEN]Chunk +} + +type DBIG struct { + w [2 * NLEN]Chunk +} + +/***************** 32-bit specific code ****************/ + +/* First the 32/64-bit dependent BIG code */ +/* Note that because of the lack of a 128-bit integer, 32 and 64-bit code needs to be done differently */ + +/* return a*b as DBIG */ +func mul(a *BIG, b *BIG) *DBIG { + c := NewDBIG() + + // BIGMULS+=1; + + var d [NLEN]DChunk + + for i := 0; i < NLEN; i++ { + d[i] = DChunk(a.w[i]) * DChunk(b.w[i]) + } + s := d[0] + t := s + c.w[0] = Chunk(t) & BMASK + co := t >> BASEBITS + + for k := 1; k < NLEN; k++ { + s += d[k] + t = co + s + for i := k; i >= 1+k/2; i-- { + t += DChunk(a.w[i]-a.w[k-i]) * DChunk(b.w[k-i]-b.w[i]) + } + c.w[k] = Chunk(t) & BMASK + co = t >> BASEBITS + } + + for k := NLEN; k < 2*NLEN-1; k++ { + s -= d[k-NLEN] + t = co + s + for i := NLEN - 1; i >= 1+k/2; i-- { + t += DChunk(a.w[i]-a.w[k-i]) * DChunk(b.w[k-i]-b.w[i]) + } + c.w[k] = Chunk(t) & BMASK + co = t >> BASEBITS + } + c.w[2*NLEN-1] = Chunk(co) + + return c +} + +/* return a^2 as DBIG */ +func sqr(a *BIG) *DBIG { + c := NewDBIG() + // BIGSQRS+=1; + t := DChunk(a.w[0]) * DChunk(a.w[0]) + c.w[0] = Chunk(t) & BMASK + co := t >> BASEBITS + + for j := 1; j < NLEN-1; { + t = DChunk(a.w[j]) * DChunk(a.w[0]) + for i := 1; i < (j+1)/2; i++ { + t += DChunk(a.w[j-i]) * DChunk(a.w[i]) + } + t += t + t += co + c.w[j] = Chunk(t) & BMASK + co = t >> BASEBITS + j++ + t = DChunk(a.w[j]) * DChunk(a.w[0]) + for i := 1; i < (j+1)/2; i++ { + t += DChunk(a.w[j-i]) * DChunk(a.w[i]) + } + t += t + t += co + t += DChunk(a.w[j/2]) * DChunk(a.w[j/2]) + c.w[j] = Chunk(t) & BMASK + co = t >> BASEBITS + j++ + } + + for j := NLEN - 1 + (NLEN % 2); j < DNLEN-3; { + t = DChunk(a.w[NLEN-1]) * DChunk(a.w[j-NLEN+1]) + for i := j - NLEN + 2; i < (j+1)/2; i++ { + t += DChunk(a.w[j-i]) * DChunk(a.w[i]) + } + t += t + t += co + c.w[j] = Chunk(t) & BMASK + co = t >> BASEBITS + j++ + t = DChunk(a.w[NLEN-1]) * DChunk(a.w[j-NLEN+1]) + for i := j - NLEN + 2; i < (j+1)/2; i++ { + t += DChunk(a.w[j-i]) * DChunk(a.w[i]) + } + t += t + t += co + t += DChunk(a.w[j/2]) * DChunk(a.w[j/2]) + c.w[j] = Chunk(t) & BMASK + co = t >> BASEBITS + j++ + } + + t = DChunk(a.w[NLEN-2]) * DChunk(a.w[NLEN-1]) + t += t + t += co + c.w[DNLEN-3] = Chunk(t) & BMASK + co = t >> BASEBITS + + t = DChunk(a.w[NLEN-1])*DChunk(a.w[NLEN-1]) + co + c.w[DNLEN-2] = Chunk(t) & BMASK + co = t >> BASEBITS + c.w[DNLEN-1] = Chunk(co) + + return c +} + +func monty(m *BIG, mc Chunk, d *DBIG) *BIG { + var dd [NLEN]DChunk + + var v [NLEN]Chunk + b := NewBIG() + + t := DChunk(d.w[0]) + v[0] = (Chunk(t) * mc) & BMASK + t += DChunk(v[0]) * DChunk(m.w[0]) + c := (t >> BASEBITS) + DChunk(d.w[1]) + s := DChunk(0) + + for k := 1; k < NLEN; k++ { + t = c + s + DChunk(v[0])*DChunk(m.w[k]) + for i := k - 1; i > k/2; i-- { + t += DChunk(v[k-i]-v[i]) * DChunk(m.w[i]-m.w[k-i]) + } + v[k] = (Chunk(t) * mc) & BMASK + t += DChunk(v[k]) * DChunk(m.w[0]) + c = (t >> BASEBITS) + DChunk(d.w[k+1]) + dd[k] = DChunk(v[k]) * DChunk(m.w[k]) + s += dd[k] + } + for k := NLEN; k < 2*NLEN-1; k++ { + t = c + s + for i := NLEN - 1; i >= 1+k/2; i-- { + t += DChunk(v[k-i]-v[i]) * DChunk(m.w[i]-m.w[k-i]) + } + b.w[k-NLEN] = Chunk(t) & BMASK + c = (t >> BASEBITS) + DChunk(d.w[k+1]) + s -= dd[k-NLEN+1] + } + b.w[NLEN-1] = Chunk(c) & BMASK + return b +} + +/* set this[i]+=x*y+c, and return high part */ +func muladd(a Chunk, b Chunk, c Chunk, r Chunk) (Chunk, Chunk) { + var prod = DChunk(a)*DChunk(b) + DChunk(c) + DChunk(r) + bot := Chunk(prod) & BMASK + top := Chunk(prod >> BASEBITS) + return top, bot +} + +/***************************************************************************/ + +func (r *BIG) get(i int) Chunk { + return r.w[i] +} + +func (r *BIG) set(i int, x Chunk) { + r.w[i] = x +} + +func (r *BIG) xortop(x Chunk) { + r.w[NLEN-1] ^= x +} + +/* normalise BIG - force all digits < 2^BASEBITS */ +func (r *BIG) norm() Chunk { + carry := Chunk(0) + for i := 0; i < NLEN-1; i++ { + d := r.w[i] + carry + r.w[i] = d & BMASK + carry = d >> BASEBITS + } + r.w[NLEN-1] = (r.w[NLEN-1] + carry) + return (r.w[NLEN-1] >> ((8 * MODBYTES) % BASEBITS)) +} + +/* Shift right by less than a word */ +func (r *BIG) fshr(k uint) int { + w := r.w[0] & ((Chunk(1) << k) - 1) /* shifted out part */ + for i := 0; i < NLEN-1; i++ { + r.w[i] = (r.w[i] >> k) | ((r.w[i+1] << (BASEBITS - k)) & BMASK) + } + r.w[NLEN-1] = r.w[NLEN-1] >> k + return int(w) +} + +/* Shift right by less than a word */ +func (r *BIG) fshl(k uint) int { + r.w[NLEN-1] = (r.w[NLEN-1] << k) | (r.w[NLEN-2] >> (BASEBITS - k)) + for i := NLEN - 2; i > 0; i-- { + r.w[i] = ((r.w[i] << k) & BMASK) | (r.w[i-1] >> (BASEBITS - k)) + } + r.w[0] = (r.w[0] << k) & BMASK + return int(r.w[NLEN-1] >> ((8 * MODBYTES) % BASEBITS)) /* return excess - only used in ff.c */ +} + +func NewBIG() *BIG { + b := new(BIG) + for i := 0; i < NLEN; i++ { + b.w[i] = 0 + } + return b +} + +func NewBIGints(x [21]Chunk) *BIG { + b := new(BIG) + for i := 0; i < NLEN; i++ { + b.w[i] = x[i] + } + return b +} + +func NewBIGint(x int) *BIG { + b := new(BIG) + b.w[0] = Chunk(x) + for i := 1; i < NLEN; i++ { + b.w[i] = 0 + } + return b +} + +func NewBIGcopy(x *BIG) *BIG { + b := new(BIG) + for i := 0; i < NLEN; i++ { + b.w[i] = x.w[i] + } + return b +} + +func NewBIGdcopy(x *DBIG) *BIG { + b := new(BIG) + for i := 0; i < NLEN; i++ { + b.w[i] = x.w[i] + } + return b +} + +/* test for zero */ +func (r *BIG) iszilch() bool { + d := Chunk(0) + for i := 0; i < NLEN; i++ { + d |= r.w[i] + } + return (1 & ((d - 1) >> BASEBITS)) != 0 +} + +/* set to zero */ +func (r *BIG) zero() { + for i := 0; i < NLEN; i++ { + r.w[i] = 0 + } +} + +/* Test for equal to one */ +func (r *BIG) isunity() bool { + d := Chunk(0) + for i := 1; i < NLEN; i++ { + d |= r.w[i] + } + return (1 & ((d - 1) >> BASEBITS) & (((r.w[0] ^ 1) - 1) >> BASEBITS)) != 0 +} + +/* set to one */ +func (r *BIG) one() { + r.w[0] = 1 + for i := 1; i < NLEN; i++ { + r.w[i] = 0 + } +} + +/* Copy from another BIG */ +func (r *BIG) copy(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = x.w[i] + } +} + +/* Copy from another DBIG */ +func (r *BIG) dcopy(x *DBIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = x.w[i] + } +} + +/* Conditional swap of two bigs depending on d using XOR - no branches */ +func (r *BIG) cswap(b *BIG, d int) Chunk { + c := Chunk(-d) + s := Chunk(0) + v := r.w[0] ^ b.w[1] + va := v + v + va >>= 1 + for i := 0; i < NLEN; i++ { + t := c & (r.w[i] ^ b.w[i]) + t ^= v + e := r.w[i] ^ t + s ^= e // to force calculation of e + r.w[i] = e ^ va + e = b.w[i] ^ t + s ^= e + b.w[i] = e ^ va + } + return s +} + +func (r *BIG) cmove(g *BIG, d int) Chunk { + b := Chunk(-d) + s := Chunk(0) + v := r.w[0] ^ g.w[1] + va := v + v + va >>= 1 + for i := 0; i < NLEN; i++ { + t := (r.w[i] ^ g.w[i]) & b + t ^= v + e := r.w[i] ^ t + s ^= e + r.w[i] = e ^ va + } + return s +} + +/* general shift right */ +func (r *BIG) shr(k uint) { + n := (k % BASEBITS) + m := int(k / BASEBITS) + for i := 0; i < NLEN-m-1; i++ { + r.w[i] = (r.w[m+i] >> n) | ((r.w[m+i+1] << (BASEBITS - n)) & BMASK) + } + r.w[NLEN-m-1] = r.w[NLEN-1] >> n + for i := NLEN - m; i < NLEN; i++ { + r.w[i] = 0 + } +} + +/* general shift left */ +func (r *BIG) shl(k uint) { + n := k % BASEBITS + m := int(k / BASEBITS) + + r.w[NLEN-1] = (r.w[NLEN-1-m] << n) + if NLEN >= m+2 { + r.w[NLEN-1] |= (r.w[NLEN-m-2] >> (BASEBITS - n)) + } + for i := NLEN - 2; i > m; i-- { + r.w[i] = ((r.w[i-m] << n) & BMASK) | (r.w[i-m-1] >> (BASEBITS - n)) + } + r.w[m] = (r.w[0] << n) & BMASK + for i := 0; i < m; i++ { + r.w[i] = 0 + } +} + +/* return number of bits */ +func (r *BIG) nbits() int { + t := NewBIGcopy(r) + k := NLEN - 1 + t.norm() + for k >= 0 && t.w[k] == 0 { + k-- + } + if k < 0 { + return 0 + } + bts := int(BASEBITS) * k + c := t.w[k] + for c != 0 { + c /= 2 + bts++ + } + return bts +} + +func (r *BIG) Nbits() int { + return r.nbits() +} + +/* Convert to Hex String */ +func (r *BIG) ToString() string { + s := "" + len := r.nbits() + + if len%4 == 0 { + len /= 4 + } else { + len /= 4 + len++ + + } + MB := int(MODBYTES * 2) + if len < MB { + len = MB + } + + for i := len - 1; i >= 0; i-- { + b := NewBIGcopy(r) + + b.shr(uint(i * 4)) + s += strconv.FormatInt(int64(b.w[0]&15), 16) + } + return s +} + +func (r *BIG) add(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = r.w[i] + x.w[i] + } +} + +func (r *BIG) or(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = r.w[i] | x.w[i] + } +} + +/* return this+x */ +func (r *BIG) Plus(x *BIG) *BIG { + s := new(BIG) + for i := 0; i < NLEN; i++ { + s.w[i] = r.w[i] + x.w[i] + } + s.norm() + return s +} + +/* this+=x, where x is int */ +func (r *BIG) inc(x int) { + r.norm() + r.w[0] += Chunk(x) +} + +/* this*=c and catch overflow in DBIG */ +func (r *BIG) pxmul(c int) *DBIG { + m := NewDBIG() + carry := Chunk(0) + for j := 0; j < NLEN; j++ { + carry, m.w[j] = muladd(r.w[j], Chunk(c), carry, m.w[j]) + } + m.w[NLEN] = carry + return m +} + +/* return this-x */ +func (r *BIG) Minus(x *BIG) *BIG { + d := new(BIG) + for i := 0; i < NLEN; i++ { + d.w[i] = r.w[i] - x.w[i] + } + return d +} + +/* this-=x */ +func (r *BIG) sub(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = r.w[i] - x.w[i] + } +} + +/* reverse subtract this=x-this */ +func (r *BIG) rsub(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = x.w[i] - r.w[i] + } +} + +/* this-=x, where x is int */ +func (r *BIG) dec(x int) { + r.norm() + r.w[0] -= Chunk(x) +} + +/* this*=x, where x is small intNEXCESS */ +func (r *BIG) pmul(c int) Chunk { + carry := Chunk(0) + // r.norm(); + for i := 0; i < NLEN; i++ { + ak := r.w[i] + r.w[i] = 0 + carry, r.w[i] = muladd(ak, Chunk(c), carry, r.w[i]) + } + return carry +} + +/* convert this BIG to byte array */ +func (r *BIG) tobytearray(b []byte, n int) { + //r.norm(); + c := NewBIGcopy(r) + c.norm() + for i := int(MODBYTES) - 1; i >= 0; i-- { + b[i+n] = byte(c.w[0]) + c.fshr(8) + } +} + +/* convert from byte array to BIG */ +func frombytearray(b []byte, n int) *BIG { + m := NewBIG() + l := len(b) + for i := 0; i < int(MODBYTES); i++ { + m.fshl(8) + if i < l { + m.w[0] += Chunk(int(b[i+n] & 0xff)) + } else { + m.w[0] += Chunk(int(0 & 0xff)) + } + } + return m +} + +func (r *BIG) ToBytes(b []byte) { + r.tobytearray(b, 0) +} + +func FromBytes(b []byte) *BIG { + return frombytearray(b, 0) +} + +/* divide by 3 */ +func (r *BIG) div3() int { + carry := Chunk(0) + r.norm() + base := (Chunk(1) << BASEBITS) + for i := NLEN - 1; i >= 0; i-- { + ak := (carry*base + r.w[i]) + r.w[i] = ak / 3 + carry = ak % 3 + } + return int(carry) +} + +/* return a*b where result fits in a BIG */ +func smul(a *BIG, b *BIG) *BIG { + carry := Chunk(0) + c := NewBIG() + for i := 0; i < NLEN; i++ { + carry = 0 + for j := 0; j < NLEN; j++ { + if i+j < NLEN { + carry, c.w[i+j] = muladd(a.w[i], b.w[j], carry, c.w[i+j]) + } + } + } + return c +} + +/* Compare a and b, return 0 if a==b, -1 if ab. Inputs must be normalised */ +func Comp(a *BIG, b *BIG) int { + gt := Chunk(0) + eq := Chunk(1) + for i := NLEN - 1; i >= 0; i-- { + gt |= ((b.w[i] - a.w[i]) >> BASEBITS) & eq + eq &= ((b.w[i] ^ a.w[i]) - 1) >> BASEBITS + } + return int(gt + gt + eq - 1) +} + +/* return parity */ +func (r *BIG) parity() int { + return int(r.w[0] % 2) +} + +/* return n-th bit */ +func (r *BIG) bit(n int) int { + return int((r.w[n/int(BASEBITS)] & (Chunk(1) << (uint(n) % BASEBITS))) >> (uint(n) % BASEBITS)) + // if (r.w[n/int(BASEBITS)] & (Chunk(1) << (uint(n) % BASEBITS))) > 0 { + // return 1 + // } + // return 0 +} + +/* return n last bits */ +func (r *BIG) lastbits(n int) int { + msk := (1 << uint(n)) - 1 + r.norm() + return (int(r.w[0])) & msk +} + +/* set x = x mod 2^m */ +func (r *BIG) mod2m(m uint) { + wd := int(m / BASEBITS) + bt := m % BASEBITS + msk := (Chunk(1) << bt) - 1 + r.w[wd] &= msk + for i := wd + 1; i < NLEN; i++ { + r.w[i] = 0 + } +} + +/* a=1/a mod 2^256. This is very fast! */ +func (r *BIG) invmod2m() { + U := NewBIG() + b := NewBIG() + c := NewBIG() + + U.inc(invmod256(r.lastbits(8))) + + for i := 8; i < BIGBITS; i <<= 1 { + U.norm() + ui := uint(i) + b.copy(r) + b.mod2m(ui) + t1 := smul(U, b) + t1.shr(ui) + c.copy(r) + c.shr(ui) + c.mod2m(ui) + + t2 := smul(U, c) + t2.mod2m(ui) + t1.add(t2) + t1.norm() + b = smul(t1, U) + t1.copy(b) + t1.mod2m(ui) + + t2.one() + t2.shl(ui) + t1.rsub(t2) + t1.norm() + t1.shl(ui) + U.add(t1) + } + U.mod2m(8 * MODBYTES) + r.copy(U) + r.norm() +} + +func (r *BIG) ctmod(m *BIG, bd uint) { + k := bd + sr := NewBIG() + c := NewBIGcopy(m) + r.norm() + + c.shl(k) + + for { + sr.copy(r) + sr.sub(c) + sr.norm() + r.cmove(sr, int(1-((sr.w[NLEN-1]>>uint(CHUNK-1))&1))) + if k == 0 { + break + } + c.fshr(1) + k -= 1 + } +} + +/* reduce this mod m */ +func (r *BIG) Mod(m *BIG) { + k := r.nbits() - m.nbits() + if k < 0 { + k = 0 + } + r.ctmod(m, uint(k)) +} + +func (r *BIG) ctdiv(m *BIG, bd uint) { + k := bd + e := NewBIGint(1) + sr := NewBIG() + a := NewBIGcopy(r) + c := NewBIGcopy(m) + r.norm() + r.zero() + + c.shl(k) + e.shl(k) + + for { + sr.copy(a) + sr.sub(c) + sr.norm() + d := int(1 - ((sr.w[NLEN-1] >> uint(CHUNK-1)) & 1)) + a.cmove(sr, d) + sr.copy(r) + sr.add(e) + sr.norm() + r.cmove(sr, d) + if k == 0 { + break + } + c.fshr(1) + e.fshr(1) + k -= 1 + } +} + +/* divide this by m */ +func (r *BIG) div(m *BIG) { + k := r.nbits() - m.nbits() + if k < 0 { + k = 0 + } + r.ctdiv(m, uint(k)) +} + +/* get 8*MODBYTES size random number */ +func Random(rng *core.RAND) *BIG { + m := NewBIG() + var j int = 0 + var r byte = 0 + /* generate random BIG */ + for i := 0; i < 8*int(MODBYTES); i++ { + if j == 0 { + r = rng.GetByte() + } else { + r >>= 1 + } + + b := Chunk(int(r & 1)) + m.shl(1) + m.w[0] += b + j++ + j &= 7 + } + return m +} + +/* Create random BIG in portable way, one bit at a time */ +func Randomnum(q *BIG, rng *core.RAND) *BIG { + d := NewDBIG() + var j int = 0 + var r byte = 0 + for i := 0; i < 2*q.nbits(); i++ { + if j == 0 { + r = rng.GetByte() + } else { + r >>= 1 + } + + b := Chunk(int(r & 1)) + d.shl(1) + d.w[0] += b + j++ + j &= 7 + } + m := d.Mod(q) + return m +} + +func Randtrunc(q *BIG, trunc int, rng *core.RAND) *BIG { + m := Randomnum(q, rng) + if q.nbits() > trunc { + m.mod2m(uint(trunc)) + } + return m +} + +/* return a*b mod m */ +func Modmul(a1, b1, m *BIG) *BIG { + a := NewBIGcopy(a1) + b := NewBIGcopy(b1) + a.Mod(m) + b.Mod(m) + d := mul(a, b) + return d.ctmod(m, uint(m.nbits())) +} + +/* return a^2 mod m */ +func Modsqr(a1, m *BIG) *BIG { + a := NewBIGcopy(a1) + a.Mod(m) + d := sqr(a) + return d.ctmod(m, uint(m.nbits())) +} + +/* return -a mod m */ +func Modneg(a1, m *BIG) *BIG { + a := NewBIGcopy(a1) + a.Mod(m) + a.rsub(m) + a.norm() + return a +} + +/* return a+b mod m */ +func Modadd(a1, b1, m *BIG) *BIG { + a := NewBIGcopy(a1) + b := NewBIGcopy(b1) + a.Mod(m) + b.Mod(m) + a.add(b) + a.norm() + a.ctmod(m, 1) + return a +} + +/* Jacobi Symbol (this/p). Returns 0, 1 or -1 */ +func (r *BIG) Jacobi(p *BIG) int { + m := 0 + t := NewBIGint(0) + x := NewBIGint(0) + n := NewBIGint(0) + zilch := NewBIGint(0) + one := NewBIGint(1) + if p.parity() == 0 || Comp(r, zilch) == 0 || Comp(p, one) <= 0 { + return 0 + } + r.norm() + x.copy(r) + n.copy(p) + x.Mod(p) + + for Comp(n, one) > 0 { + if Comp(x, zilch) == 0 { + return 0 + } + n8 := n.lastbits(3) + k := 0 + for x.parity() == 0 { + k++ + x.shr(1) + } + if k%2 == 1 { + m += (n8*n8 - 1) / 8 + } + m += (n8 - 1) * (x.lastbits(2) - 1) / 4 + t.copy(n) + t.Mod(x) + n.copy(x) + x.copy(t) + m %= 2 + + } + if m == 0 { + return 1 + } + return -1 +} + +/* this=1/this mod p. Binary method */ +func (r *BIG) Invmodp(p *BIG) { + r.Mod(p) + if r.iszilch() { + return + } + u := NewBIGcopy(r) + v := NewBIGcopy(p) + x1 := NewBIGint(1) + x2 := NewBIGint(0) + t := NewBIGint(0) + one := NewBIGint(1) + for Comp(u, one) != 0 && Comp(v, one) != 0 { + for u.parity() == 0 { + u.fshr(1) + t.copy(x1) + t.add(p) + x1.cmove(t, x1.parity()) + x1.norm() + x1.fshr(1) + } + for v.parity() == 0 { + v.fshr(1) + t.copy(x2) + t.add(p) + x2.cmove(t, x2.parity()) + x2.norm() + x2.fshr(1) + } + if Comp(u, v) >= 0 { + u.sub(v) + u.norm() + t.copy(x1) + t.add(p) + x1.cmove(t, (Comp(x1, x2)>>1)&1) + x1.sub(x2) + x1.norm() + } else { + v.sub(u) + v.norm() + t.copy(x2) + t.add(p) + x2.cmove(t, (Comp(x2, x1)>>1)&1) + x2.sub(x1) + x2.norm() + } + } + r.copy(x1) + r.cmove(x2, Comp(u, one)&1) +} + +/* return this^e mod m */ +func (r *BIG) Powmod(e1 *BIG, m *BIG) *BIG { + e := NewBIGcopy(e1) + r.norm() + e.norm() + a := NewBIGint(1) + z := NewBIGcopy(e) + s := NewBIGcopy(r) + for true { + bt := z.parity() + z.fshr(1) + if bt == 1 { + a = Modmul(a, s, m) + } + if z.iszilch() { + break + } + s = Modsqr(s, m) + } + return a +} + +/* Arazi and Qi inversion mod 256 */ +func invmod256(a int) int { + var t1 int = 0 + c := (a >> 1) & 1 + t1 += c + t1 &= 1 + t1 = 2 - t1 + t1 <<= 1 + U := t1 + 1 + + // i=2 + b := a & 3 + t1 = U * b + t1 >>= 2 + c = (a >> 2) & 3 + t2 := (U * c) & 3 + t1 += t2 + t1 *= U + t1 &= 3 + t1 = 4 - t1 + t1 <<= 2 + U += t1 + + // i=4 + b = a & 15 + t1 = U * b + t1 >>= 4 + c = (a >> 4) & 15 + t2 = (U * c) & 15 + t1 += t2 + t1 *= U + t1 &= 15 + t1 = 16 - t1 + t1 <<= 4 + U += t1 + + return U +} + +func logb2(w uint32) uint { + v := w + v |= (v >> 1) + v |= (v >> 2) + v |= (v >> 4) + v |= (v >> 8) + v |= (v >> 16) + + v = v - ((v >> 1) & 0x55555555) + v = (v & 0x33333333) + ((v >> 2) & 0x33333333) + r := uint((((v + (v >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24) + return (r) +} + +// Optimized combined shift, subtract and norm +func ssn(r *BIG, a *BIG, m *BIG) int { + n := NLEN - 1 + m.w[0] = (m.w[0] >> 1) | ((m.w[1] << (BASEBITS - 1)) & BMASK) + r.w[0] = a.w[0] - m.w[0] + carry := r.w[0] >> BASEBITS + r.w[0] &= BMASK + for i := 1; i < n; i++ { + m.w[i] = (m.w[i] >> 1) | ((m.w[i+1] << (BASEBITS - 1)) & BMASK) + r.w[i] = a.w[i] - m.w[i] + carry + carry = r.w[i] >> BASEBITS + r.w[i] &= BMASK + } + m.w[n] >>= 1 + r.w[n] = a.w[n] - m.w[n] + carry + return int((r.w[n] >> uint(CHUNK-1)) & 1) +} diff --git a/ec/bls48581/BLS256.go b/ec/bls48581/BLS256.go new file mode 100644 index 0000000..adb76b3 --- /dev/null +++ b/ec/bls48581/BLS256.go @@ -0,0 +1,155 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Boneh-Lynn-Shacham signature 256-bit API Functions */ + +/* Loosely (for now) following https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-bls-signature-02 */ + +// Minimal-signature-size variant + +package bls48581 + +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +//import "fmt" + +const BFS int = int(MODBYTES) +const BGS int = int(MODBYTES) +const BLS_OK int = 0 +const BLS_FAIL int = -1 + +var G2_TAB []*FP16 + +func ceil(a int, b int) int { + return (((a)-1)/(b) + 1) +} + +/* output u \in F_p */ +func hash_to_field(hash int, hlen int, DST []byte, M []byte, ctr int) []*FP { + q := NewBIGints(Modulus) + nbq := q.nbits() + L := ceil(nbq+AESKEY*8, 8) + var u []*FP + var fd = make([]byte, L) + OKM := core.XMD_Expand(hash, hlen, L*ctr, DST, M) + + for i := 0; i < ctr; i++ { + for j := 0; j < L; j++ { + fd[j] = OKM[i*L+j] + } + u = append(u, NewFPbig(DBIG_fromBytes(fd).ctmod(q, uint(8*L-nbq)))) + } + return u +} + +/* hash a message to an ECP point, using SHA2, random oracle method */ +func bls256_hash_to_point(M []byte) *ECP { + DST := []byte("BLS_SIG_BLS48581G1_XMD:SHA-512_SVDW_RO_NUL_") + u := hash_to_field(core.MC_SHA2, HASH_TYPE, DST, M, 2) + + P := ECP_map2point(u[0]) + P1 := ECP_map2point(u[1]) + P.Add(P1) + P.Cfp() + P.Affine() + return P +} + +func Init() int { + G := ECP8_generator() + if G.Is_infinity() { + return BLS_FAIL + } + G2_TAB = precomp(G) + return BLS_OK +} + +/* generate key pair, private key S, public key W */ +func KeyPairGenerate(IKM []byte, S []byte, W []byte) int { + r := NewBIGints(CURVE_Order) + nbr := r.nbits() + L := ceil(3*ceil(nbr, 8), 2) + LEN := core.InttoBytes(L, 2) + AIKM := make([]byte, len(IKM)+1) + for i := 0; i < len(IKM); i++ { + AIKM[i] = IKM[i] + } + AIKM[len(IKM)] = 0 + + G := ECP8_generator() + if G.Is_infinity() { + return BLS_FAIL + } + SALT := []byte("BLS-SIG-KEYGEN-SALT-") + PRK := core.HKDF_Extract(core.MC_SHA2, HASH_TYPE, SALT, AIKM) + OKM := core.HKDF_Expand(core.MC_SHA2, HASH_TYPE, L, PRK, LEN) + + dx := DBIG_fromBytes(OKM[:]) + s := dx.ctmod(r, uint(8*L-nbr)) + s.ToBytes(S) + // SkToPk + G = G2mul(G, s) + G.ToBytes(W, true) + return BLS_OK +} + +/* Sign message m using private key S to produce signature SIG */ +func Core_Sign(SIG []byte, M []byte, S []byte) int { + D := bls256_hash_to_point(M) + s := FromBytes(S) + D = G1mul(D, s) + D.ToBytes(SIG, true) + return BLS_OK +} + +/* Verify signature given message M, the signature SIG, and the public key W */ + +func Core_Verify(SIG []byte, M []byte, W []byte) int { + HM := bls256_hash_to_point(M) + + D := ECP_fromBytes(SIG) + if !G1member(D) { + return BLS_FAIL + } + D.Neg() + + PK := ECP8_fromBytes(W) + if !G2member(PK) { + return BLS_FAIL + } + + // Use new multi-pairing mechanism + r := Initmp() + Another_pc(r, G2_TAB, D) + Another(r, PK, HM) + v := Miller(r) + + //.. or alternatively + // G := ECP8_generator() + // if G.Is_infinity() {return BLS_FAIL} + // v := Ate2(G, D, PK, HM) + + v = Fexp(v) + + if v.Isunity() { + return BLS_OK + } else { + return BLS_FAIL + } +} diff --git a/ec/bls48581/CONFIG_BIG.go b/ec/bls48581/CONFIG_BIG.go new file mode 100644 index 0000000..699a6e2 --- /dev/null +++ b/ec/bls48581/CONFIG_BIG.go @@ -0,0 +1,34 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package bls48581 + +// BIG length in bytes and number base +const MODBYTES uint = 73 +const BASEBITS uint = 29 + +// BIG lengths and Masks +const NLEN int = int((1 + ((8*MODBYTES - 1) / BASEBITS))) +const DNLEN int = 2 * NLEN +const BMASK Chunk = ((Chunk(1) << BASEBITS) - 1) +const HBITS uint = (BASEBITS / 2) +const HMASK Chunk = ((Chunk(1) << HBITS) - 1) +const NEXCESS int = (1 << (uint(CHUNK) - BASEBITS - 1)) + +const BIGBITS int = int(MODBYTES * 8) diff --git a/ec/bls48581/CONFIG_CURVE.go b/ec/bls48581/CONFIG_CURVE.go new file mode 100644 index 0000000..dc23507 --- /dev/null +++ b/ec/bls48581/CONFIG_CURVE.go @@ -0,0 +1,76 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package bls48581 + +// Curve types +const WEIERSTRASS int = 0 +const EDWARDS int = 1 +const MONTGOMERY int = 2 + +// Pairing Friendly? +const NOT int = 0 +const BN int = 1 +const BLS12 int = 2 +const BLS24 int = 3 +const BLS48 int = 4 + +// Pairing Twist type +const D_TYPE int = 0 +const M_TYPE int = 1 + +// Sparsity +const FP_ZERO int = 0 +const FP_ONE int = 1 +const FP_SPARSEST int = 2 +const FP_SPARSER int = 3 +const FP_SPARSE int = 4 +const FP_DENSE int = 5 + +// Pairing x parameter sign +const POSITIVEX int = 0 +const NEGATIVEX int = 1 + +// Curve type + +const CURVETYPE int = WEIERSTRASS +const CURVE_A int = 0 +const CURVE_PAIRING_TYPE int = BLS48 + +// Pairings only + +const SEXTIC_TWIST int = D_TYPE +const SIGN_OF_X int = NEGATIVEX +const ATE_BITS int = 33 +const G2_TABLE int = 36 +const HTC_ISO int = 0 +const HTC_ISO_G2 int = 0 + +// associated hash function and AES key size + +const HASH_TYPE int = 64 +const AESKEY int = 32 + +const ALLOW_ALT_COMPRESS bool = false + +// These are manually decided policy decisions. To block any potential patent issues set to false. + +const USE_GLV bool = true +const USE_GS_G2 bool = true +const USE_GS_GT bool = true diff --git a/ec/bls48581/CONFIG_FIELD.go b/ec/bls48581/CONFIG_FIELD.go new file mode 100644 index 0000000..1d47ce8 --- /dev/null +++ b/ec/bls48581/CONFIG_FIELD.go @@ -0,0 +1,47 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package bls48581 + +// Modulus types +const NOT_SPECIAL int = 0 +const PSEUDO_MERSENNE int = 1 +const MONTGOMERY_FRIENDLY int = 2 +const GENERALISED_MERSENNE int = 3 + +const NEGATOWER int = 0 +const POSITOWER int = 1 + +// Modulus details +const MODBITS uint = 581 /* Number of bits in Modulus */ +const PM1D2 uint = 1 /* Modulus mod 8 */ +const RIADZ int = 2 /* hash-to-point Z */ +const RIADZG2A int = 2 /* G2 hash-to-point Z */ +const RIADZG2B int = 0 /* G2 hash-to-point Z */ +const MODTYPE int = NOT_SPECIAL //NOT_SPECIAL +const QNRI int = 0 // Fp2 QNR +const TOWER int = POSITOWER // Tower type +const FEXCESS int32 = ((int32(1) << 14) - 1) + +// Modulus Masks +const OMASK Chunk = ((Chunk(-1)) << (MODBITS % BASEBITS)) +const TBITS uint = MODBITS % BASEBITS // Number of active bits in top word +const TMASK Chunk = (Chunk(1) << TBITS) - 1 + +const BIG_ENDIAN_SIGN bool = false diff --git a/ec/bls48581/DBIG.go b/ec/bls48581/DBIG.go new file mode 100644 index 0000000..d9f814b --- /dev/null +++ b/ec/bls48581/DBIG.go @@ -0,0 +1,298 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* MiotCL double length DBIG number class */ + +package bls48581 + +import "strconv" + +//import "fmt" + +func NewDBIG() *DBIG { + b := new(DBIG) + for i := 0; i < DNLEN; i++ { + b.w[i] = 0 + } + return b +} + +func NewDBIGcopy(x *DBIG) *DBIG { + b := new(DBIG) + for i := 0; i < DNLEN; i++ { + b.w[i] = x.w[i] + } + return b +} + +func NewDBIGscopy(x *BIG) *DBIG { + b := new(DBIG) + for i := 0; i < NLEN-1; i++ { + b.w[i] = x.w[i] + } + b.w[NLEN-1] = x.get(NLEN-1) & BMASK /* top word normalized */ + b.w[NLEN] = x.get(NLEN-1) >> BASEBITS + + for i := NLEN + 1; i < DNLEN; i++ { + b.w[i] = 0 + } + return b +} + +/* normalise this */ +func (r *DBIG) norm() { + carry := Chunk(0) + for i := 0; i < DNLEN-1; i++ { + d := r.w[i] + carry + r.w[i] = d & BMASK + carry = d >> BASEBITS + } + r.w[DNLEN-1] = (r.w[DNLEN-1] + carry) +} + +/* split DBIG at position n, return higher half, keep lower half */ +func (r *DBIG) split(n uint) *BIG { + t := NewBIG() + m := n % BASEBITS + carry := r.w[DNLEN-1] << (BASEBITS - m) + + for i := DNLEN - 2; i >= NLEN-1; i-- { + nw := (r.w[i] >> m) | carry + carry = (r.w[i] << (BASEBITS - m)) & BMASK + t.set(i-NLEN+1, nw) + } + r.w[NLEN-1] &= ((Chunk(1) << m) - 1) + return t +} + +func (r *DBIG) cmove(g *DBIG, d int) Chunk { + var b = Chunk(-d) + s := Chunk(0) + v := r.w[0] ^ g.w[1] + va := v + v + va >>= 1 + for i := 0; i < DNLEN; i++ { + t := (r.w[i] ^ g.w[i]) & b + t ^= v + e := r.w[i] ^ t + s ^= e + r.w[i] = e ^ va + } + return s +} + +/* Compare a and b, return 0 if a==b, -1 if ab. Inputs must be normalised */ +func dcomp(a *DBIG, b *DBIG) int { + gt := Chunk(0) + eq := Chunk(1) + for i := DNLEN - 1; i >= 0; i-- { + gt |= ((b.w[i] - a.w[i]) >> BASEBITS) & eq + eq &= ((b.w[i] ^ a.w[i]) - 1) >> BASEBITS + } + return int(gt + gt + eq - 1) +} + +/* Copy from another DBIG */ +func (r *DBIG) copy(x *DBIG) { + for i := 0; i < DNLEN; i++ { + r.w[i] = x.w[i] + } +} + +/* Copy from another BIG to upper half */ +func (r *DBIG) ucopy(x *BIG) { + for i := 0; i < NLEN; i++ { + r.w[i] = 0 + } + for i := NLEN; i < DNLEN; i++ { + r.w[i] = x.w[i-NLEN] + } +} + +func (r *DBIG) add(x *DBIG) { + for i := 0; i < DNLEN; i++ { + r.w[i] = r.w[i] + x.w[i] + } +} + +/* this-=x */ +func (r *DBIG) sub(x *DBIG) { + for i := 0; i < DNLEN; i++ { + r.w[i] = r.w[i] - x.w[i] + } +} + +/* this-=x */ +func (r *DBIG) rsub(x *DBIG) { + for i := 0; i < DNLEN; i++ { + r.w[i] = x.w[i] - r.w[i] + } +} + +/* general shift left */ +func (r *DBIG) shl(k uint) { + n := k % BASEBITS + m := int(k / BASEBITS) + + r.w[DNLEN-1] = (r.w[DNLEN-1-m] << n) | (r.w[DNLEN-m-2] >> (BASEBITS - n)) + for i := DNLEN - 2; i > m; i-- { + r.w[i] = ((r.w[i-m] << n) & BMASK) | (r.w[i-m-1] >> (BASEBITS - n)) + } + r.w[m] = (r.w[0] << n) & BMASK + for i := 0; i < m; i++ { + r.w[i] = 0 + } +} + +/* general shift right */ +func (r *DBIG) shr(k uint) { + n := (k % BASEBITS) + m := int(k / BASEBITS) + for i := 0; i < DNLEN-m-1; i++ { + r.w[i] = (r.w[m+i] >> n) | ((r.w[m+i+1] << (BASEBITS - n)) & BMASK) + } + r.w[DNLEN-m-1] = r.w[DNLEN-1] >> n + for i := DNLEN - m; i < DNLEN; i++ { + r.w[i] = 0 + } +} + +func (r *DBIG) ctmod(m *BIG, bd uint) *BIG { + k := bd + r.norm() + c := NewDBIGscopy(m) + dr := NewDBIG() + + c.shl(k) + + for { + dr.copy(r) + dr.sub(c) + dr.norm() + r.cmove(dr, int(1-((dr.w[DNLEN-1]>>uint(CHUNK-1))&1))) + if k == 0 { + break + } + k -= 1 + c.shr(1) + } + return NewBIGdcopy(r) +} + +/* reduces this DBIG mod a BIG, and returns the BIG */ +func (r *DBIG) Mod(m *BIG) *BIG { + k := r.nbits() - m.nbits() + if k < 0 { + k = 0 + } + return r.ctmod(m, uint(k)) +} + +func (r *DBIG) ctdiv(m *BIG, bd uint) *BIG { + k := bd + c := NewDBIGscopy(m) + a := NewBIGint(0) + e := NewBIGint(1) + sr := NewBIG() + dr := NewDBIG() + r.norm() + + c.shl(k) + e.shl(k) + + for { + dr.copy(r) + dr.sub(c) + dr.norm() + d := int(1 - ((dr.w[DNLEN-1] >> uint(CHUNK-1)) & 1)) + r.cmove(dr, d) + sr.copy(a) + sr.add(e) + sr.norm() + a.cmove(sr, d) + if k == 0 { + break + } + k -= 1 + c.shr(1) + e.shr(1) + } + return a +} + +/* return this/c */ +func (r *DBIG) div(m *BIG) *BIG { + k := r.nbits() - m.nbits() + if k < 0 { + k = 0 + } + return r.ctdiv(m, uint(k)) +} + +/* Convert to Hex String */ +func (r *DBIG) toString() string { + s := "" + len := r.nbits() + + if len%4 == 0 { + len /= 4 + } else { + len /= 4 + len++ + + } + + for i := len - 1; i >= 0; i-- { + b := NewDBIGcopy(r) + + b.shr(uint(i * 4)) + s += strconv.FormatInt(int64(b.w[0]&15), 16) + } + return s +} + +/* return number of bits */ +func (r *DBIG) nbits() int { + k := DNLEN - 1 + t := NewDBIGcopy(r) + t.norm() + for k >= 0 && t.w[k] == 0 { + k-- + } + if k < 0 { + return 0 + } + bts := int(BASEBITS) * k + c := t.w[k] + for c != 0 { + c /= 2 + bts++ + } + return bts +} + +/* convert from byte array to BIG */ +func DBIG_fromBytes(b []byte) *DBIG { + m := NewDBIG() + for i := 0; i < len(b); i++ { + m.shl(8) + m.w[0] += Chunk(int(b[i] & 0xff)) + } + return m +} diff --git a/ec/bls48581/ECDH.go b/ec/bls48581/ECDH.go new file mode 100644 index 0000000..642fbf2 --- /dev/null +++ b/ec/bls48581/ECDH.go @@ -0,0 +1,381 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* ECDH/ECIES/ECDSA API Functions */ + +package bls48581 + +//import "fmt" +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +const INVALID_PUBLIC_KEY int = -2 +const ERROR int = -3 + +//const INVALID int = -4 +const EFS int = int(MODBYTES) +const EGS int = int(MODBYTES) + +// Transform a point multiplier to RFC7748 form +func RFC7748(r *BIG) { + lg := 0 + t := NewBIGint(1) + c := CURVE_Cof_I + for c != 1 { + lg++ + c /= 2 + } + n := uint(8*EGS - lg + 1) + r.mod2m(n) + t.shl(n) + r.add(t) + c = r.lastbits(lg) + r.dec(c) +} + +/* return true if S is in ranger 0 < S < order , else return false */ +func ECDH_IN_RANGE(S []byte) bool { + r := NewBIGints(CURVE_Order) + s := FromBytes(S) + if s.iszilch() { + return false + } + if Comp(s, r) >= 0 { + return false + } + return true +} + +/* Calculate a public/private EC GF(p) key pair W,S where W=S.G mod EC(p), + * where S is the secret key and W is the public key + * and G is fixed generator. + * If RNG is NULL then the private key is provided externally in S + * otherwise it is generated randomly internally */ +func ECDH_KEY_PAIR_GENERATE(RNG *core.RAND, S []byte, W []byte) int { + res := 0 + var s *BIG + var G *ECP + + G = ECP_generator() + r := NewBIGints(CURVE_Order) + + if RNG == nil { + s = FromBytes(S) + } else { + if CURVETYPE != WEIERSTRASS { + s = Random(RNG) // from random bytes + } else { + s = Randomnum(r, RNG) // Removes biases + } + } + + if CURVETYPE != WEIERSTRASS { + RFC7748(s) // For Montgomery or Edwards, apply RFC7748 transformation + } + + s.ToBytes(S) + WP := G.clmul(s, r) + WP.ToBytes(W, false) // To use point compression on public keys, change to true + + return res +} + +/* validate public key */ +func ECDH_PUBLIC_KEY_VALIDATE(W []byte) int { + WP := ECP_fromBytes(W) + res := 0 + + r := NewBIGints(CURVE_Order) + + if WP.Is_infinity() { + res = INVALID_PUBLIC_KEY + } + if res == 0 { + + q := NewBIGints(Modulus) + nb := q.nbits() + k := NewBIGint(1) + k.shl(uint((nb + 4) / 2)) + k.add(q) + k.div(r) + + for k.parity() == 0 { + k.shr(1) + WP.dbl() + } + + if !k.isunity() { + WP = WP.mul(k) + } + if WP.Is_infinity() { + res = INVALID_PUBLIC_KEY + } + + } + return res +} + +/* IEEE-1363 Diffie-Hellman online calculation Z=S.WD */ +// type = 0 is just x coordinate output +// type = 1 for standard compressed output +// type = 2 for standard uncompress output 04|x|y +func ECDH_ECPSVDP_DH(S []byte, WD []byte, Z []byte, typ int) int { + res := 0 + + s := FromBytes(S) + + W := ECP_fromBytes(WD) + if W.Is_infinity() { + res = ERROR + } + + if res == 0 { + r := NewBIGints(CURVE_Order) + W = W.clmul(s, r) + if W.Is_infinity() { + res = ERROR + } else { + if CURVETYPE != MONTGOMERY { + if typ > 0 { + if typ == 1 { + W.ToBytes(Z, true) + } else { + W.ToBytes(Z, false) + } + } else { + W.GetX().ToBytes(Z) + } + return res + } else { + W.GetX().ToBytes(Z) + } + } + } + return res +} + +/* IEEE ECDSA Signature, C and D are signature on F using private key S */ +func ECDH_ECPSP_DSA(sha int, RNG *core.RAND, S []byte, F []byte, C []byte, D []byte) int { + var T [EGS]byte + + B := core.GPhashit(core.MC_SHA2, sha, EGS, 0, F, -1, nil) + G := ECP_generator() + + r := NewBIGints(CURVE_Order) + s := FromBytes(S) + f := FromBytes(B[:]) + + c := NewBIGint(0) + d := NewBIGint(0) + V := NewECP() + + for d.iszilch() { + u := Randomnum(r, RNG) + w := Randomnum(r, RNG) /* IMPORTANT - side channel masking to protect invmodp() */ + + V.Copy(G) + V = V.clmul(u, r) + vx := V.GetX() + c.copy(vx) + c.Mod(r) + if c.iszilch() { + continue + } + u.copy(Modmul(u, w, r)) + u.Invmodp(r) + d.copy(Modmul(s, c, r)) + d.copy(Modadd(d, f, r)) + d.copy(Modmul(d, w, r)) + d.copy(Modmul(u, d, r)) + } + + c.ToBytes(T[:]) + for i := 0; i < EGS; i++ { + C[i] = T[i] + } + d.ToBytes(T[:]) + for i := 0; i < EGS; i++ { + D[i] = T[i] + } + return 0 +} + +/* IEEE1363 ECDSA Signature Verification. Signature C and D on F is verified using public key W */ +func ECDH_ECPVP_DSA(sha int, W []byte, F []byte, C []byte, D []byte) int { + res := 0 + + B := core.GPhashit(core.MC_SHA2, sha, EGS, 0, F, -1, nil) + + G := ECP_generator() + r := NewBIGints(CURVE_Order) + + c := FromBytes(C) + d := FromBytes(D) + f := FromBytes(B[:]) + + if c.iszilch() || Comp(c, r) >= 0 || d.iszilch() || Comp(d, r) >= 0 { + res = ERROR + } + + if res == 0 { + d.Invmodp(r) + f.copy(Modmul(f, d, r)) + h2 := Modmul(c, d, r) + + WP := ECP_fromBytes(W) + if WP.Is_infinity() { + res = ERROR + } else { + P := NewECP() + P.Copy(WP) + + P = P.Mul2(h2, G, f) + + if P.Is_infinity() { + res = ERROR + } else { + d = P.GetX() + d.Mod(r) + + if Comp(d, c) != 0 { + res = ERROR + } + } + } + } + + return res +} + +/* IEEE1363 ECIES encryption. Encryption of plaintext M uses public key W and produces ciphertext V,C,T */ +func ECDH_ECIES_ENCRYPT(sha int, P1 []byte, P2 []byte, RNG *core.RAND, W []byte, M []byte, V []byte, T []byte) []byte { + var Z [EFS]byte + var VZ [3*EFS + 1]byte + var K1 [AESKEY]byte + var K2 [AESKEY]byte + var U [EGS]byte + + if ECDH_KEY_PAIR_GENERATE(RNG, U[:], V) != 0 { + return nil + } + if ECDH_ECPSVDP_DH(U[:], W, Z[:], 0) != 0 { + return nil + } + + for i := 0; i < 2*EFS+1; i++ { + VZ[i] = V[i] + } + for i := 0; i < EFS; i++ { + VZ[2*EFS+1+i] = Z[i] + } + + K := core.KDF2(core.MC_SHA2, sha, VZ[:], P1, 2*AESKEY) + + for i := 0; i < AESKEY; i++ { + K1[i] = K[i] + K2[i] = K[AESKEY+i] + } + + C := core.AES_CBC_IV0_ENCRYPT(K1[:], M) + + L2 := core.InttoBytes(len(P2), 8) + + var AC []byte + + for i := 0; i < len(C); i++ { + AC = append(AC, C[i]) + } + for i := 0; i < len(P2); i++ { + AC = append(AC, P2[i]) + } + for i := 0; i < 8; i++ { + AC = append(AC, L2[i]) + } + + core.HMAC(core.MC_SHA2, sha, T, len(T), K2[:], AC) + + return C +} + +/* constant time n-byte compare */ +func ncomp(T1 []byte, T2 []byte, n int) bool { + res := 0 + for i := 0; i < n; i++ { + res |= int(T1[i] ^ T2[i]) + } + if res == 0 { + return true + } + return false +} + +/* IEEE1363 ECIES decryption. Decryption of ciphertext V,C,T using private key U outputs plaintext M */ +func ECDH_ECIES_DECRYPT(sha int, P1 []byte, P2 []byte, V []byte, C []byte, T []byte, U []byte) []byte { + var Z [EFS]byte + var VZ [3*EFS + 1]byte + var K1 [AESKEY]byte + var K2 [AESKEY]byte + + var TAG []byte = T[:] + + if ECDH_ECPSVDP_DH(U, V, Z[:], 0) != 0 { + return nil + } + + for i := 0; i < 2*EFS+1; i++ { + VZ[i] = V[i] + } + for i := 0; i < EFS; i++ { + VZ[2*EFS+1+i] = Z[i] + } + + K := core.KDF2(core.MC_SHA2, sha, VZ[:], P1, 2*AESKEY) + + for i := 0; i < AESKEY; i++ { + K1[i] = K[i] + K2[i] = K[AESKEY+i] + } + + M := core.AES_CBC_IV0_DECRYPT(K1[:], C) + + if M == nil { + return nil + } + + L2 := core.InttoBytes(len(P2), 8) + + var AC []byte + + for i := 0; i < len(C); i++ { + AC = append(AC, C[i]) + } + for i := 0; i < len(P2); i++ { + AC = append(AC, P2[i]) + } + for i := 0; i < 8; i++ { + AC = append(AC, L2[i]) + } + + core.HMAC(core.MC_SHA2, sha, TAG, len(TAG), K2[:], AC) + + if !ncomp(T, TAG, len(T)) { + return nil + } + + return M +} diff --git a/ec/bls48581/ECP.go b/ec/bls48581/ECP.go new file mode 100644 index 0000000..d7a85c9 --- /dev/null +++ b/ec/bls48581/ECP.go @@ -0,0 +1,1850 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package bls48581 + +//import "fmt" +/* Elliptic Curve Point Structure */ + +type ECP struct { + x *FP + y *FP + z *FP +} + +/* Constructors */ +func NewECP() *ECP { + E := new(ECP) + E.x = NewFP() + E.y = NewFPint(1) + if CURVETYPE == EDWARDS { + E.z = NewFPint(1) + } else { + E.z = NewFP() + } + return E +} + +/* set (x,y) from two BIGs */ +func NewECPbigs(ix *BIG, iy *BIG) *ECP { + E := new(ECP) + E.x = NewFPbig(ix) + E.y = NewFPbig(iy) + E.z = NewFPint(1) + E.x.norm() + rhs := RHS(E.x) + + if CURVETYPE == MONTGOMERY { + if rhs.qr(nil) != 1 { + E.inf() + } + } else { + y2 := NewFPcopy(E.y) + y2.sqr() + if !y2.Equals(rhs) { + E.inf() + } + } + return E +} + +/* set (x,y) from BIG and a bit */ +func NewECPbigint(ix *BIG, s int) *ECP { + E := new(ECP) + E.x = NewFPbig(ix) + E.y = NewFP() + E.x.norm() + rhs := RHS(E.x) + E.z = NewFPint(1) + hint := NewFP() + if rhs.qr(hint) == 1 { + ny := rhs.sqrt(hint) + if ny.sign() != s { + ny.neg() + ny.norm() + } + E.y.copy(ny) + } else { + E.inf() + } + return E +} + +/* set from x - calculate y from curve equation */ +func NewECPbig(ix *BIG) *ECP { + E := new(ECP) + E.x = NewFPbig(ix) + E.y = NewFP() + E.x.norm() + rhs := RHS(E.x) + E.z = NewFPint(1) + hint := NewFP() + if rhs.qr(hint) == 1 { + if CURVETYPE != MONTGOMERY { + E.y.copy(rhs.sqrt(hint)) + } + } else { + E.inf() + } + return E +} + +/* test for O point-at-infinity */ +func (E *ECP) Is_infinity() bool { + // if E.INF {return true} + + if CURVETYPE == EDWARDS { + return (E.x.iszilch() && E.y.Equals(E.z)) + } + if CURVETYPE == WEIERSTRASS { + return (E.x.iszilch() && E.z.iszilch()) + } + if CURVETYPE == MONTGOMERY { + return E.z.iszilch() + } + return true +} + +/* Conditional swap of P and Q dependant on d */ +func (E *ECP) cswap(Q *ECP, d int) { + E.x.cswap(Q.x, d) + if CURVETYPE != MONTGOMERY { + E.y.cswap(Q.y, d) + } + E.z.cswap(Q.z, d) +} + +/* Conditional move of Q to P dependant on d */ +func (E *ECP) cmove(Q *ECP, d int) { + E.x.cmove(Q.x, d) + if CURVETYPE != MONTGOMERY { + E.y.cmove(Q.y, d) + } + E.z.cmove(Q.z, d) +} + +/* return 1 if b==c, no branching */ +func teq(b int32, c int32) int { + x := b ^ c + x -= 1 // if x=0, x now -1 + return int((x >> 31) & 1) +} + +/* this=P */ +func (E *ECP) Copy(P *ECP) { + E.x.copy(P.x) + if CURVETYPE != MONTGOMERY { + E.y.copy(P.y) + } + E.z.copy(P.z) +} + +/* this=-this */ +func (E *ECP) Neg() { + if CURVETYPE == WEIERSTRASS { + E.y.neg() + E.y.norm() + } + if CURVETYPE == EDWARDS { + E.x.neg() + E.x.norm() + } + return +} + +/* Constant time select from pre-computed table */ +func (E *ECP) selector(W []*ECP, b int32) { + MP := NewECP() + m := b >> 31 + babs := (b ^ m) - m + + babs = (babs - 1) / 2 + + E.cmove(W[0], teq(babs, 0)) // conditional move + E.cmove(W[1], teq(babs, 1)) + E.cmove(W[2], teq(babs, 2)) + E.cmove(W[3], teq(babs, 3)) + E.cmove(W[4], teq(babs, 4)) + E.cmove(W[5], teq(babs, 5)) + E.cmove(W[6], teq(babs, 6)) + E.cmove(W[7], teq(babs, 7)) + + MP.Copy(E) + MP.Neg() + E.cmove(MP, int(m&1)) +} + +/* set this=O */ +func (E *ECP) inf() { + E.x.zero() + if CURVETYPE != MONTGOMERY { + E.y.one() + } + if CURVETYPE != EDWARDS { + E.z.zero() + } else { + E.z.one() + } +} + +/* Test P == Q */ +func (E *ECP) Equals(Q *ECP) bool { + a := NewFP() + b := NewFP() + a.copy(E.x) + a.mul(Q.z) + a.reduce() + b.copy(Q.x) + b.mul(E.z) + b.reduce() + if !a.Equals(b) { + return false + } + if CURVETYPE != MONTGOMERY { + a.copy(E.y) + a.mul(Q.z) + a.reduce() + b.copy(Q.y) + b.mul(E.z) + b.reduce() + if !a.Equals(b) { + return false + } + } + + return true +} + +/* Calculate RHS of curve equation */ +func RHS(x *FP) *FP { + r := NewFPcopy(x) + r.sqr() + + if CURVETYPE == WEIERSTRASS { // x^3+Ax+B + b := NewFPbig(NewBIGints(CURVE_B)) + r.mul(x) + if CURVE_A == -3 { + cx := NewFPcopy(x) + cx.imul(3) + cx.neg() + cx.norm() + r.add(cx) + } + r.add(b) + } + if CURVETYPE == EDWARDS { // (Ax^2-1)/(Bx^2-1) + b := NewFPbig(NewBIGints(CURVE_B)) + + one := NewFPint(1) + b.mul(r) + b.sub(one) + b.norm() + if CURVE_A == -1 { + r.neg() + } + r.sub(one) + r.norm() + b.inverse(nil) + r.mul(b) + } + if CURVETYPE == MONTGOMERY { // x^3+Ax^2+x + x3 := NewFP() + x3.copy(r) + x3.mul(x) + r.imul(CURVE_A) + r.add(x3) + r.add(x) + } + r.reduce() + return r +} + +/* set to affine - from (x,y,z) to (x,y) */ +func (E *ECP) Affine() { + if E.Is_infinity() { + return + } + one := NewFPint(1) + if E.z.Equals(one) { + return + } + E.z.inverse(nil) + E.x.mul(E.z) + E.x.reduce() + + if CURVETYPE != MONTGOMERY { + E.y.mul(E.z) + E.y.reduce() + } + E.z.copy(one) +} + +/* extract x as a BIG */ +func (E *ECP) GetX() *BIG { + W := NewECP() + W.Copy(E) + W.Affine() + return W.x.redc() +} + +/* extract y as a BIG */ +func (E *ECP) GetY() *BIG { + W := NewECP() + W.Copy(E) + W.Affine() + return W.y.redc() +} + +/* get sign of Y */ +func (E *ECP) GetS() int { + W := NewECP() + W.Copy(E) + W.Affine() + return W.y.sign() +} + +/* extract x as an FP */ +func (E *ECP) getx() *FP { + return E.x +} + +/* extract y as an FP */ +func (E *ECP) gety() *FP { + return E.y +} + +/* extract z as an FP */ +func (E *ECP) getz() *FP { + return E.z +} + +/* convert to byte array */ +func (E *ECP) ToBytes(b []byte, compress bool) { + var t [int(MODBYTES)]byte + MB := int(MODBYTES) + alt := false + W := NewECP() + W.Copy(E) + W.Affine() + W.x.redc().ToBytes(t[:]) + + if CURVETYPE == MONTGOMERY { + for i := 0; i < MB; i++ { + b[i] = t[i] + } + //b[0] = 0x06 + return + } + + if (MODBITS-1)%8 <= 4 && ALLOW_ALT_COMPRESS { + alt = true + } + + if alt { + for i := 0; i < MB; i++ { + b[i] = t[i] + } + if compress { + b[0] |= 0x80 + if W.y.islarger() == 1 { + b[0] |= 0x20 + } + } else { + W.y.redc().ToBytes(t[:]) + for i := 0; i < MB; i++ { + b[i+MB] = t[i] + } + } + } else { + for i := 0; i < MB; i++ { + b[i+1] = t[i] + } + if compress { + b[0] = 0x02 + if W.y.sign() == 1 { + b[0] = 0x03 + } + return + } + b[0] = 0x04 + W.y.redc().ToBytes(t[:]) + for i := 0; i < MB; i++ { + b[i+MB+1] = t[i] + } + } +} + +/* convert from byte array to point */ +func ECP_fromBytes(b []byte) *ECP { + var t [int(MODBYTES)]byte + MB := int(MODBYTES) + p := NewBIGints(Modulus) + alt := false + + if CURVETYPE == MONTGOMERY { + for i := 0; i < MB; i++ { + t[i] = b[i] + } + px := FromBytes(t[:]) + if Comp(px, p) >= 0 { + return NewECP() + } + return NewECPbig(px) + } + + if (MODBITS-1)%8 <= 4 && ALLOW_ALT_COMPRESS { + alt = true + } + + if alt { + for i := 0; i < MB; i++ { + t[i] = b[i] + } + t[0] &= 0x1f + px := FromBytes(t[:]) + if (b[0] & 0x80) == 0 { + for i := 0; i < MB; i++ { + t[i] = b[i+MB] + } + py := FromBytes(t[:]) + return NewECPbigs(px, py) + } else { + sgn := (b[0] & 0x20) >> 5 + P := NewECPbigint(px, 0) + cmp := P.y.islarger() + if (sgn == 1 && cmp != 1) || (sgn == 0 && cmp == 1) { + P.Neg() + } + return P + } + } else { + for i := 0; i < MB; i++ { + t[i] = b[i+1] + } + px := FromBytes(t[:]) + if Comp(px, p) >= 0 { + return NewECP() + } + + if b[0] == 0x04 { + for i := 0; i < MB; i++ { + t[i] = b[i+MB+1] + } + py := FromBytes(t[:]) + if Comp(py, p) >= 0 { + return NewECP() + } + return NewECPbigs(px, py) + } + + if b[0] == 0x02 || b[0] == 0x03 { + return NewECPbigint(px, int(b[0]&1)) + } + } + return NewECP() +} + +/* convert to hex string */ +func (E *ECP) ToString() string { + W := NewECP() + W.Copy(E) + W.Affine() + if W.Is_infinity() { + return "infinity" + } + if CURVETYPE == MONTGOMERY { + return "(" + W.x.redc().ToString() + ")" + } else { + return "(" + W.x.redc().ToString() + "," + W.y.redc().ToString() + ")" + } +} + +/* this*=2 */ +func (E *ECP) dbl() { + + if CURVETYPE == WEIERSTRASS { + if CURVE_A == 0 { + t0 := NewFPcopy(E.y) + t0.sqr() + t1 := NewFPcopy(E.y) + t1.mul(E.z) + t2 := NewFPcopy(E.z) + t2.sqr() + + E.z.copy(t0) + E.z.add(t0) + E.z.norm() + E.z.add(E.z) + E.z.add(E.z) + E.z.norm() + t2.imul(3 * CURVE_B_I) + + x3 := NewFPcopy(t2) + x3.mul(E.z) + + y3 := NewFPcopy(t0) + y3.add(t2) + y3.norm() + E.z.mul(t1) + t1.copy(t2) + t1.add(t2) + t2.add(t1) + t0.sub(t2) + t0.norm() + y3.mul(t0) + y3.add(x3) + t1.copy(E.x) + t1.mul(E.y) + E.x.copy(t0) + E.x.norm() + E.x.mul(t1) + E.x.add(E.x) + E.x.norm() + E.y.copy(y3) + E.y.norm() + } else { + t0 := NewFPcopy(E.x) + t1 := NewFPcopy(E.y) + t2 := NewFPcopy(E.z) + t3 := NewFPcopy(E.x) + z3 := NewFPcopy(E.z) + y3 := NewFP() + x3 := NewFP() + b := NewFP() + + if CURVE_B_I == 0 { + b.copy(NewFPbig(NewBIGints(CURVE_B))) + } + + t0.sqr() //1 x^2 + t1.sqr() //2 y^2 + t2.sqr() //3 + + t3.mul(E.y) //4 + t3.add(t3) + t3.norm() //5 + z3.mul(E.x) //6 + z3.add(z3) + z3.norm() //7 + y3.copy(t2) + + if CURVE_B_I == 0 { + y3.mul(b) + } else { + y3.imul(CURVE_B_I) + } + + y3.sub(z3) //9 *** + x3.copy(y3) + x3.add(y3) + x3.norm() //10 + + y3.add(x3) //11 + x3.copy(t1) + x3.sub(y3) + x3.norm() //12 + y3.add(t1) + y3.norm() //13 + y3.mul(x3) //14 + x3.mul(t3) //15 + t3.copy(t2) + t3.add(t2) //16 + t2.add(t3) //17 + + if CURVE_B_I == 0 { + z3.mul(b) + } else { + z3.imul(CURVE_B_I) + } + + z3.sub(t2) //19 + z3.sub(t0) + z3.norm() //20 *** + t3.copy(z3) + t3.add(z3) //21 + + z3.add(t3) + z3.norm() //22 + t3.copy(t0) + t3.add(t0) //23 + t0.add(t3) //24 + t0.sub(t2) + t0.norm() //25 + + t0.mul(z3) //26 + y3.add(t0) //27 + t0.copy(E.y) + t0.mul(E.z) //28 + t0.add(t0) + t0.norm() //29 + z3.mul(t0) //30 + x3.sub(z3) //x3.norm();//31 + t0.add(t0) + t0.norm() //32 + t1.add(t1) + t1.norm() //33 + z3.copy(t0) + z3.mul(t1) //34 + + E.x.copy(x3) + E.x.norm() + E.y.copy(y3) + E.y.norm() + E.z.copy(z3) + E.z.norm() + } + } + + if CURVETYPE == EDWARDS { + C := NewFPcopy(E.x) + D := NewFPcopy(E.y) + H := NewFPcopy(E.z) + J := NewFP() + + E.x.mul(E.y) + E.x.add(E.x) + E.x.norm() + C.sqr() + D.sqr() + if CURVE_A == -1 { + C.neg() + } + E.y.copy(C) + E.y.add(D) + E.y.norm() + + H.sqr() + H.add(H) + E.z.copy(E.y) + J.copy(E.y) + J.sub(H) + J.norm() + E.x.mul(J) + C.sub(D) + C.norm() + E.y.mul(C) + E.z.mul(J) + + } + if CURVETYPE == MONTGOMERY { + A := NewFPcopy(E.x) + B := NewFPcopy(E.x) + AA := NewFP() + BB := NewFP() + C := NewFP() + + A.add(E.z) + A.norm() + AA.copy(A) + AA.sqr() + B.sub(E.z) + B.norm() + BB.copy(B) + BB.sqr() + C.copy(AA) + C.sub(BB) + C.norm() + + E.x.copy(AA) + E.x.mul(BB) + + A.copy(C) + A.imul((CURVE_A + 2) / 4) + + BB.add(A) + BB.norm() + E.z.copy(BB) + E.z.mul(C) + } + return +} + +/* this+=Q */ +func (E *ECP) Add(Q *ECP) { + + if CURVETYPE == WEIERSTRASS { + if CURVE_A == 0 { + b := 3 * CURVE_B_I + t0 := NewFPcopy(E.x) + t0.mul(Q.x) + t1 := NewFPcopy(E.y) + t1.mul(Q.y) + t2 := NewFPcopy(E.z) + t2.mul(Q.z) + t3 := NewFPcopy(E.x) + t3.add(E.y) + t3.norm() + t4 := NewFPcopy(Q.x) + t4.add(Q.y) + t4.norm() + t3.mul(t4) + t4.copy(t0) + t4.add(t1) + + t3.sub(t4) + t3.norm() + t4.copy(E.y) + t4.add(E.z) + t4.norm() + x3 := NewFPcopy(Q.y) + x3.add(Q.z) + x3.norm() + + t4.mul(x3) + x3.copy(t1) + x3.add(t2) + + t4.sub(x3) + t4.norm() + x3.copy(E.x) + x3.add(E.z) + x3.norm() + y3 := NewFPcopy(Q.x) + y3.add(Q.z) + y3.norm() + x3.mul(y3) + y3.copy(t0) + y3.add(t2) + y3.rsub(x3) + y3.norm() + x3.copy(t0) + x3.add(t0) + t0.add(x3) + t0.norm() + t2.imul(b) + + z3 := NewFPcopy(t1) + z3.add(t2) + z3.norm() + t1.sub(t2) + t1.norm() + y3.imul(b) + + x3.copy(y3) + x3.mul(t4) + t2.copy(t3) + t2.mul(t1) + x3.rsub(t2) + y3.mul(t0) + t1.mul(z3) + y3.add(t1) + t0.mul(t3) + z3.mul(t4) + z3.add(t0) + + E.x.copy(x3) + E.x.norm() + E.y.copy(y3) + E.y.norm() + E.z.copy(z3) + E.z.norm() + } else { + + t0 := NewFPcopy(E.x) + t1 := NewFPcopy(E.y) + t2 := NewFPcopy(E.z) + t3 := NewFPcopy(E.x) + t4 := NewFPcopy(Q.x) + z3 := NewFP() + y3 := NewFPcopy(Q.x) + x3 := NewFPcopy(Q.y) + b := NewFP() + + if CURVE_B_I == 0 { + b.copy(NewFPbig(NewBIGints(CURVE_B))) + } + + t0.mul(Q.x) //1 + t1.mul(Q.y) //2 + t2.mul(Q.z) //3 + + t3.add(E.y) + t3.norm() //4 + t4.add(Q.y) + t4.norm() //5 + t3.mul(t4) //6 + t4.copy(t0) + t4.add(t1) //7 + t3.sub(t4) + t3.norm() //8 + t4.copy(E.y) + t4.add(E.z) + t4.norm() //9 + x3.add(Q.z) + x3.norm() //10 + t4.mul(x3) //11 + x3.copy(t1) + x3.add(t2) //12 + + t4.sub(x3) + t4.norm() //13 + x3.copy(E.x) + x3.add(E.z) + x3.norm() //14 + y3.add(Q.z) + y3.norm() //15 + + x3.mul(y3) //16 + y3.copy(t0) + y3.add(t2) //17 + + y3.rsub(x3) + y3.norm() //18 + z3.copy(t2) + + if CURVE_B_I == 0 { + z3.mul(b) + } else { + z3.imul(CURVE_B_I) + } + + x3.copy(y3) + x3.sub(z3) + x3.norm() //20 + z3.copy(x3) + z3.add(x3) //21 + + x3.add(z3) //22 + z3.copy(t1) + z3.sub(x3) + z3.norm() //23 + x3.add(t1) + x3.norm() //24 + + if CURVE_B_I == 0 { + y3.mul(b) + } else { + y3.imul(CURVE_B_I) + } + + t1.copy(t2) + t1.add(t2) //26 + t2.add(t1) //27 + + y3.sub(t2) //28 + + y3.sub(t0) + y3.norm() //29 + t1.copy(y3) + t1.add(y3) //30 + y3.add(t1) + y3.norm() //31 + + t1.copy(t0) + t1.add(t0) //32 + t0.add(t1) //33 + t0.sub(t2) + t0.norm() //34 + t1.copy(t4) + t1.mul(y3) //35 + t2.copy(t0) + t2.mul(y3) //36 + y3.copy(x3) + y3.mul(z3) //37 + y3.add(t2) //38 + x3.mul(t3) //39 + x3.sub(t1) //40 + z3.mul(t4) //41 + t1.copy(t3) + t1.mul(t0) //42 + z3.add(t1) + E.x.copy(x3) + E.x.norm() + E.y.copy(y3) + E.y.norm() + E.z.copy(z3) + E.z.norm() + + } + } + if CURVETYPE == EDWARDS { + b := NewFPbig(NewBIGints(CURVE_B)) + A := NewFPcopy(E.z) + B := NewFP() + C := NewFPcopy(E.x) + D := NewFPcopy(E.y) + EE := NewFP() + F := NewFP() + G := NewFP() + + A.mul(Q.z) + B.copy(A) + B.sqr() + C.mul(Q.x) + D.mul(Q.y) + + EE.copy(C) + EE.mul(D) + EE.mul(b) + F.copy(B) + F.sub(EE) + G.copy(B) + G.add(EE) + + if CURVE_A == 1 { + EE.copy(D) + EE.sub(C) + } + C.add(D) + + B.copy(E.x) + B.add(E.y) + D.copy(Q.x) + D.add(Q.y) + B.norm() + D.norm() + B.mul(D) + B.sub(C) + B.norm() + F.norm() + B.mul(F) + E.x.copy(A) + E.x.mul(B) + G.norm() + if CURVE_A == 1 { + EE.norm() + C.copy(EE) + C.mul(G) + } + if CURVE_A == -1 { + C.norm() + C.mul(G) + } + E.y.copy(A) + E.y.mul(C) + E.z.copy(F) + E.z.mul(G) + } + return +} + +/* Differential Add for Montgomery curves. this+=Q where W is this-Q and is affine. */ +func (E *ECP) dadd(Q *ECP, W *ECP) { + A := NewFPcopy(E.x) + B := NewFPcopy(E.x) + C := NewFPcopy(Q.x) + D := NewFPcopy(Q.x) + DA := NewFP() + CB := NewFP() + + A.add(E.z) + B.sub(E.z) + + C.add(Q.z) + D.sub(Q.z) + A.norm() + D.norm() + + DA.copy(D) + DA.mul(A) + C.norm() + B.norm() + + CB.copy(C) + CB.mul(B) + + A.copy(DA) + A.add(CB) + A.norm() + A.sqr() + B.copy(DA) + B.sub(CB) + B.norm() + B.sqr() + + E.x.copy(A) + E.z.copy(W.x) + E.z.mul(B) + +} + +/* this-=Q */ +func (E *ECP) Sub(Q *ECP) { + NQ := NewECP() + NQ.Copy(Q) + NQ.Neg() + E.Add(NQ) +} + +/* constant time multiply by small integer of length bts - use ladder */ +func (E *ECP) pinmul(e int32, bts int32) *ECP { + if CURVETYPE == MONTGOMERY { + return E.mul(NewBIGint(int(e))) + } else { + P := NewECP() + R0 := NewECP() + R1 := NewECP() + R1.Copy(E) + + for i := bts - 1; i >= 0; i-- { + b := int((e >> uint32(i)) & 1) + P.Copy(R1) + P.Add(R0) + R0.cswap(R1, b) + R1.Copy(P) + R0.dbl() + R0.cswap(R1, b) + } + P.Copy(R0) + return P + } +} + +// Point multiplication, multiplies a point P by a scalar e +// This code has no inherent awareness of the order of the curve, or the order of the point. +// The order of the curve will be h.r, where h is a cofactor, and r is a large prime +// Typically P will be of order r (but not always), and typically e will be less than r (but not always) +// A problem can arise if a secret e is a few bits less than r, as the leading zeros in e will leak via a timing attack +// The secret e may however be greater than r (see RFC7748 which combines elimination of a small cofactor h with the point multiplication, using an e>r) +// Our solution is to use as a multiplier an e, whose length in bits is that of the logical OR of e and r, hence allowing e>r while forcing inclusion of leading zeros if e= 0; i-- { + b := int(e.bit(i)) + P.Copy(R1) + P.dadd(R0, D) + R0.cswap(R1, b) + R1.Copy(P) + R0.dbl() + R0.cswap(R1, b) + } + P.Copy(R0) + } else { + // fixed size windows + mt := NewBIG() + t := NewBIG() + Q := NewECP() + C := NewECP() + + var W []*ECP + var w [1 + (NLEN*int(BASEBITS)+3)/4]int8 + + Q.Copy(E) + Q.dbl() + + W = append(W, NewECP()) + W[0].Copy(E) + + for i := 1; i < 8; i++ { + W = append(W, NewECP()) + W[i].Copy(W[i-1]) + W[i].Add(Q) + } + + // make exponent odd - add 2P if even, P if odd + t.copy(e) + s := int(t.parity()) + t.inc(1) + t.norm() + ns := int(t.parity()) + mt.copy(t) + mt.inc(1) + mt.norm() + t.cmove(mt, s) + Q.cmove(E, ns) + C.Copy(Q) + + nb := 1 + (max+3)/4 + + // convert exponent to signed 4-bit window + for i := 0; i < nb; i++ { + w[i] = int8(t.lastbits(5) - 16) + t.dec(int(w[i])) + t.norm() + t.fshr(4) + } + w[nb] = int8(t.lastbits(5)) + + //P.Copy(W[(int(w[nb])-1)/2]) + P.selector(W, int32(w[nb])) + for i := nb - 1; i >= 0; i-- { + Q.selector(W, int32(w[i])) + P.dbl() + P.dbl() + P.dbl() + P.dbl() + P.Add(Q) + } + P.Sub(C) /* apply correction */ + } + return P +} + +/* Public version */ +func (E *ECP) Mul(e *BIG) *ECP { + return E.mul(e) +} + +// Generic multi-multiplication, fixed 4-bit window, P=Sigma e_i*X_i +func ECP_muln(n int, X []*ECP, e []*BIG) *ECP { + P := NewECP() + R := NewECP() + S := NewECP() + var B []*ECP + t := NewBIG() + for i := 0; i < 16; i++ { + B = append(B, NewECP()) + } + mt := NewBIGcopy(e[0]) + mt.norm() + for i := 1; i < n; i++ { // find biggest + t.copy(e[i]) + t.norm() + k := Comp(t, mt) + mt.cmove(t, (k+1)/2) + } + nb := (mt.nbits() + 3) / 4 + for i := nb - 1; i >= 0; i-- { + for j := 0; j < 16; j++ { + B[j].inf() + } + for j := 0; j < n; j++ { + mt.copy(e[j]) + mt.norm() + mt.shr(uint(i * 4)) + k := mt.lastbits(4) + B[k].Add(X[j]) + } + R.inf() + S.inf() + for j := 15; j >= 1; j-- { + R.Add(B[j]) + S.Add(R) + } + for j := 0; j < 4; j++ { + P.dbl() + } + P.Add(S) + } + return P +} + +/* Return e.this+f.Q */ + +func (E *ECP) Mul2(e *BIG, Q *ECP, f *BIG) *ECP { + te := NewBIG() + tf := NewBIG() + mt := NewBIG() + S := NewECP() + T := NewECP() + C := NewECP() + var W []*ECP + var w [1 + (NLEN*int(BASEBITS)+1)/2]int8 + + te.copy(e) + tf.copy(f) + + // precompute table + for i := 0; i < 8; i++ { + W = append(W, NewECP()) + } + W[1].Copy(E) + W[1].Sub(Q) + W[2].Copy(E) + W[2].Add(Q) + S.Copy(Q) + S.dbl() + W[0].Copy(W[1]) + W[0].Sub(S) + W[3].Copy(W[2]) + W[3].Add(S) + T.Copy(E) + T.dbl() + W[5].Copy(W[1]) + W[5].Add(T) + W[6].Copy(W[2]) + W[6].Add(T) + W[4].Copy(W[5]) + W[4].Sub(S) + W[7].Copy(W[6]) + W[7].Add(S) + + // if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction + + s := int(te.parity()) + te.inc(1) + te.norm() + ns := int(te.parity()) + mt.copy(te) + mt.inc(1) + mt.norm() + te.cmove(mt, s) + T.cmove(E, ns) + C.Copy(T) + + s = int(tf.parity()) + tf.inc(1) + tf.norm() + ns = int(tf.parity()) + mt.copy(tf) + mt.inc(1) + mt.norm() + tf.cmove(mt, s) + S.cmove(Q, ns) + C.Add(S) + + mt.copy(te) + mt.add(tf) + mt.norm() + nb := 1 + (mt.nbits()+1)/2 + + // convert exponent to signed 2-bit window + for i := 0; i < nb; i++ { + a := (te.lastbits(3) - 4) + te.dec(int(a)) + te.norm() + te.fshr(2) + b := (tf.lastbits(3) - 4) + tf.dec(int(b)) + tf.norm() + tf.fshr(2) + w[i] = int8(4*a + b) + } + w[nb] = int8(4*te.lastbits(3) + tf.lastbits(3)) + //S.Copy(W[(w[nb]-1)/2]) + S.selector(W, int32(w[nb])) + for i := nb - 1; i >= 0; i-- { + T.selector(W, int32(w[i])) + S.dbl() + S.dbl() + S.Add(T) + } + S.Sub(C) /* apply correction */ + return S +} + +func (E *ECP) Cfp() { + cf := CURVE_Cof_I + if cf == 1 { + return + } + if cf == 4 { + E.dbl() + E.dbl() + return + } + if cf == 8 { + E.dbl() + E.dbl() + E.dbl() + return + } + c := NewBIGints(CURVE_Cof) + E.Copy(E.mul(c)) +} + +/* Hunt and Peck a BIG to a curve point */ +func ECP_hap2point(h *BIG) *ECP { + var P *ECP + x := NewBIGcopy(h) + + for true { + if CURVETYPE != MONTGOMERY { + P = NewECPbigint(x, 0) + } else { + P = NewECPbig(x) + } + x.inc(1) + x.norm() + if !P.Is_infinity() { + break + } + } + return P +} + +/* Constant time Map to Point */ +func ECP_map2point(h *FP) *ECP { + P := NewECP() + + if CURVETYPE == MONTGOMERY { + // Elligator 2 + X1 := NewFP() + X2 := NewFP() + w := NewFP() + one := NewFPint(1) + A := NewFPint(CURVE_A) + t := NewFPcopy(h) + N := NewFP() + D := NewFP() + hint := NewFP() + + t.sqr() + + if PM1D2 == 2 { + t.add(t) + } + if PM1D2 == 1 { + t.neg() + } + if PM1D2 > 2 { + t.imul(QNRI) + } + + t.norm() + D.copy(t) + D.add(one) + D.norm() + + X1.copy(A) + X1.neg() + X1.norm() + X2.copy(X1) + X2.mul(t) + + w.copy(X1) + w.sqr() + N.copy(w) + N.mul(X1) + w.mul(A) + w.mul(D) + N.add(w) + t.copy(D) + t.sqr() + t.mul(X1) + N.add(t) + N.norm() + + t.copy(N) + t.mul(D) + qres := t.qr(hint) + w.copy(t) + w.inverse(hint) + D.copy(w) + D.mul(N) + X1.mul(D) + X2.mul(D) + X1.cmove(X2, 1-qres) + + a := X1.redc() + P.Copy(NewECPbig(a)) + } + if CURVETYPE == EDWARDS { + // Elligator 2 - map to Montgomery, place point, map back + X1 := NewFP() + X2 := NewFP() + t := NewFPcopy(h) + w := NewFP() + one := NewFPint(1) + A := NewFP() + w1 := NewFP() + w2 := NewFP() + B := NewFPbig(NewBIGints(CURVE_B)) + Y := NewFP() + K := NewFP() + D := NewFP() + hint := NewFP() + //Y3:=NewFP() + rfc := 0 + + if MODTYPE != GENERALISED_MERSENNE { + A.copy(B) + + if CURVE_A == 1 { + A.add(one) + B.sub(one) + } else { + A.sub(one) + B.add(one) + } + A.norm() + B.norm() + + A.div2() + B.div2() + B.div2() + + K.copy(B) + K.neg() + K.norm() + //K.inverse(nil) + K.invsqrt(K, w1) + + rfc = RIADZ + if rfc == 1 { // RFC7748 + A.mul(K) + K.mul(w1) + //K=K.sqrt(nil) + } else { + B.sqr() + } + } else { + rfc = 1 + A.copy(NewFPint(156326)) + } + + t.sqr() + qnr := 0 + if PM1D2 == 2 { + t.add(t) + qnr = 2 + } + if PM1D2 == 1 { + t.neg() + qnr = -1 + } + if PM1D2 > 2 { + t.imul(QNRI) + qnr = QNRI + } + t.norm() + + D.copy(t) + D.add(one) + D.norm() + X1.copy(A) + X1.neg() + X1.norm() + X2.copy(X1) + X2.mul(t) + + // Figure out RHS of Montgomery curve in rational form gx1/d^3 + + w.copy(X1) + w.sqr() + w1.copy(w) + w1.mul(X1) + w.mul(A) + w.mul(D) + w1.add(w) + w2.copy(D) + w2.sqr() + + if rfc == 0 { + w.copy(X1) + w.mul(B) + w2.mul(w) + w1.add(w2) + } else { + w2.mul(X1) + w1.add(w2) + } + w1.norm() + + B.copy(w1) + B.mul(D) + qres := B.qr(hint) + w.copy(B) + w.inverse(hint) + D.copy(w) + D.mul(w1) + X1.mul(D) + X2.mul(D) + D.sqr() + + w1.copy(B) + w1.imul(qnr) + w.copy(NewFPbig(NewBIGints(CURVE_HTPC))) + w.mul(hint) + w2.copy(D) + w2.mul(h) + + X1.cmove(X2, 1-qres) + B.cmove(w1, 1-qres) + hint.cmove(w, 1-qres) + D.cmove(w2, 1-qres) + + Y.copy(B.sqrt(hint)) + Y.mul(D) + + /* + Y.copy(B.sqrt(hint)) + Y.mul(D) + + B.imul(qnr) + w.copy(NewFPbig(NewBIGints(CURVE_HTPC))) + hint.mul(w) + + Y3.copy(B.sqrt(hint)) + D.mul(h) + Y3.mul(D) + + X1.cmove(X2,1-qres) + Y.cmove(Y3,1-qres) + */ + w.copy(Y) + w.neg() + w.norm() + Y.cmove(w, qres^Y.sign()) + + if rfc == 0 { + X1.mul(K) + Y.mul(K) + } + + if MODTYPE == GENERALISED_MERSENNE { + t.copy(X1) + t.sqr() + w.copy(t) + w.add(one) + w.norm() + t.sub(one) + t.norm() + w1.copy(t) + w1.mul(Y) + w1.add(w1) + X2.copy(w1) + X2.add(w1) + X2.norm() + t.sqr() + Y.sqr() + Y.add(Y) + Y.add(Y) + Y.norm() + B.copy(t) + B.add(Y) + B.norm() + + w2.copy(Y) + w2.sub(t) + w2.norm() + w2.mul(X1) + t.mul(X1) + Y.div2() + w1.copy(Y) + w1.mul(w) + w1.rsub(t) + w1.norm() + + t.copy(X2) + t.mul(w1) + P.x.copy(t) + t.copy(w2) + t.mul(B) + P.y.copy(t) + t.copy(w1) + t.mul(B) + P.z.copy(t) + + return P + } else { + w1.copy(X1) + w1.add(one) + w1.norm() + w2.copy(X1) + w2.sub(one) + w2.norm() + t.copy(w1) + t.mul(Y) + X1.mul(w1) + + if rfc == 1 { + X1.mul(K) + } + Y.mul(w2) + P.x.copy(X1) + P.y.copy(Y) + P.z.copy(t) + + return P + } + } + if CURVETYPE == WEIERSTRASS { + // swu method + A := NewFP() + B := NewFP() + X1 := NewFP() + X2 := NewFP() + X3 := NewFP() + one := NewFPint(1) + Y := NewFP() + D := NewFP() + t := NewFPcopy(h) + w := NewFP() + D2 := NewFP() + hint := NewFP() + GX1 := NewFP() + //Y3:=NewFP() + sgn := t.sign() + + if CURVE_A != 0 || HTC_ISO != 0 { + if HTC_ISO != 0 { + /* CAHCZS + A.copy(NewFPbig(NewBIGints(CURVE_Ad))) + B.copy(NewFPbig(NewBIGints(CURVE_Bd))) + CAHCZF */ + } else { + A.copy(NewFPint(CURVE_A)) + B.copy(NewFPbig(NewBIGints(CURVE_B))) + } + // SSWU method + t.sqr() + t.imul(RIADZ) + w.copy(t) + w.add(one) + w.norm() + + w.mul(t) + D.copy(A) + D.mul(w) + + w.add(one) + w.norm() + w.mul(B) + w.neg() + w.norm() + + X2.copy(w) + X3.copy(t) + X3.mul(X2) + + // x^3+Ad^2x+Bd^3 + GX1.copy(X2) + GX1.sqr() + D2.copy(D) + D2.sqr() + w.copy(A) + w.mul(D2) + GX1.add(w) + GX1.norm() + GX1.mul(X2) + D2.mul(D) + w.copy(B) + w.mul(D2) + GX1.add(w) + GX1.norm() + + w.copy(GX1) + w.mul(D) + qr := w.qr(hint) + D.copy(w) + D.inverse(hint) + D.mul(GX1) + X2.mul(D) + X3.mul(D) + t.mul(h) + D2.copy(D) + D2.sqr() + + D.copy(D2) + D.mul(t) + t.copy(w) + t.imul(RIADZ) + X1.copy(NewFPbig(NewBIGints(CURVE_HTPC))) + X1.mul(hint) + + X2.cmove(X3, 1-qr) + D2.cmove(D, 1-qr) + w.cmove(t, 1-qr) + hint.cmove(X1, 1-qr) + + Y.copy(w.sqrt(hint)) + Y.mul(D2) + /* + Y.copy(w.sqrt(hint)) + Y.mul(D2) + + D2.mul(t) + w.imul(RIADZ) + + X1.copy(NewFPbig(NewBIGints(CURVE_HTPC))) + hint.mul(X1) + + Y3.copy(w.sqrt(hint)) + Y3.mul(D2) + + X2.cmove(X3,1-qr) + Y.cmove(Y3,1-qr) + */ + ne := Y.sign() ^ sgn + w.copy(Y) + w.neg() + w.norm() + Y.cmove(w, ne) + + if HTC_ISO != 0 { + /* CAHCZS + k:=0 + isox:=HTC_ISO + isoy:=3*(isox-1)/2 + + //xnum + xnum:=NewFPbig(NewBIGints(PC[k])); k+=1 + for i:=0;i> 31 + babs := (b ^ m) - m + + babs = (babs - 1) / 2 + + E.cmove(W[0], teq(babs, 0)) // conditional move + E.cmove(W[1], teq(babs, 1)) + E.cmove(W[2], teq(babs, 2)) + E.cmove(W[3], teq(babs, 3)) + E.cmove(W[4], teq(babs, 4)) + E.cmove(W[5], teq(babs, 5)) + E.cmove(W[6], teq(babs, 6)) + E.cmove(W[7], teq(babs, 7)) + + MP.Copy(E) + MP.neg() + E.cmove(MP, int(m&1)) +} + +/* Test if P == Q */ +func (E *ECP8) Equals(Q *ECP8) bool { + + a := NewFP8copy(E.x) + b := NewFP8copy(Q.x) + a.mul(Q.z) + b.mul(E.z) + + if !a.Equals(b) { + return false + } + a.copy(E.y) + b.copy(Q.y) + a.mul(Q.z) + b.mul(E.z) + if !a.Equals(b) { + return false + } + + return true +} + +/* set to Affine - (x,y,z) to (x,y) */ +func (E *ECP8) Affine() { + if E.Is_infinity() { + return + } + one := NewFP8int(1) + if E.z.Equals(one) { + E.x.reduce() + E.y.reduce() + return + } + E.z.inverse(nil) + + E.x.mul(E.z) + E.x.reduce() + E.y.mul(E.z) + E.y.reduce() + E.z.copy(one) +} + +/* extract affine x as FP2 */ +func (E *ECP8) GetX() *FP8 { + W := NewECP8() + W.Copy(E) + W.Affine() + return W.x +} + +/* extract affine y as FP2 */ +func (E *ECP8) GetY() *FP8 { + W := NewECP8() + W.Copy(E) + W.Affine() + return W.y +} + +/* extract projective x */ +func (E *ECP8) getx() *FP8 { + return E.x +} + +/* extract projective y */ +func (E *ECP8) gety() *FP8 { + return E.y +} + +/* extract projective z */ +func (E *ECP8) getz() *FP8 { + return E.z +} + +/* convert to byte array */ +func (E *ECP8) ToBytes(b []byte, compress bool) { + var t [8 * int(MODBYTES)]byte + MB := 8 * int(MODBYTES) + alt := false + W := NewECP8() + W.Copy(E) + W.Affine() + W.x.ToBytes(t[:]) + + if (MODBITS-1)%8 <= 4 && ALLOW_ALT_COMPRESS { + alt = true + } + + if alt { + for i := 0; i < MB; i++ { + b[i] = t[i] + } + if !compress { + W.y.ToBytes(t[:]) + for i := 0; i < MB; i++ { + b[i+MB] = t[i] + } + } else { + b[0] |= 0x80 + if W.y.islarger() == 1 { + b[0] |= 0x20 + } + } + + } else { + for i := 0; i < MB; i++ { + b[i+1] = t[i] + } + if !compress { + b[0] = 0x04 + W.y.ToBytes(t[:]) + for i := 0; i < MB; i++ { + b[i+MB+1] = t[i] + } + } else { + b[0] = 0x02 + if W.y.sign() == 1 { + b[0] = 0x03 + } + } + } +} + +/* convert from byte array to point */ +func ECP8_fromBytes(b []byte) *ECP8 { + var t [8 * int(MODBYTES)]byte + MB := 8 * int(MODBYTES) + typ := int(b[0]) + alt := false + + if (MODBITS-1)%8 <= 4 && ALLOW_ALT_COMPRESS { + alt = true + } + + if alt { + for i := 0; i < MB; i++ { + t[i] = b[i] + } + t[0] &= 0x1f + rx := FP8_fromBytes(t[:]) + if (b[0] & 0x80) == 0 { + for i := 0; i < MB; i++ { + t[i] = b[i+MB] + } + ry := FP8_fromBytes(t[:]) + return NewECP8fp8s(rx, ry) + } else { + sgn := (b[0] & 0x20) >> 5 + P := NewECP8fp8(rx, 0) + cmp := P.y.islarger() + if (sgn == 1 && cmp != 1) || (sgn == 0 && cmp == 1) { + P.neg() + } + return P + } + } else { + for i := 0; i < MB; i++ { + t[i] = b[i+1] + } + rx := FP8_fromBytes(t[:]) + if typ == 0x04 { + for i := 0; i < MB; i++ { + t[i] = b[i+MB+1] + } + ry := FP8_fromBytes(t[:]) + return NewECP8fp8s(rx, ry) + } else { + return NewECP8fp8(rx, typ&1) + } + } +} + +/* convert this to hex string */ +func (E *ECP8) ToString() string { + W := NewECP8() + W.Copy(E) + W.Affine() + if W.Is_infinity() { + return "infinity" + } + return "(" + W.x.toString() + "," + W.y.toString() + ")" +} + +/* Calculate RHS of twisted curve equation x^3+B/i */ +func RHS8(x *FP8) *FP8 { + r := NewFP8copy(x) + r.sqr() + b2 := NewFP2big(NewBIGints(CURVE_B)) + b4 := NewFP4fp2(b2) + b := NewFP8fp4(b4) + + if SEXTIC_TWIST == D_TYPE { + b.div_i() + } + if SEXTIC_TWIST == M_TYPE { + b.times_i() + } + r.mul(x) + r.add(b) + + r.reduce() + return r +} + +/* construct this from (x,y) - but set to O if not on curve */ +func NewECP8fp8s(ix *FP8, iy *FP8) *ECP8 { + E := new(ECP8) + E.x = NewFP8copy(ix) + E.y = NewFP8copy(iy) + E.z = NewFP8int(1) + E.x.norm() + rhs := RHS8(E.x) + y2 := NewFP8copy(E.y) + y2.sqr() + if !y2.Equals(rhs) { + E.inf() + } + return E +} + +/* construct this from x - but set to O if not on curve */ +func NewECP8fp8(ix *FP8, s int) *ECP8 { + E := new(ECP8) + h := NewFP() + E.x = NewFP8copy(ix) + E.y = NewFP8int(1) + E.z = NewFP8int(1) + E.x.norm() + rhs := RHS8(E.x) + if rhs.qr(h) == 1 { + rhs.sqrt(h) + if rhs.sign() != s { + rhs.neg() + } + rhs.reduce() + E.y.copy(rhs) + + } else { + E.inf() + } + return E +} + +/* this+=this */ +func (E *ECP8) dbl() int { + iy := NewFP8copy(E.y) + if SEXTIC_TWIST == D_TYPE { + iy.times_i() + } + + t0 := NewFP8copy(E.y) + t0.sqr() + if SEXTIC_TWIST == D_TYPE { + t0.times_i() + } + t1 := NewFP8copy(iy) + t1.mul(E.z) + t2 := NewFP8copy(E.z) + t2.sqr() + + E.z.copy(t0) + E.z.add(t0) + E.z.norm() + E.z.add(E.z) + E.z.add(E.z) + E.z.norm() + + t2.imul(3 * CURVE_B_I) + if SEXTIC_TWIST == M_TYPE { + t2.times_i() + } + x3 := NewFP8copy(t2) + x3.mul(E.z) + + y3 := NewFP8copy(t0) + + y3.add(t2) + y3.norm() + E.z.mul(t1) + t1.copy(t2) + t1.add(t2) + t2.add(t1) + t2.norm() + t0.sub(t2) + t0.norm() //y^2-9bz^2 + y3.mul(t0) + y3.add(x3) //(y^2+3z*2)(y^2-9z^2)+3b.z^2.8y^2 + t1.copy(E.x) + t1.mul(iy) // + E.x.copy(t0) + E.x.norm() + E.x.mul(t1) + E.x.add(E.x) //(y^2-9bz^2)xy2 + + E.x.norm() + E.y.copy(y3) + E.y.norm() + + return 1 +} + +/* this+=Q - return 0 for add, 1 for double, -1 for O */ +func (E *ECP8) Add(Q *ECP8) int { + b := 3 * CURVE_B_I + t0 := NewFP8copy(E.x) + t0.mul(Q.x) // x.Q.x + t1 := NewFP8copy(E.y) + t1.mul(Q.y) // y.Q.y + + t2 := NewFP8copy(E.z) + t2.mul(Q.z) + t3 := NewFP8copy(E.x) + t3.add(E.y) + t3.norm() //t3=X1+Y1 + t4 := NewFP8copy(Q.x) + t4.add(Q.y) + t4.norm() //t4=X2+Y2 + t3.mul(t4) //t3=(X1+Y1)(X2+Y2) + t4.copy(t0) + t4.add(t1) //t4=X1.X2+Y1.Y2 + + t3.sub(t4) + t3.norm() + if SEXTIC_TWIST == D_TYPE { + t3.times_i() //t3=(X1+Y1)(X2+Y2)-(X1.X2+Y1.Y2) = X1.Y2+X2.Y1 + } + t4.copy(E.y) + t4.add(E.z) + t4.norm() //t4=Y1+Z1 + x3 := NewFP8copy(Q.y) + x3.add(Q.z) + x3.norm() //x3=Y2+Z2 + + t4.mul(x3) //t4=(Y1+Z1)(Y2+Z2) + x3.copy(t1) // + x3.add(t2) //X3=Y1.Y2+Z1.Z2 + + t4.sub(x3) + t4.norm() + if SEXTIC_TWIST == D_TYPE { + t4.times_i() //t4=(Y1+Z1)(Y2+Z2) - (Y1.Y2+Z1.Z2) = Y1.Z2+Y2.Z1 + } + x3.copy(E.x) + x3.add(E.z) + x3.norm() // x3=X1+Z1 + y3 := NewFP8copy(Q.x) + y3.add(Q.z) + y3.norm() // y3=X2+Z2 + x3.mul(y3) // x3=(X1+Z1)(X2+Z2) + y3.copy(t0) + y3.add(t2) // y3=X1.X2+Z1+Z2 + y3.rsub(x3) + y3.norm() // y3=(X1+Z1)(X2+Z2) - (X1.X2+Z1.Z2) = X1.Z2+X2.Z1 + + if SEXTIC_TWIST == D_TYPE { + t0.times_i() // x.Q.x + t1.times_i() // y.Q.y + } + x3.copy(t0) + x3.add(t0) + t0.add(x3) + t0.norm() + t2.imul(b) + if SEXTIC_TWIST == M_TYPE { + t2.times_i() + } + z3 := NewFP8copy(t1) + z3.add(t2) + z3.norm() + t1.sub(t2) + t1.norm() + y3.imul(b) + if SEXTIC_TWIST == M_TYPE { + y3.times_i() + } + x3.copy(y3) + x3.mul(t4) + t2.copy(t3) + t2.mul(t1) + x3.rsub(t2) + y3.mul(t0) + t1.mul(z3) + y3.add(t1) + t0.mul(t3) + z3.mul(t4) + z3.add(t0) + + E.x.copy(x3) + E.x.norm() + E.y.copy(y3) + E.y.norm() + E.z.copy(z3) + E.z.norm() + + return 0 +} + +/* set this-=Q */ +func (E *ECP8) Sub(Q *ECP8) int { + NQ := NewECP8() + NQ.Copy(Q) + NQ.neg() + D := E.Add(NQ) + return D +} + +func ECP8_frob_constants() [3]*FP2 { + Fra := NewBIGints(Fra) + Frb := NewBIGints(Frb) + X := NewFP2bigs(Fra, Frb) + + F0 := NewFP2copy(X) + F0.sqr() + F2 := NewFP2copy(F0) + F2.mul_ip() + F2.norm() + F1 := NewFP2copy(F2) + F1.sqr() + F2.mul(F1) + + F2.mul_ip() + F2.norm() + + F1.copy(X) + if SEXTIC_TWIST == M_TYPE { + F1.mul_ip() + F1.norm() + F1.inverse(nil) + F0.copy(F1) + F0.sqr() + F1.mul(F0) + } + if SEXTIC_TWIST == D_TYPE { + F0.copy(F1) + F0.sqr() + F1.mul(F0) + F0.mul_ip() + F0.norm() + F1.mul_ip() + F1.norm() + F1.mul_ip() + F1.norm() + } + + F := [3]*FP2{F0, F1, F2} + return F +} + +/* set this*=q, where q is Modulus, using Frobenius */ +func (E *ECP8) frob(F [3]*FP2, n int) { + for i := 0; i < n; i++ { + E.x.frob(F[2]) + if SEXTIC_TWIST == M_TYPE { + E.x.qmul(F[0]) + E.x.times_i2() + } + if SEXTIC_TWIST == D_TYPE { + E.x.qmul(F[0]) + E.x.times_i2() + } + E.y.frob(F[2]) + if SEXTIC_TWIST == M_TYPE { + E.y.qmul(F[1]) + E.y.times_i2() + E.y.times_i() + } + if SEXTIC_TWIST == D_TYPE { + E.y.qmul(F[1]) + E.y.times_i() + } + + E.z.frob(F[2]) + } +} + +/* P*=e */ +func (E *ECP8) mul(e *BIG) *ECP8 { + /* fixed size windows */ + mt := NewBIG() + t := NewBIG() + P := NewECP8() + Q := NewECP8() + C := NewECP8() + + if E.Is_infinity() { + return NewECP8() + } + + var W []*ECP8 + var w [1 + (NLEN*int(BASEBITS)+3)/4]int8 + + /* precompute table */ + Q.Copy(E) + Q.dbl() + + W = append(W, NewECP8()) + W[0].Copy(E) + + for i := 1; i < 8; i++ { + W = append(W, NewECP8()) + W[i].Copy(W[i-1]) + W[i].Add(Q) + } + + /* make exponent odd - add 2P if even, P if odd */ + t.copy(e) + s := int(t.parity()) + t.inc(1) + t.norm() + ns := int(t.parity()) + mt.copy(t) + mt.inc(1) + mt.norm() + t.cmove(mt, s) + Q.cmove(E, ns) + C.Copy(Q) + + nb := 1 + (t.nbits()+3)/4 + /* convert exponent to signed 4-bit window */ + for i := 0; i < nb; i++ { + w[i] = int8(t.lastbits(5) - 16) + t.dec(int(w[i])) + t.norm() + t.fshr(4) + } + w[nb] = int8(t.lastbits(5)) + + //P.Copy(W[(w[nb]-1)/2]) + P.selector(W, int32(w[nb])) + for i := nb - 1; i >= 0; i-- { + Q.selector(W, int32(w[i])) + P.dbl() + P.dbl() + P.dbl() + P.dbl() + P.Add(Q) + } + P.Sub(C) + P.Affine() + return P +} + +/* Public version */ +func (E *ECP8) Mul(e *BIG) *ECP8 { + return E.mul(e) +} + +/* needed for SOK */ +func (E *ECP8) Cfp() { + + F := ECP8_frob_constants() + x := NewBIGints(CURVE_Bnx) + + xQ := E.mul(x) + x2Q := xQ.mul(x) + x3Q := x2Q.mul(x) + x4Q := x3Q.mul(x) + x5Q := x4Q.mul(x) + x6Q := x5Q.mul(x) + x7Q := x6Q.mul(x) + x8Q := x7Q.mul(x) + + if SIGN_OF_X == NEGATIVEX { + xQ.neg() + x3Q.neg() + x5Q.neg() + x7Q.neg() + } + x8Q.Sub(x7Q) + x8Q.Sub(E) + + x7Q.Sub(x6Q) + x7Q.frob(F, 1) + + x6Q.Sub(x5Q) + x6Q.frob(F, 2) + + x5Q.Sub(x4Q) + x5Q.frob(F, 3) + + x4Q.Sub(x3Q) + x4Q.frob(F, 4) + + x3Q.Sub(x2Q) + x3Q.frob(F, 5) + + x2Q.Sub(xQ) + x2Q.frob(F, 6) + + xQ.Sub(E) + xQ.frob(F, 7) + + E.dbl() + E.frob(F, 8) + + E.Add(x8Q) + E.Add(x7Q) + E.Add(x6Q) + E.Add(x5Q) + + E.Add(x4Q) + E.Add(x3Q) + E.Add(x2Q) + E.Add(xQ) + + E.Affine() +} + +func ECP8_generator() *ECP8 { + var G *ECP8 + G = NewECP8fp8s( + NewFP8fp4s( + NewFP4fp2s( + NewFP2bigs(NewBIGints(CURVE_Pxaaa), NewBIGints(CURVE_Pxaab)), + NewFP2bigs(NewBIGints(CURVE_Pxaba), NewBIGints(CURVE_Pxabb))), + NewFP4fp2s( + NewFP2bigs(NewBIGints(CURVE_Pxbaa), NewBIGints(CURVE_Pxbab)), + NewFP2bigs(NewBIGints(CURVE_Pxbba), NewBIGints(CURVE_Pxbbb)))), + NewFP8fp4s( + NewFP4fp2s( + NewFP2bigs(NewBIGints(CURVE_Pyaaa), NewBIGints(CURVE_Pyaab)), + NewFP2bigs(NewBIGints(CURVE_Pyaba), NewBIGints(CURVE_Pyabb))), + NewFP4fp2s( + NewFP2bigs(NewBIGints(CURVE_Pybaa), NewBIGints(CURVE_Pybab)), + NewFP2bigs(NewBIGints(CURVE_Pybba), NewBIGints(CURVE_Pybbb))))) + return G +} + +func ECP8_hap2point(h *BIG) *ECP8 { + one := NewBIGint(1) + x := NewBIGcopy(h) + var X2 *FP2 + var X4 *FP4 + var X8 *FP8 + var Q *ECP8 + for true { + X2 = NewFP2bigs(one, x) + X4 = NewFP4fp2(X2) + X8 = NewFP8fp4(X4) + Q = NewECP8fp8(X8, 0) + if !Q.Is_infinity() { + break + } + x.inc(1) + x.norm() + } + return Q +} + +/* Deterministic mapping of Fp to point on curve */ +func ECP8_map2point(H *FP8) *ECP8 { + // Shallue and van de Woestijne + NY := NewFP8int(1) + T := NewFP8copy(H) + sgn := T.sign() + + Z := NewFPint(RIADZG2A) + X1 := NewFP8fp(Z) + X3 := NewFP8copy(X1) + A := RHS8(X1) + W := NewFP8copy(A) + W.sqrt(nil) + + s := NewFPbig(NewBIGints(SQRTm3)) + Z.mul(s) + + T.sqr() + Y := NewFP8copy(A) + Y.mul(T) + T.copy(NY) + T.add(Y) + T.norm() + Y.rsub(NY) + Y.norm() + NY.copy(T) + NY.mul(Y) + + NY.tmul(Z) + NY.inverse(nil) + + W.tmul(Z) + if W.sign() == 1 { + W.neg() + W.norm() + } + W.tmul(Z) + W.mul(H) + W.mul(Y) + W.mul(NY) + + X1.neg() + X1.norm() + X1.div2() + X2 := NewFP8copy(X1) + X1.sub(W) + X1.norm() + X2.add(W) + X2.norm() + A.add(A) + A.add(A) + A.norm() + T.sqr() + T.mul(NY) + T.sqr() + A.mul(T) + X3.add(A) + X3.norm() + + Y.copy(RHS8(X2)) + X3.cmove(X2, Y.qr(nil)) + Y.copy(RHS8(X1)) + X3.cmove(X1, Y.qr(nil)) + Y.copy(RHS8(X3)) + Y.sqrt(nil) + + ne := Y.sign() ^ sgn + W.copy(Y) + W.neg() + W.norm() + Y.cmove(W, ne) + + return NewECP8fp8s(X3, Y) +} + +/* Map octet string to curve point */ +func ECP8_mapit(h []byte) *ECP8 { + q := NewBIGints(Modulus) + dx := DBIG_fromBytes(h) + x := dx.Mod(q) + + Q := ECP8_hap2point(x) + Q.Cfp() + return Q +} + +/* P=u0.Q0+u1*Q1+u2*Q2+u3*Q3.. */ +// Bos & Costello https://eprint.iacr.org/2013/458.pdf +// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf +// Side channel attack secure +func mul16(Q []*ECP8, u []*BIG) *ECP8 { + W := NewECP8() + P := NewECP8() + var T1 []*ECP8 + var T2 []*ECP8 + var T3 []*ECP8 + var T4 []*ECP8 + mt := NewBIG() + var t []*BIG + var bt int8 + var k int + + var w1 [NLEN*int(BASEBITS) + 1]int8 + var s1 [NLEN*int(BASEBITS) + 1]int8 + var w2 [NLEN*int(BASEBITS) + 1]int8 + var s2 [NLEN*int(BASEBITS) + 1]int8 + var w3 [NLEN*int(BASEBITS) + 1]int8 + var s3 [NLEN*int(BASEBITS) + 1]int8 + var w4 [NLEN*int(BASEBITS) + 1]int8 + var s4 [NLEN*int(BASEBITS) + 1]int8 + + for i := 0; i < 16; i++ { + t = append(t, NewBIGcopy(u[i])) + } + + T1 = append(T1, NewECP8()) + T1[0].Copy(Q[0]) // Q[0] + T1 = append(T1, NewECP8()) + T1[1].Copy(T1[0]) + T1[1].Add(Q[1]) // Q[0]+Q[1] + T1 = append(T1, NewECP8()) + T1[2].Copy(T1[0]) + T1[2].Add(Q[2]) // Q[0]+Q[2] + T1 = append(T1, NewECP8()) + T1[3].Copy(T1[1]) + T1[3].Add(Q[2]) // Q[0]+Q[1]+Q[2] + T1 = append(T1, NewECP8()) + T1[4].Copy(T1[0]) + T1[4].Add(Q[3]) // Q[0]+Q[3] + T1 = append(T1, NewECP8()) + T1[5].Copy(T1[1]) + T1[5].Add(Q[3]) // Q[0]+Q[1]+Q[3] + T1 = append(T1, NewECP8()) + T1[6].Copy(T1[2]) + T1[6].Add(Q[3]) // Q[0]+Q[2]+Q[3] + T1 = append(T1, NewECP8()) + T1[7].Copy(T1[3]) + T1[7].Add(Q[3]) // Q[0]+Q[1]+Q[2]+Q[3] + + T2 = append(T2, NewECP8()) + T2[0].Copy(Q[4]) // Q[0] + T2 = append(T2, NewECP8()) + T2[1].Copy(T2[0]) + T2[1].Add(Q[5]) // Q[0]+Q[1] + T2 = append(T2, NewECP8()) + T2[2].Copy(T2[0]) + T2[2].Add(Q[6]) // Q[0]+Q[2] + T2 = append(T2, NewECP8()) + T2[3].Copy(T2[1]) + T2[3].Add(Q[6]) // Q[0]+Q[1]+Q[2] + T2 = append(T2, NewECP8()) + T2[4].Copy(T2[0]) + T2[4].Add(Q[7]) // Q[0]+Q[3] + T2 = append(T2, NewECP8()) + T2[5].Copy(T2[1]) + T2[5].Add(Q[7]) // Q[0]+Q[1]+Q[3] + T2 = append(T2, NewECP8()) + T2[6].Copy(T2[2]) + T2[6].Add(Q[7]) // Q[0]+Q[2]+Q[3] + T2 = append(T2, NewECP8()) + T2[7].Copy(T2[3]) + T2[7].Add(Q[7]) // Q[0]+Q[1]+Q[2]+Q[3] + + T3 = append(T3, NewECP8()) + T3[0].Copy(Q[8]) // Q[0] + T3 = append(T3, NewECP8()) + T3[1].Copy(T3[0]) + T3[1].Add(Q[9]) // Q[0]+Q[1] + T3 = append(T3, NewECP8()) + T3[2].Copy(T3[0]) + T3[2].Add(Q[10]) // Q[0]+Q[2] + T3 = append(T3, NewECP8()) + T3[3].Copy(T3[1]) + T3[3].Add(Q[10]) // Q[0]+Q[1]+Q[2] + T3 = append(T3, NewECP8()) + T3[4].Copy(T3[0]) + T3[4].Add(Q[11]) // Q[0]+Q[3] + T3 = append(T3, NewECP8()) + T3[5].Copy(T3[1]) + T3[5].Add(Q[11]) // Q[0]+Q[1]+Q[3] + T3 = append(T3, NewECP8()) + T3[6].Copy(T3[2]) + T3[6].Add(Q[11]) // Q[0]+Q[2]+Q[3] + T3 = append(T3, NewECP8()) + T3[7].Copy(T3[3]) + T3[7].Add(Q[11]) // Q[0]+Q[1]+Q[2]+Q[3] + + T4 = append(T4, NewECP8()) + T4[0].Copy(Q[12]) // Q[0] + T4 = append(T4, NewECP8()) + T4[1].Copy(T4[0]) + T4[1].Add(Q[13]) // Q[0]+Q[1] + T4 = append(T4, NewECP8()) + T4[2].Copy(T4[0]) + T4[2].Add(Q[14]) // Q[0]+Q[2] + T4 = append(T4, NewECP8()) + T4[3].Copy(T4[1]) + T4[3].Add(Q[14]) // Q[0]+Q[1]+Q[2] + T4 = append(T4, NewECP8()) + T4[4].Copy(T4[0]) + T4[4].Add(Q[15]) // Q[0]+Q[3] + T4 = append(T4, NewECP8()) + T4[5].Copy(T4[1]) + T4[5].Add(Q[15]) // Q[0]+Q[1]+Q[3] + T4 = append(T4, NewECP8()) + T4[6].Copy(T4[2]) + T4[6].Add(Q[15]) // Q[0]+Q[2]+Q[3] + T4 = append(T4, NewECP8()) + T4[7].Copy(T4[3]) + T4[7].Add(Q[15]) // Q[0]+Q[1]+Q[2]+Q[3] + + // Make them odd + pb1 := 1 - t[0].parity() + t[0].inc(pb1) + + pb2 := 1 - t[4].parity() + t[4].inc(pb2) + + pb3 := 1 - t[8].parity() + t[8].inc(pb3) + + pb4 := 1 - t[12].parity() + t[12].inc(pb4) + + // Number of bits + mt.zero() + for i := 0; i < 16; i++ { + t[i].norm() + mt.or(t[i]) + } + + nb := 1 + mt.nbits() + + // Sign pivot + s1[nb-1] = 1 + s2[nb-1] = 1 + s3[nb-1] = 1 + s4[nb-1] = 1 + for i := 0; i < nb-1; i++ { + t[0].fshr(1) + s1[i] = 2*int8(t[0].parity()) - 1 + t[4].fshr(1) + s2[i] = 2*int8(t[4].parity()) - 1 + t[8].fshr(1) + s3[i] = 2*int8(t[8].parity()) - 1 + t[12].fshr(1) + s4[i] = 2*int8(t[12].parity()) - 1 + + } + + // Recoded exponents + for i := 0; i < nb; i++ { + w1[i] = 0 + k = 1 + for j := 1; j < 4; j++ { + bt = s1[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w1[i] += bt * int8(k) + k *= 2 + } + w2[i] = 0 + k = 1 + for j := 5; j < 8; j++ { + bt = s2[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w2[i] += bt * int8(k) + k *= 2 + } + w3[i] = 0 + k = 1 + for j := 9; j < 12; j++ { + bt = s3[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w3[i] += bt * int8(k) + k *= 2 + } + w4[i] = 0 + k = 1 + for j := 13; j < 16; j++ { + bt = s4[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w4[i] += bt * int8(k) + k *= 2 + } + } + + // Main loop + P.selector(T1, int32(2*w1[nb-1]+1)) + W.selector(T2, int32(2*w2[nb-1]+1)) + P.Add(W) + W.selector(T3, int32(2*w3[nb-1]+1)) + P.Add(W) + W.selector(T4, int32(2*w4[nb-1]+1)) + P.Add(W) + for i := nb - 2; i >= 0; i-- { + P.dbl() + W.selector(T1, int32(2*w1[i]+s1[i])) + P.Add(W) + W.selector(T2, int32(2*w2[i]+s2[i])) + P.Add(W) + W.selector(T3, int32(2*w3[i]+s3[i])) + P.Add(W) + W.selector(T4, int32(2*w4[i]+s4[i])) + P.Add(W) + + } + + // apply correction + W.Copy(P) + W.Sub(Q[0]) + P.cmove(W, pb1) + W.Copy(P) + W.Sub(Q[4]) + P.cmove(W, pb2) + W.Copy(P) + W.Sub(Q[8]) + P.cmove(W, pb3) + W.Copy(P) + W.Sub(Q[12]) + P.cmove(W, pb4) + + P.Affine() + return P +} diff --git a/ec/bls48581/FP.go b/ec/bls48581/FP.go new file mode 100644 index 0000000..ce506b6 --- /dev/null +++ b/ec/bls48581/FP.go @@ -0,0 +1,760 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Finite Field arithmetic */ +/* CLINT mod p functions */ + +package bls48581 + +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +type FP struct { + x *BIG + XES int32 +} + +/* Constructors */ + +func NewFP() *FP { + F := new(FP) + F.x = NewBIG() + F.XES = 1 + return F +} + +func NewFPint(a int) *FP { + F := new(FP) + if a < 0 { + m := NewBIGints(Modulus) + m.inc(a) + m.norm() + F.x = NewBIGcopy(m) + } else { + F.x = NewBIGint(a) + } + F.nres() + return F +} + +func NewFPbig(a *BIG) *FP { + F := new(FP) + F.x = NewBIGcopy(a) + F.nres() + return F +} + +func NewFPcopy(a *FP) *FP { + F := new(FP) + F.x = NewBIGcopy(a.x) + F.XES = a.XES + return F +} + +func NewFPrand(rng *core.RAND) *FP { + m := NewBIGints(Modulus) + w := Randomnum(m, rng) + F := NewFPbig(w) + return F +} + +func (F *FP) ToString() string { + F.reduce() + return F.redc().ToString() +} + +/* convert to Montgomery n-residue form */ +func (F *FP) nres() { + if MODTYPE != PSEUDO_MERSENNE && MODTYPE != GENERALISED_MERSENNE { + r := NewBIGints(R2modp) + d := mul(F.x, r) + F.x.copy(mod(d)) + F.XES = 2 + } else { + md := NewBIGints(Modulus) + F.x.Mod(md) + F.XES = 1 + } +} + +/* convert back to regular form */ +func (F *FP) redc() *BIG { + if MODTYPE != PSEUDO_MERSENNE && MODTYPE != GENERALISED_MERSENNE { + d := NewDBIGscopy(F.x) + return mod(d) + } else { + r := NewBIGcopy(F.x) + return r + } +} + +/* reduce a DBIG to a BIG using the appropriate form of the modulus */ + +func mod(d *DBIG) *BIG { + if MODTYPE == PSEUDO_MERSENNE { + t := d.split(MODBITS) + b := NewBIGdcopy(d) + + v := t.pmul(int(MConst)) + + t.add(b) + t.norm() + + tw := t.w[NLEN-1] + t.w[NLEN-1] &= TMASK + t.w[0] += (MConst * ((tw >> TBITS) + (v << (BASEBITS - TBITS)))) + + t.norm() + return t + } + if MODTYPE == MONTGOMERY_FRIENDLY { + for i := 0; i < NLEN; i++ { + top, bot := muladd(d.w[i], MConst-1, d.w[i], d.w[NLEN+i-1]) + d.w[NLEN+i-1] = bot + d.w[NLEN+i] += top + } + b := NewBIG() + + for i := 0; i < NLEN; i++ { + b.w[i] = d.w[NLEN+i] + } + b.norm() + return b + } + + if MODTYPE == GENERALISED_MERSENNE { // GoldiLocks only + t := d.split(MODBITS) + b := NewBIGdcopy(d) + b.add(t) + dd := NewDBIGscopy(t) + dd.shl(MODBITS / 2) + + tt := dd.split(MODBITS) + lo := NewBIGdcopy(dd) + b.add(tt) + b.add(lo) + b.norm() + tt.shl(MODBITS / 2) + b.add(tt) + + carry := b.w[NLEN-1] >> TBITS + b.w[NLEN-1] &= TMASK + b.w[0] += carry + + ix := 224 / int(BASEBITS) + b.w[ix] += carry << (224 % BASEBITS) + b.norm() + return b + } + + if MODTYPE == NOT_SPECIAL { + md := NewBIGints(Modulus) + return monty(md, MConst, d) + } + return NewBIG() +} + +// find appoximation to quotient of a/m +// Out by at most 2. +// Note that MAXXES is bounded to be 2-bits less than half a word +func quo(n *BIG, m *BIG) int { + var num Chunk + var den Chunk + hb := uint(CHUNK) / 2 + if TBITS < hb { + sh := hb - TBITS + num = (n.w[NLEN-1] << sh) | (n.w[NLEN-2] >> (BASEBITS - sh)) + den = (m.w[NLEN-1] << sh) | (m.w[NLEN-2] >> (BASEBITS - sh)) + + } else { + num = n.w[NLEN-1] + den = m.w[NLEN-1] + } + return int(num / (den + 1)) +} + +/* reduce this mod Modulus */ +func (F *FP) reduce() { + m := NewBIGints(Modulus) + r := NewBIGints(Modulus) + var sb uint + F.x.norm() + + if F.XES > 16 { + q := quo(F.x, m) + carry := r.pmul(q) + r.w[NLEN-1] += carry << BASEBITS + F.x.sub(r) + F.x.norm() + sb = 2 + } else { + sb = logb2(uint32(F.XES - 1)) + } + + m.fshl(sb) + for sb > 0 { + sr := ssn(r, F.x, m) + F.x.cmove(r, 1-sr) + sb -= 1 + } + + F.XES = 1 +} + +/* test this=0? */ +func (F *FP) iszilch() bool { + W := NewFPcopy(F) + W.reduce() + return W.x.iszilch() +} + +func (F *FP) islarger() int { + if F.iszilch() { + return 0 + } + sx := NewBIGints(Modulus) + fx := F.redc() + sx.sub(fx) + sx.norm() + return Comp(fx, sx) +} + +func (F *FP) ToBytes(b []byte) { + F.redc().ToBytes(b) +} + +func FP_fromBytes(b []byte) *FP { + t := FromBytes(b) + return NewFPbig(t) +} + +func (F *FP) isunity() bool { + W := NewFPcopy(F) + W.reduce() + return W.redc().isunity() +} + +/* copy from FP b */ +func (F *FP) copy(b *FP) { + F.x.copy(b.x) + F.XES = b.XES +} + +/* set this=0 */ +func (F *FP) zero() { + F.x.zero() + F.XES = 1 +} + +/* set this=1 */ +func (F *FP) one() { + F.x.one() + F.nres() +} + +/* return sign */ +func (F *FP) sign() int { + if BIG_ENDIAN_SIGN { + m := NewBIGints(Modulus) + m.dec(1) + m.fshr(1) + n := NewFPcopy(F) + n.reduce() + w := n.redc() + cp := Comp(w, m) + return ((cp + 1) & 2) >> 1 + } else { + W := NewFPcopy(F) + W.reduce() + return W.redc().parity() + } +} + +/* normalise this */ +func (F *FP) norm() { + F.x.norm() +} + +/* swap FPs depending on d */ +func (F *FP) cswap(b *FP, d int) { + c := int32(d) + c = ^(c - 1) + t := c & (F.XES ^ b.XES) + F.XES ^= t + b.XES ^= t + F.x.cswap(b.x, d) +} + +/* copy FPs depending on d */ +func (F *FP) cmove(b *FP, d int) { + F.x.cmove(b.x, d) + c := int32(-d) + F.XES ^= (F.XES ^ b.XES) & c +} + +/* this*=b mod Modulus */ +func (F *FP) mul(b *FP) { + + if int64(F.XES)*int64(b.XES) > int64(FEXCESS) { + F.reduce() + } + + d := mul(F.x, b.x) + F.x.copy(mod(d)) + F.XES = 2 +} + +/* this = -this mod Modulus */ +func (F *FP) neg() { + m := NewBIGints(Modulus) + sb := logb2(uint32(F.XES - 1)) + + m.fshl(sb) + F.x.rsub(m) + + F.XES = (1 << sb) + 1 + if F.XES > FEXCESS { + F.reduce() + } +} + +/* this*=c mod Modulus, where c is a small int */ +func (F *FP) imul(c int) { + // F.norm() + s := false + if c < 0 { + c = -c + s = true + } + + if MODTYPE == PSEUDO_MERSENNE || MODTYPE == GENERALISED_MERSENNE { + d := F.x.pxmul(c) + F.x.copy(mod(d)) + F.XES = 2 + } else { + if F.XES*int32(c) <= FEXCESS { + F.x.pmul(c) + F.XES *= int32(c) + } else { + n := NewFPint(c) + F.mul(n) + } + } + if s { + F.neg() + F.norm() + } +} + +/* this*=this mod Modulus */ +func (F *FP) sqr() { + if int64(F.XES)*int64(F.XES) > int64(FEXCESS) { + F.reduce() + } + d := sqr(F.x) + F.x.copy(mod(d)) + F.XES = 2 +} + +/* this+=b */ +func (F *FP) add(b *FP) { + F.x.add(b.x) + F.XES += b.XES + if F.XES > FEXCESS { + F.reduce() + } +} + +/* this-=b */ +func (F *FP) sub(b *FP) { + n := NewFPcopy(b) + n.neg() + F.add(n) +} + +func (F *FP) rsub(b *FP) { + F.neg() + F.add(b) +} + +/* this/=2 mod Modulus */ +func (F *FP) div2() { + p := NewBIGints(Modulus) + pr := F.x.parity() + w := NewBIGcopy(F.x) + F.x.fshr(1) + w.add(p) + w.norm() + w.fshr(1) + F.x.cmove(w, pr) +} + +/* return jacobi symbol (this/Modulus) */ +func (F *FP) jacobi() int { + w := F.redc() + p := NewBIGints(Modulus) + return w.Jacobi(p) +} + +/* return TRUE if this==a */ +func (F *FP) Equals(a *FP) bool { + f := NewFPcopy(F) + s := NewFPcopy(a) + + s.reduce() + f.reduce() + if Comp(s.x, f.x) == 0 { + return true + } + return false +} + +func (F *FP) pow(e *BIG) *FP { + var tb []*FP + var w [1 + (NLEN*int(BASEBITS)+3)/4]int8 + F.norm() + t := NewBIGcopy(e) + t.norm() + nb := 1 + (t.nbits()+3)/4 + + for i := 0; i < nb; i++ { + lsbs := t.lastbits(4) + t.dec(lsbs) + t.norm() + w[i] = int8(lsbs) + t.fshr(4) + } + tb = append(tb, NewFPint(1)) + tb = append(tb, NewFPcopy(F)) + for i := 2; i < 16; i++ { + tb = append(tb, NewFPcopy(tb[i-1])) + tb[i].mul(F) + } + r := NewFPcopy(tb[w[nb-1]]) + for i := nb - 2; i >= 0; i-- { + r.sqr() + r.sqr() + r.sqr() + r.sqr() + r.mul(tb[w[i]]) + } + r.reduce() + return r +} + +// See https://eprint.iacr.org/2018/1038 +// return this^(p-3)/4 or this^(p-5)/8 +func (F *FP) fpow() *FP { + ac := [11]int{1, 2, 3, 6, 12, 15, 30, 60, 120, 240, 255} + var xp []*FP + // phase 1 + xp = append(xp, NewFPcopy(F)) + xp = append(xp, NewFPcopy(F)) + xp[1].sqr() + xp = append(xp, NewFPcopy(xp[1])) + xp[2].mul(F) + xp = append(xp, NewFPcopy(xp[2])) + xp[3].sqr() + xp = append(xp, NewFPcopy(xp[3])) + xp[4].sqr() + xp = append(xp, NewFPcopy(xp[4])) + xp[5].mul(xp[2]) + xp = append(xp, NewFPcopy(xp[5])) + xp[6].sqr() + xp = append(xp, NewFPcopy(xp[6])) + xp[7].sqr() + xp = append(xp, NewFPcopy(xp[7])) + xp[8].sqr() + xp = append(xp, NewFPcopy(xp[8])) + xp[9].sqr() + xp = append(xp, NewFPcopy(xp[9])) + xp[10].mul(xp[5]) + var n, c int + + e := int(PM1D2) + + n = int(MODBITS) + if MODTYPE == GENERALISED_MERSENNE { // Goldilocks ONLY + n /= 2 + } + + n -= (e + 1) + c = (int(MConst) + (1 << e) + 1) / (1 << (e + 1)) + + nd := 0 + for c%2 == 0 { + c /= 2 + n -= 1 + nd++ + } + + bw := 0 + w := 1 + for w < c { + w *= 2 + bw += 1 + } + k := w - c + + i := 10 + key := NewFP() + + if k != 0 { + for ac[i] > k { + i-- + } + key.copy(xp[i]) + k -= ac[i] + } + + for k != 0 { + i-- + if ac[i] > k { + continue + } + key.mul(xp[i]) + k -= ac[i] + } + // phase 2 + xp[1].copy(xp[2]) + xp[2].copy(xp[5]) + xp[3].copy(xp[10]) + + j := 3 + m := 8 + nw := n - bw + t := NewFP() + for 2*m < nw { + t.copy(xp[j]) + j++ + for i = 0; i < m; i++ { + t.sqr() + } + xp[j].copy(xp[j-1]) + xp[j].mul(t) + m *= 2 + } + lo := nw - m + r := NewFPcopy(xp[j]) + + for lo != 0 { + m /= 2 + j-- + if lo < m { + continue + } + lo -= m + t.copy(r) + for i = 0; i < m; i++ { + t.sqr() + } + r.copy(t) + r.mul(xp[j]) + } + // phase 3 + if bw != 0 { + for i = 0; i < bw; i++ { + r.sqr() + } + r.mul(key) + } + + if MODTYPE == GENERALISED_MERSENNE { // Goldilocks ONLY + key.copy(r) + r.sqr() + r.mul(F) + for i = 0; i < n+1; i++ { + r.sqr() + } + r.mul(key) + } + for nd > 0 { + r.sqr() + nd-- + } + return r +} + +// calculates r=x^(p-1-2^e)/2^{e+1) where 2^e|p-1 +func (F *FP) progen() { + if MODTYPE == PSEUDO_MERSENNE || MODTYPE == GENERALISED_MERSENNE { + F.copy(F.fpow()) + return + } + e := uint(PM1D2) + m := NewBIGints(Modulus) + m.dec(1) + m.shr(e) + m.dec(1) + m.fshr(1) + F.copy(F.pow(m)) +} + +/* this=1/this mod Modulus */ +func (F *FP) inverse(h *FP) { + e := int(PM1D2) + F.norm() + s := NewFPcopy(F) + for i := 0; i < e-1; i++ { + s.sqr() + s.mul(F) + } + if h == nil { + F.progen() + } else { + F.copy(h) + } + for i := 0; i <= e; i++ { + F.sqr() + } + F.mul(s) + F.reduce() +} + +/* test for Quadratic residue */ +func (F *FP) qr(h *FP) int { + r := NewFPcopy(F) + e := int(PM1D2) + r.progen() + if h != nil { + h.copy(r) + } + + r.sqr() + r.mul(F) + for i := 0; i < e-1; i++ { + r.sqr() + } + + if r.isunity() { + return 1 + } else { + return 0 + } +} + +/* return sqrt(this) mod Modulus */ +func (F *FP) sqrt(h *FP) *FP { + e := int(PM1D2) + g := NewFPcopy(F) + if h == nil { + g.progen() + } else { + g.copy(h) + } + + m := NewBIGints(ROI) + v := NewFPbig(m) + + t := NewFPcopy(g) + t.sqr() + t.mul(F) + + r := NewFPcopy(F) + r.mul(g) + b := NewFPcopy(t) + + for k := e; k > 1; k-- { + for j := 1; j < k-1; j++ { + b.sqr() + } + var u int + if b.isunity() { + u = 0 + } else { + u = 1 + } + g.copy(r) + g.mul(v) + r.cmove(g, u) + v.sqr() + g.copy(t) + g.mul(v) + t.cmove(g, u) + b.copy(t) + } + sgn := r.sign() + nr := NewFPcopy(r) + nr.neg() + nr.norm() + r.cmove(nr, sgn) + return r +} + +func (F *FP) invsqrt(i *FP, s *FP) int { + h := NewFP() + qr := F.qr(h) + s.copy(F.sqrt(h)) + i.copy(F) + i.inverse(h) + return qr +} + +// Two for the price of one - See Hamburg https://eprint.iacr.org/2012/309.pdf +// Calculate inverse of i and square root of s, return QR +func FP_tpo(i *FP, s *FP) int { + w := NewFPcopy(s) + t := NewFPcopy(i) + w.mul(i) + t.mul(w) + qr := t.invsqrt(i, s) + i.mul(w) + s.mul(i) + return qr +} + +/* return sqrt(this) mod Modulus +func (F *FP) sqrt() *FP { + F.reduce() + if PM1D2 == 2 { + var v *FP + i := NewFPcopy(F) + i.x.shl(1) + if MODTYPE == PSEUDO_MERSENNE || MODTYPE == GENERALISED_MERSENNE { + v = i.fpow() + } else { + b := NewBIGints(Modulus) + b.dec(5) + b.norm() + b.shr(3) + v = i.pow(b) + } + + i.mul(v) + i.mul(v) + i.x.dec(1) + r := NewFPcopy(F) + r.mul(v) + r.mul(i) + r.reduce() + return r + } else { + var r *FP + if MODTYPE == PSEUDO_MERSENNE || MODTYPE == GENERALISED_MERSENNE { + r = F.fpow() + r.mul(F) + } else { + b := NewBIGints(Modulus) + b.inc(1) + b.norm() + b.shr(2) + r = F.pow(b) + } + return r + } +} */ diff --git a/ec/bls48581/FP16.go b/ec/bls48581/FP16.go new file mode 100644 index 0000000..66a2954 --- /dev/null +++ b/ec/bls48581/FP16.go @@ -0,0 +1,616 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Finite Field arithmetic Fp^16 functions */ + +/* FP4 elements are of the form a+ib, where i is sqrt(-1+sqrt(-1)) */ + +package bls48581 + +//import "fmt" + +type FP16 struct { + a *FP8 + b *FP8 +} + +func NewFP16() *FP16 { + F := new(FP16) + F.a = NewFP8() + F.b = NewFP8() + return F +} + +/* Constructors */ +func NewFP16int(a int) *FP16 { + F := new(FP16) + F.a = NewFP8int(a) + F.b = NewFP8() + return F +} + +func NewFP16copy(x *FP16) *FP16 { + F := new(FP16) + F.a = NewFP8copy(x.a) + F.b = NewFP8copy(x.b) + return F +} + +func NewFP16fp8s(c *FP8, d *FP8) *FP16 { + F := new(FP16) + F.a = NewFP8copy(c) + F.b = NewFP8copy(d) + return F +} + +func NewFP16fp8(c *FP8) *FP16 { + F := new(FP16) + F.a = NewFP8copy(c) + F.b = NewFP8() + return F +} + +/* reduce all components of this mod Modulus */ +func (F *FP16) reduce() { + F.a.reduce() + F.b.reduce() +} + +/* normalise all components of this mod Modulus */ +func (F *FP16) norm() { + F.a.norm() + F.b.norm() +} + +/* test this==0 ? */ +func (F *FP16) iszilch() bool { + return F.a.iszilch() && F.b.iszilch() +} + +func (F *FP16) ToBytes(bf []byte) { + var t [8 * int(MODBYTES)]byte + MB := 8 * int(MODBYTES) + F.b.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i] = t[i] + } + F.a.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i+MB] = t[i] + } +} + +func FP16_fromBytes(bf []byte) *FP16 { + var t [8 * int(MODBYTES)]byte + MB := 8 * int(MODBYTES) + for i := 0; i < MB; i++ { + t[i] = bf[i] + } + tb := FP8_fromBytes(t[:]) + for i := 0; i < MB; i++ { + t[i] = bf[i+MB] + } + ta := FP8_fromBytes(t[:]) + return NewFP16fp8s(ta, tb) +} + +/* Conditional move */ +func (F *FP16) cmove(g *FP16, d int) { + F.a.cmove(g.a, d) + F.b.cmove(g.b, d) +} + +/* test this==1 ? */ +func (F *FP16) isunity() bool { + one := NewFP8int(1) + return F.a.Equals(one) && F.b.iszilch() +} + +/* test is w real? That is in a+ib test b is zero */ +func (F *FP16) isreal() bool { + return F.b.iszilch() +} + +/* extract real part a */ +func (F *FP16) real() *FP8 { + return F.a +} + +func (F *FP16) geta() *FP8 { + return F.a +} + +/* extract imaginary part b */ +func (F *FP16) getb() *FP8 { + return F.b +} + +/* test this=x? */ +func (F *FP16) Equals(x *FP16) bool { + return (F.a.Equals(x.a) && F.b.Equals(x.b)) +} + +/* copy this=x */ +func (F *FP16) copy(x *FP16) { + F.a.copy(x.a) + F.b.copy(x.b) +} + +/* set this=0 */ +func (F *FP16) zero() { + F.a.zero() + F.b.zero() +} + +/* set this=1 */ +func (F *FP16) one() { + F.a.one() + F.b.zero() +} + +/* set this=-this */ +func (F *FP16) neg() { + F.norm() + m := NewFP8copy(F.a) + t := NewFP8() + m.add(F.b) + m.neg() + t.copy(m) + t.add(F.b) + F.b.copy(m) + F.b.add(F.a) + F.a.copy(t) + F.norm() +} + +/* this=conjugate(this) */ +func (F *FP16) conj() { + F.b.neg() + F.norm() +} + +/* this=-conjugate(this) */ +func (F *FP16) nconj() { + F.a.neg() + F.norm() +} + +/* this+=x */ +func (F *FP16) add(x *FP16) { + F.a.add(x.a) + F.b.add(x.b) +} + +/* this-=x */ +func (F *FP16) sub(x *FP16) { + m := NewFP16copy(x) + m.neg() + F.add(m) +} + +/* this-=x */ +func (F *FP16) rsub(x *FP16) { + F.neg() + F.add(x) +} + +/* this*=s where s is FP8 */ +func (F *FP16) pmul(s *FP8) { + F.a.mul(s) + F.b.mul(s) +} + +/* this*=s where s is FP2 */ +func (F *FP16) qmul(s *FP2) { + F.a.qmul(s) + F.b.qmul(s) +} + +/* this*=s where s is FP */ +func (F *FP16) tmul(s *FP) { + F.a.tmul(s) + F.b.tmul(s) +} + +/* this*=c where c is int */ +func (F *FP16) imul(c int) { + F.a.imul(c) + F.b.imul(c) +} + +/* this*=this */ +func (F *FP16) sqr() { + t1 := NewFP8copy(F.a) + t2 := NewFP8copy(F.b) + t3 := NewFP8copy(F.a) + + t3.mul(F.b) + t1.add(F.b) + t2.times_i() + + t2.add(F.a) + + t1.norm() + t2.norm() + + F.a.copy(t1) + F.a.mul(t2) + + t2.copy(t3) + t2.times_i() + t2.add(t3) + t2.norm() + t2.neg() + F.a.add(t2) + + F.b.copy(t3) + F.b.add(t3) + + F.norm() +} + +/* this*=y */ +func (F *FP16) mul(y *FP16) { + t1 := NewFP8copy(F.a) + t2 := NewFP8copy(F.b) + t3 := NewFP8() + t4 := NewFP8copy(F.b) + + t1.mul(y.a) + t2.mul(y.b) + t3.copy(y.b) + t3.add(y.a) + t4.add(F.a) + + t3.norm() + t4.norm() + + t4.mul(t3) + + t3.copy(t1) + t3.neg() + t4.add(t3) + t4.norm() + + t3.copy(t2) + t3.neg() + F.b.copy(t4) + F.b.add(t3) + + t2.times_i() + F.a.copy(t2) + F.a.add(t1) + + F.norm() +} + +/* convert this to hex string */ +func (F *FP16) toString() string { + return ("[" + F.a.toString() + "," + F.b.toString() + "]") +} + +/* this=1/this */ +func (F *FP16) inverse() { + t1 := NewFP8copy(F.a) + t2 := NewFP8copy(F.b) + + t1.sqr() + t2.sqr() + t2.times_i() + t2.norm() + t1.sub(t2) + t1.norm() + + t1.inverse(nil) + + F.a.mul(t1) + t1.neg() + t1.norm() + F.b.mul(t1) +} + +/* this*=i where i = sqrt(sqrt(-1+sqrt(-1))) */ +func (F *FP16) times_i() { + s := NewFP8copy(F.b) + t := NewFP8copy(F.a) + s.times_i() + F.a.copy(s) + F.b.copy(t) + F.norm() +} + +func (F *FP16) times_i2() { + F.a.times_i() + F.b.times_i() +} + +func (F *FP16) times_i4() { + F.a.times_i2() + F.b.times_i2() +} + +/* this=this^p using Frobenius */ +func (F *FP16) frob(f *FP2) { + ff := NewFP2copy(f) + ff.sqr() + ff.norm() + + F.a.frob(ff) + F.b.frob(ff) + F.b.qmul(f) + F.b.times_i() + +} + +/* this=this^e */ +func (F *FP16) pow(e *BIG) *FP16 { + w := NewFP16copy(F) + w.norm() + z := NewBIGcopy(e) + r := NewFP16int(1) + z.norm() + for true { + bt := z.parity() + z.fshr(1) + if bt == 1 { + r.mul(w) + } + if z.iszilch() { + break + } + w.sqr() + } + r.reduce() + return r +} + +/* XTR xtr_a function */ +/* +func (F *FP16) xtr_A(w *FP16, y *FP16, z *FP16) { + r := NewFP16copy(w) + t := NewFP16copy(w) + r.sub(y) + r.norm() + r.pmul(F.a) + t.add(y) + t.norm() + t.pmul(F.b) + t.times_i() + + F.copy(r) + F.add(t) + F.add(z) + + F.norm() +} +*/ +/* XTR xtr_d function */ +/* +func (F *FP16) xtr_D() { + w := NewFP16copy(F) + F.sqr() + w.conj() + w.add(w) + w.norm() + F.sub(w) + F.reduce() +} +*/ +/* r=x^n using XTR method on traces of FP48s */ +/* +func (F *FP16) xtr_pow(n *BIG) *FP16 { + sf := NewFP16copy(F) + sf.norm() + a := NewFP16int(3) + b := NewFP16copy(sf) + c := NewFP16copy(b) + c.xtr_D() + t := NewFP16() + r := NewFP16() + + par := n.parity() + v := NewBIGcopy(n) + v.norm() + v.fshr(1) + if par == 0 { + v.dec(1) + v.norm() + } + + nb := v.nbits() + for i := nb - 1; i >= 0; i-- { + if v.bit(i) != 1 { + t.copy(b) + sf.conj() + c.conj() + b.xtr_A(a, sf, c) + sf.conj() + c.copy(t) + c.xtr_D() + a.xtr_D() + } else { + t.copy(a) + t.conj() + a.copy(b) + a.xtr_D() + b.xtr_A(c, sf, t) + c.xtr_D() + } + } + if par == 0 { + r.copy(c) + } else { + r.copy(b) + } + r.reduce() + return r +} +*/ +/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP48s. See Stam thesis. */ +/* +func (F *FP16) xtr_pow2(ck *FP16, ckml *FP16, ckm2l *FP16, a *BIG, b *BIG) *FP16 { + + e := NewBIGcopy(a) + d := NewBIGcopy(b) + w := NewBIGint(0) + e.norm() + d.norm() + cu := NewFP16copy(ck) // can probably be passed in w/o copying + cv := NewFP16copy(F) + cumv := NewFP16copy(ckml) + cum2v := NewFP16copy(ckm2l) + r := NewFP16() + t := NewFP16() + + f2 := 0 + for d.parity() == 0 && e.parity() == 0 { + d.fshr(1) + e.fshr(1) + f2++ + } + + for Comp(d, e) != 0 { + if Comp(d, e) > 0 { + w.copy(e) + w.imul(4) + w.norm() + if Comp(d, w) <= 0 { + w.copy(d) + d.copy(e) + e.rsub(w) + e.norm() + + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cum2v.conj() + cumv.copy(cv) + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 0 { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } else { + if e.parity() == 1 { + d.sub(e) + d.norm() + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cu.xtr_D() + cum2v.copy(cv) + cum2v.xtr_D() + cum2v.conj() + cv.copy(t) + } else { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } + } + } + } + if Comp(d, e) < 0 { + w.copy(d) + w.imul(4) + w.norm() + if Comp(e, w) <= 0 { + e.sub(d) + e.norm() + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cumv.copy(cu) + cu.copy(t) + } else { + if e.parity() == 0 { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 1 { + w.copy(e) + e.copy(d) + w.sub(d) + w.norm() + d.copy(w) + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cumv.conj() + cum2v.copy(cu) + cum2v.xtr_D() + cum2v.conj() + cu.copy(cv) + cu.xtr_D() + cv.copy(t) + } else { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } + } + } + } + } + r.copy(cv) + r.xtr_A(cu, cumv, cum2v) + for i := 0; i < f2; i++ { + r.xtr_D() + } + r = r.xtr_pow(d) + return r +} +*/ diff --git a/ec/bls48581/FP2.go b/ec/bls48581/FP2.go new file mode 100644 index 0000000..22dce69 --- /dev/null +++ b/ec/bls48581/FP2.go @@ -0,0 +1,505 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Finite Field arithmetic Fp^2 functions */ + +/* FP2 elements are of the form a+ib, where i is sqrt(-1) */ + +package bls48581 + +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +//import "fmt" + +type FP2 struct { + a *FP + b *FP +} + +func NewFP2() *FP2 { + F := new(FP2) + F.a = NewFP() + F.b = NewFP() + return F +} + +/* Constructors */ +func NewFP2int(a int) *FP2 { + F := new(FP2) + F.a = NewFPint(a) + F.b = NewFP() + return F +} + +func NewFP2ints(a int, b int) *FP2 { + F := new(FP2) + F.a = NewFPint(a) + F.b = NewFPint(b) + return F +} + +func NewFP2copy(x *FP2) *FP2 { + F := new(FP2) + F.a = NewFPcopy(x.a) + F.b = NewFPcopy(x.b) + return F +} + +func NewFP2fps(c *FP, d *FP) *FP2 { + F := new(FP2) + F.a = NewFPcopy(c) + F.b = NewFPcopy(d) + return F +} + +func NewFP2bigs(c *BIG, d *BIG) *FP2 { + F := new(FP2) + F.a = NewFPbig(c) + F.b = NewFPbig(d) + return F +} + +func NewFP2fp(c *FP) *FP2 { + F := new(FP2) + F.a = NewFPcopy(c) + F.b = NewFP() + return F +} + +func NewFP2big(c *BIG) *FP2 { + F := new(FP2) + F.a = NewFPbig(c) + F.b = NewFP() + return F +} + +func NewFP2rand(rng *core.RAND) *FP2 { + F := NewFP2fps(NewFPrand(rng), NewFPrand(rng)) + return F +} + +/* reduce components mod Modulus */ +func (F *FP2) reduce() { + F.a.reduce() + F.b.reduce() +} + +/* normalise components of w */ +func (F *FP2) norm() { + F.a.norm() + F.b.norm() +} + +/* test this=0 ? */ +func (F *FP2) iszilch() bool { + return (F.a.iszilch() && F.b.iszilch()) +} + +func (F *FP2) islarger() int { + if F.iszilch() { + return 0 + } + cmp := F.b.islarger() + if cmp != 0 { + return cmp + } + return F.a.islarger() +} + +func (F *FP2) ToBytes(bf []byte) { + var t [int(MODBYTES)]byte + MB := int(MODBYTES) + F.b.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i] = t[i] + } + F.a.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i+MB] = t[i] + } +} + +func FP2_fromBytes(bf []byte) *FP2 { + var t [int(MODBYTES)]byte + MB := int(MODBYTES) + for i := 0; i < MB; i++ { + t[i] = bf[i] + } + tb := FP_fromBytes(t[:]) + for i := 0; i < MB; i++ { + t[i] = bf[i+MB] + } + ta := FP_fromBytes(t[:]) + return NewFP2fps(ta, tb) +} + +func (F *FP2) cmove(g *FP2, d int) { + F.a.cmove(g.a, d) + F.b.cmove(g.b, d) +} + +/* test this=1 ? */ +func (F *FP2) isunity() bool { + one := NewFPint(1) + return (F.a.Equals(one) && F.b.iszilch()) +} + +/* test this=x */ +func (F *FP2) Equals(x *FP2) bool { + return (F.a.Equals(x.a) && F.b.Equals(x.b)) +} + +/* extract a */ +func (F *FP2) GetA() *BIG { + return F.a.redc() +} + +/* extract b */ +func (F *FP2) GetB() *BIG { + return F.b.redc() +} + +/* copy this=x */ +func (F *FP2) copy(x *FP2) { + F.a.copy(x.a) + F.b.copy(x.b) +} + +/* set this=0 */ +func (F *FP2) zero() { + F.a.zero() + F.b.zero() +} + +/* set this=1 */ +func (F *FP2) one() { + F.a.one() + F.b.zero() +} + +/* Return sign */ +func (F *FP2) sign() int { + p1 := F.a.sign() + p2 := F.b.sign() + var u int + if BIG_ENDIAN_SIGN { + if F.b.iszilch() { + u = 1 + } else { + u = 0 + } + p2 ^= (p1 ^ p2) & u + return p2 + } else { + if F.a.iszilch() { + u = 1 + } else { + u = 0 + } + p1 ^= (p1 ^ p2) & u + return p1 + } +} + +/* negate this mod Modulus */ +func (F *FP2) neg() { + m := NewFPcopy(F.a) + t := NewFP() + + m.add(F.b) + m.neg() + t.copy(m) + t.add(F.b) + F.b.copy(m) + F.b.add(F.a) + F.a.copy(t) +} + +/* set to a-ib */ +func (F *FP2) conj() { + F.b.neg() + F.b.norm() +} + +/* this+=a */ +func (F *FP2) add(x *FP2) { + F.a.add(x.a) + F.b.add(x.b) +} + +/* this-=a */ +func (F *FP2) sub(x *FP2) { + m := NewFP2copy(x) + m.neg() + F.add(m) +} + +/* this-=a */ +func (F *FP2) rsub(x *FP2) { + F.neg() + F.add(x) +} + +/* this*=s, where s is an FP */ +func (F *FP2) pmul(s *FP) { + F.a.mul(s) + F.b.mul(s) +} + +/* this*=i, where i is an int */ +func (F *FP2) imul(c int) { + F.a.imul(c) + F.b.imul(c) +} + +/* this*=this */ +func (F *FP2) sqr() { + w1 := NewFPcopy(F.a) + w3 := NewFPcopy(F.a) + mb := NewFPcopy(F.b) + w1.add(F.b) + + w3.add(F.a) + w3.norm() + F.b.mul(w3) + + mb.neg() + F.a.add(mb) + + w1.norm() + F.a.norm() + + F.a.mul(w1) +} + +/* this*=y */ +/* Now using Lazy reduction */ +func (F *FP2) mul(y *FP2) { + + if int64(F.a.XES+F.b.XES)*int64(y.a.XES+y.b.XES) > int64(FEXCESS) { + if F.a.XES > 1 { + F.a.reduce() + } + if F.b.XES > 1 { + F.b.reduce() + } + } + + pR := NewDBIG() + C := NewBIGcopy(F.a.x) + D := NewBIGcopy(y.a.x) + p := NewBIGints(Modulus) + + pR.ucopy(p) + + A := mul(F.a.x, y.a.x) + B := mul(F.b.x, y.b.x) + + C.add(F.b.x) + C.norm() + D.add(y.b.x) + D.norm() + + E := mul(C, D) + FF := NewDBIGcopy(A) + FF.add(B) + B.rsub(pR) + + A.add(B) + A.norm() + E.sub(FF) + E.norm() + + F.a.x.copy(mod(A)) + F.a.XES = 3 + F.b.x.copy(mod(E)) + F.b.XES = 2 + +} + +/* +func (F *FP2) pow(b *BIG) { + w := NewFP2copy(F); + r := NewFP2int(1) + z := NewBIGcopy(b) + for true { + bt := z.parity() + z.shr(1) + if bt==1 { + r.mul(w) + } + if z.iszilch() {break} + w.sqr() + } + r.reduce() + F.copy(r) +} +*/ +func (F *FP2) qr(h *FP) int { + c := NewFP2copy(F) + c.conj() + c.mul(F) + return c.a.qr(h) +} + +/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */ +func (F *FP2) sqrt(h *FP) { + if F.iszilch() { + return + } + w1 := NewFPcopy(F.b) + w2 := NewFPcopy(F.a) + w3 := NewFP() + w4 := NewFP() + hint := NewFP() + w1.sqr() + w2.sqr() + w1.add(w2) + w1.norm() + + w1 = w1.sqrt(h) + w2.copy(F.a) + w3.copy(F.a) + + w2.add(w1) + w2.norm() + w2.div2() + + w1.copy(F.b) + w1.div2() + qr := w2.qr(hint) + + // tweak hint + w3.copy(hint) + w3.neg() + w3.norm() + w4.copy(w2) + w4.neg() + w4.norm() + + w2.cmove(w4, 1-qr) + hint.cmove(w3, 1-qr) + + F.a.copy(w2.sqrt(hint)) + w3.copy(w2) + w3.inverse(hint) + w3.mul(F.a) + F.b.copy(w3) + F.b.mul(w1) + w4.copy(F.a) + + F.a.cmove(F.b, 1-qr) + F.b.cmove(w4, 1-qr) + + /* + F.a.copy(w2.sqrt(hint)) + w3.copy(w2); w3.inverse(hint) + w3.mul(F.a) + F.b.copy(w3); F.b.mul(w1) + + hint.neg(); hint.norm() + w2.neg(); w2.norm() + + w4.copy(w2.sqrt(hint)) + w3.copy(w2); w3.inverse(hint) + w3.mul(w4) + w3.mul(w1) + + F.a.cmove(w3,1-qr) + F.b.cmove(w4,1-qr) + */ + + sgn := F.sign() + nr := NewFP2copy(F) + nr.neg() + nr.norm() + F.cmove(nr, sgn) +} + +/* output to hex string */ +func (F *FP2) ToString() string { + return ("[" + F.a.ToString() + "," + F.b.ToString() + "]") +} + +/* output to hex string */ +func (F *FP2) toString() string { + return ("[" + F.a.ToString() + "," + F.b.ToString() + "]") +} + +/* this=1/this */ +func (F *FP2) inverse(h *FP) { + F.norm() + w1 := NewFPcopy(F.a) + w2 := NewFPcopy(F.b) + + w1.sqr() + w2.sqr() + w1.add(w2) + w1.inverse(h) + F.a.mul(w1) + w1.neg() + w1.norm() + F.b.mul(w1) +} + +/* this/=2 */ +func (F *FP2) div2() { + F.a.div2() + F.b.div2() +} + +/* this*=sqrt(-1) */ +func (F *FP2) times_i() { + z := NewFPcopy(F.a) + F.a.copy(F.b) + F.a.neg() + F.b.copy(z) +} + +/* w*=(1+sqrt(-1)) */ +/* where X*2-(2^i+sqrt(-1)) is irreducible for FP4 */ +func (F *FP2) mul_ip() { + t := NewFP2copy(F) + i := QNRI + F.times_i() + for i > 0 { + t.add(t) + t.norm() + i-- + } + F.add(t) + + if TOWER == POSITOWER { + F.norm() + F.neg() + } + +} + +/* w/=(2^i+sqrt(-1)) */ +func (F *FP2) div_ip() { + z := NewFP2ints(1<= 0; i-- { + if v.bit(i) != 1 { + t.copy(b) + sf.conj() + c.conj() + b.xtr_A(a, sf, c) + sf.conj() + c.copy(t) + c.xtr_D() + a.xtr_D() + } else { + t.copy(a) + t.conj() + a.copy(b) + a.xtr_D() + b.xtr_A(c, sf, t) + c.xtr_D() + } + } + if par == 0 { + r.copy(c) + } else { + r.copy(b) + } + r.reduce() + return r +} + +/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */ +func (F *FP4) xtr_pow2(ck *FP4, ckml *FP4, ckm2l *FP4, a *BIG, b *BIG) *FP4 { + + e := NewBIGcopy(a) + d := NewBIGcopy(b) + w := NewBIGint(0) + e.norm() + d.norm() + + cu := NewFP4copy(ck) // can probably be passed in w/o copying + cv := NewFP4copy(F) + cumv := NewFP4copy(ckml) + cum2v := NewFP4copy(ckm2l) + r := NewFP4() + t := NewFP4() + + f2 := 0 + for d.parity() == 0 && e.parity() == 0 { + d.fshr(1) + e.fshr(1) + f2++ + } + + for Comp(d, e) != 0 { + if Comp(d, e) > 0 { + w.copy(e) + w.imul(4) + w.norm() + if Comp(d, w) <= 0 { + w.copy(d) + d.copy(e) + e.rsub(w) + e.norm() + + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cum2v.conj() + cumv.copy(cv) + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 0 { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } else { + if e.parity() == 1 { + d.sub(e) + d.norm() + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cu.xtr_D() + cum2v.copy(cv) + cum2v.xtr_D() + cum2v.conj() + cv.copy(t) + } else { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } + } + } + } + if Comp(d, e) < 0 { + w.copy(d) + w.imul(4) + w.norm() + if Comp(e, w) <= 0 { + e.sub(d) + e.norm() + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cumv.copy(cu) + cu.copy(t) + } else { + if e.parity() == 0 { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 1 { + w.copy(e) + e.copy(d) + w.sub(d) + w.norm() + d.copy(w) + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cumv.conj() + cum2v.copy(cu) + cum2v.xtr_D() + cum2v.conj() + cu.copy(cv) + cu.xtr_D() + cv.copy(t) + } else { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } + } + } + } + } + r.copy(cv) + r.xtr_A(cu, cumv, cum2v) + for i := 0; i < f2; i++ { + r.xtr_D() + } + r = r.xtr_pow(d) + return r +} + +/* this/=2 */ +func (F *FP4) div2() { + F.a.div2() + F.b.div2() +} + +func (F *FP4) div_i() { + u := NewFP2copy(F.a) + v := NewFP2copy(F.b) + u.div_ip() + F.a.copy(v) + F.b.copy(u) + if TOWER == POSITOWER { + F.neg() + F.norm() + } +} + +/* +func (F *FP4) pow(b *BIG) { + w := NewFP4copy(F); + r := NewFP4int(1) + z := NewBIGcopy(b) + for true { + bt := z.parity() + z.shr(1) + if bt==1 { + r.mul(w) + } + if z.iszilch() {break} + w.sqr() + } + r.reduce(); + F.copy(r); +} +*/ + +/* */ +// Test for Quadratic Residue +func (F *FP4) qr(h *FP) int { + c := NewFP4copy(F) + c.conj() + c.mul(F) + return c.a.qr(h) +} + +// sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) +func (F *FP4) sqrt(h *FP) { + if F.iszilch() { + return + } + + a := NewFP2copy(F.a) + b := NewFP2() + s := NewFP2copy(F.b) + t := NewFP2copy(F.a) + hint := NewFP() + + s.sqr() + a.sqr() + s.mul_ip() + s.norm() + a.sub(s) + + s.copy(a) + s.norm() + s.sqrt(h) + + a.copy(t) + b.copy(t) + + a.add(s) + a.norm() + a.div2() + + b.copy(F.b) + b.div2() + qr := a.qr(hint) + + // tweak hint - multiply old hint by Norm(1/Beta)^e where Beta is irreducible polynomial + s.copy(a) + twk := NewFPbig(NewBIGints(TWK)) + twk.mul(hint) + s.div_ip() + s.norm() + + a.cmove(s, 1-qr) + hint.cmove(twk, 1-qr) + + F.a.copy(a) + F.a.sqrt(hint) + s.copy(a) + s.inverse(hint) + s.mul(F.a) + F.b.copy(s) + F.b.mul(b) + t.copy(F.a) + + F.a.cmove(F.b, 1-qr) + F.b.cmove(t, 1-qr) + + sgn := F.sign() + nr := NewFP4copy(F) + nr.neg() + nr.norm() + F.cmove(nr, sgn) +} + +/* */ diff --git a/ec/bls48581/FP48.go b/ec/bls48581/FP48.go new file mode 100644 index 0000000..ceabc21 --- /dev/null +++ b/ec/bls48581/FP48.go @@ -0,0 +1,1189 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* MiotCL Fp^12 functions */ +/* FP12 elements are of the form a+i.b+i^2.c */ + +package bls48581 + +//import "fmt" + +type FP48 struct { + a *FP16 + b *FP16 + c *FP16 + stype int +} + +/* Constructors */ +func NewFP48fp16(d *FP16) *FP48 { + F := new(FP48) + F.a = NewFP16copy(d) + F.b = NewFP16() + F.c = NewFP16() + F.stype = FP_SPARSEST + return F +} + +func NewFP48() *FP48 { + F := new(FP48) + F.a = NewFP16() + F.b = NewFP16() + F.c = NewFP16() + F.stype = FP_ZERO + return F +} + +func NewFP48int(d int) *FP48 { + F := new(FP48) + F.a = NewFP16int(d) + F.b = NewFP16() + F.c = NewFP16() + if d == 1 { + F.stype = FP_ONE + } else { + F.stype = FP_SPARSEST + } + return F +} + +func NewFP48fp16s(d *FP16, e *FP16, f *FP16) *FP48 { + F := new(FP48) + F.a = NewFP16copy(d) + F.b = NewFP16copy(e) + F.c = NewFP16copy(f) + F.stype = FP_DENSE + return F +} + +func NewFP48copy(x *FP48) *FP48 { + F := new(FP48) + F.a = NewFP16copy(x.a) + F.b = NewFP16copy(x.b) + F.c = NewFP16copy(x.c) + F.stype = x.stype + return F +} + +/* reduce all components of this mod Modulus */ +func (F *FP48) reduce() { + F.a.reduce() + F.b.reduce() + F.c.reduce() +} + +/* normalise all components of this */ +func (F *FP48) norm() { + F.a.norm() + F.b.norm() + F.c.norm() +} + +/* test x==0 ? */ +func (F *FP48) iszilch() bool { + return (F.a.iszilch() && F.b.iszilch() && F.c.iszilch()) +} + +/* Conditional move */ +func (F *FP48) cmove(g *FP48, d int) { + F.a.cmove(g.a, d) + F.b.cmove(g.b, d) + F.c.cmove(g.c, d) + d = ^(d - 1) + F.stype ^= (F.stype ^ g.stype) & d +} + +/* Constant time select from pre-computed table */ +func (F *FP48) selector(g []*FP48, b int32) { + + m := b >> 31 + babs := (b ^ m) - m + + babs = (babs - 1) / 2 + + F.cmove(g[0], teq(babs, 0)) // conditional move + F.cmove(g[1], teq(babs, 1)) + F.cmove(g[2], teq(babs, 2)) + F.cmove(g[3], teq(babs, 3)) + F.cmove(g[4], teq(babs, 4)) + F.cmove(g[5], teq(babs, 5)) + F.cmove(g[6], teq(babs, 6)) + F.cmove(g[7], teq(babs, 7)) + + invF := NewFP48copy(F) + invF.conj() + F.cmove(invF, int(m&1)) +} + +/* test x==1 ? */ +func (F *FP48) Isunity() bool { + one := NewFP16int(1) + return (F.a.Equals(one) && F.b.iszilch() && F.c.iszilch()) +} + +/* return 1 if x==y, else 0 */ +func (F *FP48) Equals(x *FP48) bool { + return (F.a.Equals(x.a) && F.b.Equals(x.b) && F.c.Equals(x.c)) +} + +/* extract a from this */ +func (F *FP48) geta() *FP16 { + return F.a +} + +/* extract b */ +func (F *FP48) getb() *FP16 { + return F.b +} + +/* extract c */ +func (F *FP48) getc() *FP16 { + return F.c +} + +/* copy this=x */ +func (F *FP48) Copy(x *FP48) { + F.a.copy(x.a) + F.b.copy(x.b) + F.c.copy(x.c) + F.stype = x.stype +} + +/* set this=1 */ +func (F *FP48) one() { + F.stype = FP_ONE + F.a.one() + F.b.zero() + F.c.zero() +} + +/* set this=0 */ +func (F *FP48) zero() { + F.a.zero() + F.b.zero() + F.c.zero() + F.stype = FP_ZERO +} + +/* this=conj(this) */ +func (F *FP48) conj() { + F.a.conj() + F.b.nconj() + F.c.conj() +} + +/* Granger-Scott Unitary Squaring */ +func (F *FP48) usqr() { + A := NewFP16copy(F.a) + B := NewFP16copy(F.c) + C := NewFP16copy(F.b) + D := NewFP16() + + F.a.sqr() + D.copy(F.a) + D.add(F.a) + F.a.add(D) + + F.a.norm() + A.nconj() + + A.add(A) + F.a.add(A) + B.sqr() + B.times_i() + + D.copy(B) + D.add(B) + B.add(D) + B.norm() + + C.sqr() + D.copy(C) + D.add(C) + C.add(D) + C.norm() + + F.b.conj() + F.b.add(F.b) + F.c.nconj() + + F.c.add(F.c) + F.b.add(B) + F.c.add(C) + F.reduce() + F.stype = FP_DENSE +} + +/* Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */ +func (F *FP48) sqr() { + if F.stype == FP_ONE { + return + } + A := NewFP16copy(F.a) + B := NewFP16copy(F.b) + C := NewFP16copy(F.c) + D := NewFP16copy(F.a) + + A.sqr() + B.mul(F.c) + B.add(B) + B.norm() + C.sqr() + D.mul(F.b) + D.add(D) + + F.c.add(F.a) + F.c.add(F.b) + F.c.norm() + F.c.sqr() + + F.a.copy(A) + + A.add(B) + A.norm() + A.add(C) + A.add(D) + A.norm() + + A.neg() + B.times_i() + C.times_i() + + F.a.add(B) + + F.b.copy(C) + F.b.add(D) + F.c.add(A) + if F.stype == FP_SPARSER || F.stype == FP_SPARSEST { + F.stype = FP_SPARSE + } else { + F.stype = FP_DENSE + } + F.norm() +} + +/* FP48 full multiplication this=this*y */ +func (F *FP48) Mul(y *FP48) { + z0 := NewFP16copy(F.a) + z1 := NewFP16() + z2 := NewFP16copy(F.b) + z3 := NewFP16() + t0 := NewFP16copy(F.a) + t1 := NewFP16copy(y.a) + + z0.mul(y.a) + z2.mul(y.b) + + t0.add(F.b) + t0.norm() + t1.add(y.b) + t1.norm() + + z1.copy(t0) + z1.mul(t1) + t0.copy(F.b) + t0.add(F.c) + t0.norm() + + t1.copy(y.b) + t1.add(y.c) + t1.norm() + z3.copy(t0) + z3.mul(t1) + + t0.copy(z0) + t0.neg() + t1.copy(z2) + t1.neg() + + z1.add(t0) + //z1.norm(); + F.b.copy(z1) + F.b.add(t1) + + z3.add(t1) + z2.add(t0) + + t0.copy(F.a) + t0.add(F.c) + t0.norm() + t1.copy(y.a) + t1.add(y.c) + t1.norm() + t0.mul(t1) + z2.add(t0) + + t0.copy(F.c) + t0.mul(y.c) + t1.copy(t0) + t1.neg() + + F.c.copy(z2) + F.c.add(t1) + z3.add(t1) + t0.times_i() + F.b.add(t0) + z3.norm() + z3.times_i() + F.a.copy(z0) + F.a.add(z3) + F.stype = FP_DENSE + F.norm() +} + +/* FP48 full multiplication w=w*y */ +/* Supports sparse multiplicands */ +/* Usually w is denser than y */ +func (F *FP48) ssmul(y *FP48) { + if F.stype == FP_ONE { + F.Copy(y) + return + } + if y.stype == FP_ONE { + return + } + if y.stype >= FP_SPARSE { + z0 := NewFP16copy(F.a) + z1 := NewFP16() + z2 := NewFP16() + z3 := NewFP16() + z0.mul(y.a) + + if SEXTIC_TWIST == M_TYPE { + if y.stype == FP_SPARSE || F.stype == FP_SPARSE { + z2.getb().copy(F.b.getb()) + z2.getb().mul(y.b.getb()) + z2.geta().zero() + if y.stype != FP_SPARSE { + z2.geta().copy(F.b.getb()) + z2.geta().mul(y.b.geta()) + } + if F.stype != FP_SPARSE { + z2.geta().copy(F.b.geta()) + z2.geta().mul(y.b.getb()) + } + z2.times_i() + } else { + z2.copy(F.b) + z2.mul(y.b) + } + } else { + z2.copy(F.b) + z2.mul(y.b) + } + t0 := NewFP16copy(F.a) + t1 := NewFP16copy(y.a) + t0.add(F.b) + t0.norm() + t1.add(y.b) + t1.norm() + + z1.copy(t0) + z1.mul(t1) + t0.copy(F.b) + t0.add(F.c) + t0.norm() + t1.copy(y.b) + t1.add(y.c) + t1.norm() + + z3.copy(t0) + z3.mul(t1) + + t0.copy(z0) + t0.neg() + t1.copy(z2) + t1.neg() + + z1.add(t0) + F.b.copy(z1) + F.b.add(t1) + + z3.add(t1) + z2.add(t0) + + t0.copy(F.a) + t0.add(F.c) + t0.norm() + t1.copy(y.a) + t1.add(y.c) + t1.norm() + + t0.mul(t1) + z2.add(t0) + + if SEXTIC_TWIST == D_TYPE { + if y.stype == FP_SPARSE || F.stype == FP_SPARSE { + t0.geta().copy(F.c.geta()) + t0.geta().mul(y.c.geta()) + t0.getb().zero() + if y.stype != FP_SPARSE { + t0.getb().copy(F.c.geta()) + t0.getb().mul(y.c.getb()) + } + if F.stype != FP_SPARSE { + t0.getb().copy(F.c.getb()) + t0.getb().mul(y.c.geta()) + } + } else { + t0.copy(F.c) + t0.mul(y.c) + } + } else { + t0.copy(F.c) + t0.mul(y.c) + } + t1.copy(t0) + t1.neg() + + F.c.copy(z2) + F.c.add(t1) + z3.add(t1) + t0.times_i() + F.b.add(t0) + z3.norm() + z3.times_i() + F.a.copy(z0) + F.a.add(z3) + } else { + if F.stype == FP_SPARSER || F.stype == FP_SPARSEST { + F.smul(y) + return + } + if SEXTIC_TWIST == D_TYPE { // dense by sparser - 13m + z0 := NewFP16copy(F.a) + z2 := NewFP16copy(F.b) + z3 := NewFP16copy(F.b) + t0 := NewFP16() + t1 := NewFP16copy(y.a) + z0.mul(y.a) + + if y.stype == FP_SPARSEST { + z2.tmul(y.b.a.a.a.a) + } else { + z2.pmul(y.b.geta()) + } + F.b.add(F.a) + t1.geta().add(y.b.geta()) + + t1.norm() + F.b.norm() + F.b.mul(t1) + z3.add(F.c) + z3.norm() + + if y.stype == FP_SPARSEST { + z3.tmul(y.b.a.a.a.a) + } else { + z3.pmul(y.b.geta()) + } + + t0.copy(z0) + t0.neg() + t1.copy(z2) + t1.neg() + + F.b.add(t0) + + F.b.add(t1) + z3.add(t1) + z2.add(t0) + + t0.copy(F.a) + t0.add(F.c) + t0.norm() + z3.norm() + t0.mul(y.a) + F.c.copy(z2) + F.c.add(t0) + + z3.times_i() + F.a.copy(z0) + F.a.add(z3) + } + if SEXTIC_TWIST == M_TYPE { + z0 := NewFP16copy(F.a) + z1 := NewFP16() + z2 := NewFP16() + z3 := NewFP16() + t0 := NewFP16copy(F.a) + t1 := NewFP16() + + z0.mul(y.a) + t0.add(F.b) + t0.norm() + + z1.copy(t0) + z1.mul(y.a) + t0.copy(F.b) + t0.add(F.c) + t0.norm() + + z3.copy(t0) + + if y.stype == FP_SPARSEST { + z3.tmul(y.c.b.a.a.a) + } else { + z3.pmul(y.c.getb()) + } + z3.times_i() + + t0.copy(z0) + t0.neg() + z1.add(t0) + F.b.copy(z1) + z2.copy(t0) + + t0.copy(F.a) + t0.add(F.c) + t0.norm() + t1.copy(y.a) + t1.add(y.c) + t1.norm() + + t0.mul(t1) + z2.add(t0) + t0.copy(F.c) + + if y.stype == FP_SPARSEST { + t0.tmul(y.c.b.a.a.a) + } else { + t0.pmul(y.c.getb()) + } + t0.times_i() + t1.copy(t0) + t1.neg() + + F.c.copy(z2) + F.c.add(t1) + z3.add(t1) + t0.times_i() + F.b.add(t0) + z3.norm() + z3.times_i() + F.a.copy(z0) + F.a.add(z3) + } + } + F.stype = FP_DENSE + F.norm() +} + +/* Special case of multiplication arises from special form of ATE pairing line function */ +func (F *FP48) smul(y *FP48) { + if SEXTIC_TWIST == D_TYPE { + w1 := NewFP8copy(F.a.geta()) + w2 := NewFP8copy(F.a.getb()) + var w3 *FP8 + + w1.mul(y.a.geta()) + w2.mul(y.a.getb()) + + if y.stype == FP_SPARSEST || F.stype == FP_SPARSEST { + if y.stype == FP_SPARSEST && F.stype == FP_SPARSEST { + t := NewFPcopy(F.b.a.a.a.a) + t.mul(y.b.a.a.a.a) + w3 = NewFP8fp(t) + } else { + if y.stype != FP_SPARSEST { + w3 = NewFP8copy(y.b.geta()) + w3.tmul(F.b.a.a.a.a) + } else { + w3 = NewFP8copy(F.b.geta()) + w3.tmul(y.b.a.a.a.a) + } + } + } else { + w3 = NewFP8copy(F.b.geta()) + w3.mul(y.b.geta()) + } + ta := NewFP8copy(F.a.geta()) + tb := NewFP8copy(y.a.geta()) + ta.add(F.a.getb()) + ta.norm() + tb.add(y.a.getb()) + tb.norm() + tc := NewFP8copy(ta) + tc.mul(tb) + t := NewFP8copy(w1) + t.add(w2) + t.neg() + tc.add(t) + + ta.copy(F.a.geta()) + ta.add(F.b.geta()) + ta.norm() + tb.copy(y.a.geta()) + tb.add(y.b.geta()) + tb.norm() + td := NewFP8copy(ta) + td.mul(tb) + t.copy(w1) + t.add(w3) + t.neg() + td.add(t) + + ta.copy(F.a.getb()) + ta.add(F.b.geta()) + ta.norm() + tb.copy(y.a.getb()) + tb.add(y.b.geta()) + tb.norm() + te := NewFP8copy(ta) + te.mul(tb) + t.copy(w2) + t.add(w3) + t.neg() + te.add(t) + + w2.times_i() + w1.add(w2) + + F.a.geta().copy(w1) + F.a.getb().copy(tc) + F.b.geta().copy(td) + F.b.getb().copy(te) + F.c.geta().copy(w3) + F.c.getb().zero() + + F.a.norm() + F.b.norm() + } else { + w1 := NewFP8copy(F.a.geta()) + w2 := NewFP8copy(F.a.getb()) + var w3 *FP8 + + w1.mul(y.a.geta()) + w2.mul(y.a.getb()) + + if y.stype == FP_SPARSEST || F.stype == FP_SPARSEST { + if y.stype == FP_SPARSEST && F.stype == FP_SPARSEST { + t := NewFPcopy(F.c.b.a.a.a) + t.mul(y.c.b.a.a.a) + w3 = NewFP8fp(t) + } else { + if y.stype != FP_SPARSEST { + w3 = NewFP8copy(y.c.getb()) + w3.tmul(F.c.b.a.a.a) + } else { + w3 = NewFP8copy(F.c.getb()) + w3.tmul(y.c.b.a.a.a) + } + } + } else { + w3 = NewFP8copy(F.c.getb()) + w3.mul(y.c.getb()) + } + + ta := NewFP8copy(F.a.geta()) + tb := NewFP8copy(y.a.geta()) + ta.add(F.a.getb()) + ta.norm() + tb.add(y.a.getb()) + tb.norm() + tc := NewFP8copy(ta) + tc.mul(tb) + t := NewFP8copy(w1) + t.add(w2) + t.neg() + tc.add(t) + + ta.copy(F.a.geta()) + ta.add(F.c.getb()) + ta.norm() + tb.copy(y.a.geta()) + tb.add(y.c.getb()) + tb.norm() + td := NewFP8copy(ta) + td.mul(tb) + t.copy(w1) + t.add(w3) + t.neg() + td.add(t) + + ta.copy(F.a.getb()) + ta.add(F.c.getb()) + ta.norm() + tb.copy(y.a.getb()) + tb.add(y.c.getb()) + tb.norm() + te := NewFP8copy(ta) + te.mul(tb) + t.copy(w2) + t.add(w3) + t.neg() + te.add(t) + + w2.times_i() + w1.add(w2) + F.a.geta().copy(w1) + F.a.getb().copy(tc) + + w3.times_i() + w3.norm() + F.b.geta().zero() + F.b.getb().copy(w3) + + te.norm() + te.times_i() + F.c.geta().copy(te) + F.c.getb().copy(td) + + F.a.norm() + F.c.norm() + + } + F.stype = FP_SPARSE +} + +/* this=1/this */ +func (F *FP48) Inverse() { + f0 := NewFP16copy(F.a) + f1 := NewFP16copy(F.b) + f2 := NewFP16copy(F.a) + f3 := NewFP16() + + //F.norm() + f0.sqr() + f1.mul(F.c) + f1.times_i() + f0.sub(f1) + f0.norm() + + f1.copy(F.c) + f1.sqr() + f1.times_i() + f2.mul(F.b) + f1.sub(f2) + f1.norm() + + f2.copy(F.b) + f2.sqr() + f3.copy(F.a) + f3.mul(F.c) + f2.sub(f3) + f2.norm() + + f3.copy(F.b) + f3.mul(f2) + f3.times_i() + F.a.mul(f0) + f3.add(F.a) + F.c.mul(f1) + F.c.times_i() + + f3.add(F.c) + f3.norm() + f3.inverse() + + F.a.copy(f0) + F.a.mul(f3) + F.b.copy(f1) + F.b.mul(f3) + F.c.copy(f2) + F.c.mul(f3) + F.stype = FP_DENSE +} + +/* this=this^p using Frobenius */ +func (F *FP48) frob(f *FP2, n int) { + f2 := NewFP2copy(f) + f3 := NewFP2copy(f) + + f2.sqr() + f3.mul(f2) + + f3.mul_ip() + f3.norm() + f3.mul_ip() + f3.norm() + + for i := 0; i < n; i++ { + F.a.frob(f3) + F.b.frob(f3) + F.c.frob(f3) + + F.b.qmul(f) + F.b.times_i4() + F.b.times_i2() + F.c.qmul(f2) + F.c.times_i4() + F.c.times_i4() + F.c.times_i4() + } + F.stype = FP_DENSE +} + +/* trace function */ +func (F *FP48) trace() *FP16 { + t := NewFP16() + t.copy(F.a) + t.imul(3) + t.reduce() + return t +} + +/* convert from byte array to FP48 */ +func FP48_fromBytes(w []byte) *FP48 { + var t [16 * int(MODBYTES)]byte + MB := 16 * int(MODBYTES) + + for i := 0; i < MB; i++ { + t[i] = w[i] + } + c := FP16_fromBytes(t[:]) + for i := 0; i < MB; i++ { + t[i] = w[i+MB] + } + b := FP16_fromBytes(t[:]) + for i := 0; i < MB; i++ { + t[i] = w[i+2*MB] + } + a := FP16_fromBytes(t[:]) + return NewFP48fp16s(a, b, c) +} + +/* convert this to byte array */ +func (F *FP48) ToBytes(w []byte) { + var t [16 * int(MODBYTES)]byte + MB := 16 * int(MODBYTES) + F.c.ToBytes(t[:]) + for i := 0; i < MB; i++ { + w[i] = t[i] + } + F.b.ToBytes(t[:]) + for i := 0; i < MB; i++ { + w[i+MB] = t[i] + } + F.a.ToBytes(t[:]) + for i := 0; i < MB; i++ { + w[i+2*MB] = t[i] + } +} + +/* convert to hex string */ +func (F *FP48) ToString() string { + return ("[" + F.a.toString() + "," + F.b.toString() + "," + F.c.toString() + "]") +} + +/* this=this^e */ +func (F *FP48) Pow(e *BIG) *FP48 { + sf := NewFP48copy(F) + sf.norm() + e1 := NewBIGcopy(e) + e1.norm() + e3 := NewBIGcopy(e1) + e3.pmul(3) + e3.norm() + + w := NewFP48copy(sf) + if e3.iszilch() { + w.one() + return w + } + nb := e3.nbits() + for i := nb - 2; i >= 1; i-- { + w.usqr() + bt := e3.bit(i) - e1.bit(i) + if bt == 1 { + w.Mul(sf) + } + if bt == -1 { + sf.conj() + w.Mul(sf) + sf.conj() + } + } + w.reduce() + return w + +} + +/* constant time powering by small integer of max length bts */ +func (F *FP48) pinpow(e int, bts int) { + var R []*FP48 + R = append(R, NewFP48int(1)) + R = append(R, NewFP48copy(F)) + + for i := bts - 1; i >= 0; i-- { + b := (e >> uint(i)) & 1 + R[1-b].Mul(R[b]) + R[b].usqr() + } + F.Copy(R[0]) +} + +/* Fast compressed FP16 power of unitary FP48 */ +/* +func (F *FP48) Compow(e *BIG, r *BIG) *FP16 { + q := NewBIGints(Modulus) + f := NewFP2bigs(NewBIGints(Fra), NewBIGints(Frb)) + + m := NewBIGcopy(q) + m.Mod(r) + + a := NewBIGcopy(e) + a.Mod(m) + + b := NewBIGcopy(e) + b.div(m) + + g1 := NewFP48copy(F) + c := g1.trace() + + if b.iszilch() { + c = c.xtr_pow(e) + return c + } + + g2 := NewFP48copy(F) + g2.frob(f, 1) + cp := g2.trace() + + g1.conj() + g2.Mul(g1) + cpm1 := g2.trace() + g2.Mul(g1) + cpm2 := g2.trace() + + c = c.xtr_pow2(cp, cpm1, cpm2, a, b) + return c +} +*/ +/* p=q0^u0.q1^u1.q2^u2.q3^u3.. */ +// Bos & Costello https://eprint.iacr.org/2013/458.pdf +// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf +// Side channel attack secure + +func pow16(q []*FP48, u []*BIG) *FP48 { + var g1 []*FP48 + var g2 []*FP48 + var g3 []*FP48 + var g4 []*FP48 + var w1 [NLEN*int(BASEBITS) + 1]int8 + var s1 [NLEN*int(BASEBITS) + 1]int8 + var w2 [NLEN*int(BASEBITS) + 1]int8 + var s2 [NLEN*int(BASEBITS) + 1]int8 + var w3 [NLEN*int(BASEBITS) + 1]int8 + var s3 [NLEN*int(BASEBITS) + 1]int8 + var w4 [NLEN*int(BASEBITS) + 1]int8 + var s4 [NLEN*int(BASEBITS) + 1]int8 + var t []*BIG + r := NewFP48() + p := NewFP48() + mt := NewBIGint(0) + var bt int8 + var k int + + for i := 0; i < 16; i++ { + t = append(t, NewBIGcopy(u[i])) + } + + g1 = append(g1, NewFP48copy(q[0])) // q[0] + g1 = append(g1, NewFP48copy(g1[0])) + g1[1].Mul(q[1]) // q[0].q[1] + g1 = append(g1, NewFP48copy(g1[0])) + g1[2].Mul(q[2]) // q[0].q[2] + g1 = append(g1, NewFP48copy(g1[1])) + g1[3].Mul(q[2]) // q[0].q[1].q[2] + g1 = append(g1, NewFP48copy(g1[0])) + g1[4].Mul(q[3]) // q[0].q[3] + g1 = append(g1, NewFP48copy(g1[1])) + g1[5].Mul(q[3]) // q[0].q[1].q[3] + g1 = append(g1, NewFP48copy(g1[2])) + g1[6].Mul(q[3]) // q[0].q[2].q[3] + g1 = append(g1, NewFP48copy(g1[3])) + g1[7].Mul(q[3]) // q[0].q[1].q[2].q[3] + + g2 = append(g2, NewFP48copy(q[4])) // q[0] + g2 = append(g2, NewFP48copy(g2[0])) + g2[1].Mul(q[5]) // q[0].q[1] + g2 = append(g2, NewFP48copy(g2[0])) + g2[2].Mul(q[6]) // q[0].q[2] + g2 = append(g2, NewFP48copy(g2[1])) + g2[3].Mul(q[6]) // q[0].q[1].q[2] + g2 = append(g2, NewFP48copy(g2[0])) + g2[4].Mul(q[7]) // q[0].q[3] + g2 = append(g2, NewFP48copy(g2[1])) + g2[5].Mul(q[7]) // q[0].q[1].q[3] + g2 = append(g2, NewFP48copy(g2[2])) + g2[6].Mul(q[7]) // q[0].q[2].q[3] + g2 = append(g2, NewFP48copy(g2[3])) + g2[7].Mul(q[7]) // q[0].q[1].q[2].q[3] + + g3 = append(g3, NewFP48copy(q[8])) // q[0] + g3 = append(g3, NewFP48copy(g3[0])) + g3[1].Mul(q[9]) // q[0].q[1] + g3 = append(g3, NewFP48copy(g3[0])) + g3[2].Mul(q[10]) // q[0].q[2] + g3 = append(g3, NewFP48copy(g3[1])) + g3[3].Mul(q[10]) // q[0].q[1].q[2] + g3 = append(g3, NewFP48copy(g3[0])) + g3[4].Mul(q[11]) // q[0].q[3] + g3 = append(g3, NewFP48copy(g3[1])) + g3[5].Mul(q[11]) // q[0].q[1].q[3] + g3 = append(g3, NewFP48copy(g3[2])) + g3[6].Mul(q[11]) // q[0].q[2].q[3] + g3 = append(g3, NewFP48copy(g3[3])) + g3[7].Mul(q[11]) // q[0].q[1].q[2].q[3] + + g4 = append(g4, NewFP48copy(q[12])) // q[0] + g4 = append(g4, NewFP48copy(g4[0])) + g4[1].Mul(q[13]) // q[0].q[1] + g4 = append(g4, NewFP48copy(g4[0])) + g4[2].Mul(q[14]) // q[0].q[2] + g4 = append(g4, NewFP48copy(g4[1])) + g4[3].Mul(q[14]) // q[0].q[1].q[2] + g4 = append(g4, NewFP48copy(g4[0])) + g4[4].Mul(q[15]) // q[0].q[3] + g4 = append(g4, NewFP48copy(g4[1])) + g4[5].Mul(q[15]) // q[0].q[1].q[3] + g4 = append(g4, NewFP48copy(g4[2])) + g4[6].Mul(q[15]) // q[0].q[2].q[3] + g4 = append(g4, NewFP48copy(g4[3])) + g4[7].Mul(q[15]) // q[0].q[1].q[2].q[3] + + // Make them odd + pb1 := 1 - t[0].parity() + t[0].inc(pb1) + // t[0].norm(); + + pb2 := 1 - t[4].parity() + t[4].inc(pb2) + // t[4].norm(); + + pb3 := 1 - t[8].parity() + t[8].inc(pb3) + // t[8].norm(); + + pb4 := 1 - t[12].parity() + t[12].inc(pb4) + // t[12].norm(); + + // Number of bits + mt.zero() + for i := 0; i < 16; i++ { + t[i].norm() + mt.or(t[i]) + } + + nb := 1 + mt.nbits() + + // Sign pivot + s1[nb-1] = 1 + s2[nb-1] = 1 + s3[nb-1] = 1 + s4[nb-1] = 1 + for i := 0; i < nb-1; i++ { + t[0].fshr(1) + s1[i] = 2*int8(t[0].parity()) - 1 + t[4].fshr(1) + s2[i] = 2*int8(t[4].parity()) - 1 + t[8].fshr(1) + s3[i] = 2*int8(t[8].parity()) - 1 + t[12].fshr(1) + s4[i] = 2*int8(t[12].parity()) - 1 + + } + + // Recoded exponents + for i := 0; i < nb; i++ { + w1[i] = 0 + k = 1 + for j := 1; j < 4; j++ { + bt = s1[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w1[i] += bt * int8(k) + k *= 2 + } + w2[i] = 0 + k = 1 + for j := 5; j < 8; j++ { + bt = s2[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w2[i] += bt * int8(k) + k *= 2 + } + w3[i] = 0 + k = 1 + for j := 9; j < 12; j++ { + bt = s3[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w3[i] += bt * int8(k) + k *= 2 + } + w4[i] = 0 + k = 1 + for j := 13; j < 16; j++ { + bt = s4[i] * int8(t[j].parity()) + t[j].fshr(1) + t[j].dec(int(bt) >> 1) + t[j].norm() + w4[i] += bt * int8(k) + k *= 2 + } + } + + // Main loop + p.selector(g1, int32(2*w1[nb-1]+1)) + r.selector(g2, int32(2*w2[nb-1]+1)) + p.Mul(r) + r.selector(g3, int32(2*w3[nb-1]+1)) + p.Mul(r) + r.selector(g4, int32(2*w4[nb-1]+1)) + p.Mul(r) + for i := nb - 2; i >= 0; i-- { + p.usqr() + r.selector(g1, int32(2*w1[i]+s1[i])) + p.Mul(r) + r.selector(g2, int32(2*w2[i]+s2[i])) + p.Mul(r) + r.selector(g3, int32(2*w3[i]+s3[i])) + p.Mul(r) + r.selector(g4, int32(2*w4[i]+s4[i])) + p.Mul(r) + } + + // apply correction + r.Copy(q[0]) + r.conj() + r.Mul(p) + p.cmove(r, pb1) + r.Copy(q[4]) + r.conj() + r.Mul(p) + p.cmove(r, pb2) + r.Copy(q[8]) + r.conj() + r.Mul(p) + p.cmove(r, pb3) + r.Copy(q[12]) + r.conj() + r.Mul(p) + p.cmove(r, pb4) + + p.reduce() + return p +} diff --git a/ec/bls48581/FP8.go b/ec/bls48581/FP8.go new file mode 100644 index 0000000..dbf9c04 --- /dev/null +++ b/ec/bls48581/FP8.go @@ -0,0 +1,781 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Finite Field arithmetic Fp^8 functions */ + +/* FP4 elements are of the form a+ib, where i is sqrt(-1+sqrt(-1)) */ + +package bls48581 + +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +//import "fmt" + +type FP8 struct { + a *FP4 + b *FP4 +} + +func NewFP8() *FP8 { + F := new(FP8) + F.a = NewFP4() + F.b = NewFP4() + return F +} + +/* Constructors */ +func NewFP8int(a int) *FP8 { + F := new(FP8) + F.a = NewFP4int(a) + F.b = NewFP4() + return F +} + +/* Constructors */ +func NewFP8ints(a int, b int) *FP8 { + F := new(FP8) + F.a = NewFP4int(a) + F.b = NewFP4int(b) + return F +} + +func NewFP8copy(x *FP8) *FP8 { + F := new(FP8) + F.a = NewFP4copy(x.a) + F.b = NewFP4copy(x.b) + return F +} + +func NewFP8fp4s(c *FP4, d *FP4) *FP8 { + F := new(FP8) + F.a = NewFP4copy(c) + F.b = NewFP4copy(d) + return F +} + +func NewFP8fp4(c *FP4) *FP8 { + F := new(FP8) + F.a = NewFP4copy(c) + F.b = NewFP4() + return F +} + +func NewFP8fp(c *FP) *FP8 { + F := new(FP8) + F.a = NewFP4fp(c) + F.b = NewFP4() + return F +} + +func NewFP8rand(rng *core.RAND) *FP8 { + F := NewFP8fp4s(NewFP4rand(rng), NewFP4rand(rng)) + return F +} + +/* reduce all components of this mod Modulus */ +func (F *FP8) reduce() { + F.a.reduce() + F.b.reduce() +} + +/* normalise all components of this mod Modulus */ +func (F *FP8) norm() { + F.a.norm() + F.b.norm() +} + +/* test this==0 ? */ +func (F *FP8) iszilch() bool { + return F.a.iszilch() && F.b.iszilch() +} + +func (F *FP8) islarger() int { + if F.iszilch() { + return 0 + } + cmp := F.b.islarger() + if cmp != 0 { + return cmp + } + return F.a.islarger() +} + +func (F *FP8) ToBytes(bf []byte) { + var t [4 * int(MODBYTES)]byte + MB := 4 * int(MODBYTES) + F.b.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i] = t[i] + } + F.a.ToBytes(t[:]) + for i := 0; i < MB; i++ { + bf[i+MB] = t[i] + } +} + +func FP8_fromBytes(bf []byte) *FP8 { + var t [4 * int(MODBYTES)]byte + MB := 4 * int(MODBYTES) + for i := 0; i < MB; i++ { + t[i] = bf[i] + } + tb := FP4_fromBytes(t[:]) + for i := 0; i < MB; i++ { + t[i] = bf[i+MB] + } + ta := FP4_fromBytes(t[:]) + return NewFP8fp4s(ta, tb) +} + +/* Conditional move */ +func (F *FP8) cmove(g *FP8, d int) { + F.a.cmove(g.a, d) + F.b.cmove(g.b, d) +} + +/* test this==1 ? */ +func (F *FP8) isunity() bool { + one := NewFP4int(1) + return F.a.Equals(one) && F.b.iszilch() +} + +/* test is w real? That is in a+ib test b is zero */ +func (F *FP8) isreal() bool { + return F.b.iszilch() +} + +/* extract real part a */ +func (F *FP8) real() *FP4 { + return F.a +} + +func (F *FP8) geta() *FP4 { + return F.a +} + +/* extract imaginary part b */ +func (F *FP8) getb() *FP4 { + return F.b +} + +/* test this=x? */ +func (F *FP8) Equals(x *FP8) bool { + return (F.a.Equals(x.a) && F.b.Equals(x.b)) +} + +/* copy this=x */ +func (F *FP8) copy(x *FP8) { + F.a.copy(x.a) + F.b.copy(x.b) +} + +/* set this=0 */ +func (F *FP8) zero() { + F.a.zero() + F.b.zero() +} + +/* set this=1 */ +func (F *FP8) one() { + F.a.one() + F.b.zero() +} + +/* Return sign */ +func (F *FP8) sign() int { + p1 := F.a.sign() + p2 := F.b.sign() + var u int + if BIG_ENDIAN_SIGN { + if F.b.iszilch() { + u = 1 + } else { + u = 0 + } + p2 ^= (p1 ^ p2) & u + return p2 + } else { + if F.a.iszilch() { + u = 1 + } else { + u = 0 + } + p1 ^= (p1 ^ p2) & u + return p1 + } +} + +/* set this=-this */ +func (F *FP8) neg() { + F.norm() + m := NewFP4copy(F.a) + t := NewFP4() + m.add(F.b) + m.neg() + t.copy(m) + t.add(F.b) + F.b.copy(m) + F.b.add(F.a) + F.a.copy(t) + F.norm() +} + +/* this=conjugate(this) */ +func (F *FP8) conj() { + F.b.neg() + F.norm() +} + +/* this=-conjugate(this) */ +func (F *FP8) nconj() { + F.a.neg() + F.norm() +} + +/* this+=x */ +func (F *FP8) add(x *FP8) { + F.a.add(x.a) + F.b.add(x.b) +} + +/* this-=x */ +func (F *FP8) sub(x *FP8) { + m := NewFP8copy(x) + m.neg() + F.add(m) +} + +/* this-=x */ +func (F *FP8) rsub(x *FP8) { + F.neg() + F.add(x) +} + +/* this*=s where s is FP4 */ +func (F *FP8) pmul(s *FP4) { + F.a.mul(s) + F.b.mul(s) +} + +/* this*=s where s is FP2 */ +func (F *FP8) qmul(s *FP2) { + F.a.pmul(s) + F.b.pmul(s) +} + +/* this*=s where s is FP */ +func (F *FP8) tmul(s *FP) { + F.a.qmul(s) + F.b.qmul(s) +} + +/* this*=c where c is int */ +func (F *FP8) imul(c int) { + F.a.imul(c) + F.b.imul(c) +} + +/* this*=this */ +func (F *FP8) sqr() { + t1 := NewFP4copy(F.a) + t2 := NewFP4copy(F.b) + t3 := NewFP4copy(F.a) + + t3.mul(F.b) + t1.add(F.b) + t2.times_i() + + t2.add(F.a) + + t1.norm() + t2.norm() + + F.a.copy(t1) + F.a.mul(t2) + + t2.copy(t3) + t2.times_i() + t2.add(t3) + t2.norm() + t2.neg() + F.a.add(t2) + + F.b.copy(t3) + F.b.add(t3) + + F.norm() +} + +/* this*=y */ +func (F *FP8) mul(y *FP8) { + t1 := NewFP4copy(F.a) + t2 := NewFP4copy(F.b) + t3 := NewFP4() + t4 := NewFP4copy(F.b) + + t1.mul(y.a) + t2.mul(y.b) + t3.copy(y.b) + t3.add(y.a) + t4.add(F.a) + + t3.norm() + t4.norm() + + t4.mul(t3) + + t3.copy(t1) + t3.neg() + t4.add(t3) + t4.norm() + + t3.copy(t2) + t3.neg() + F.b.copy(t4) + F.b.add(t3) + + t2.times_i() + F.a.copy(t2) + F.a.add(t1) + + F.norm() +} + +/* convert this to hex string */ +func (F *FP8) toString() string { + return ("[" + F.a.toString() + "," + F.b.toString() + "]") +} + +/* this=1/this */ +func (F *FP8) inverse(h *FP) { + t1 := NewFP4copy(F.a) + t2 := NewFP4copy(F.b) + + t1.sqr() + t2.sqr() + t2.times_i() + t2.norm() + t1.sub(t2) + t1.norm() + + t1.inverse(h) + + F.a.mul(t1) + t1.neg() + t1.norm() + F.b.mul(t1) +} + +/* this*=i where i = sqrt(sqrt(-1+sqrt(-1))) */ +func (F *FP8) times_i() { + s := NewFP4copy(F.b) + t := NewFP4copy(F.a) + s.times_i() + F.a.copy(s) + F.b.copy(t) + F.norm() + if TOWER == POSITOWER { + F.neg() + F.norm() + } +} + +func (F *FP8) times_i2() { + F.a.times_i() + F.b.times_i() +} + +/* this=this^p using Frobenius */ +func (F *FP8) frob(f *FP2) { + ff := NewFP2copy(f) + ff.sqr() + ff.mul_ip() + ff.norm() + + F.a.frob(ff) + F.b.frob(ff) + F.b.pmul(f) + F.b.times_i() +} + +/* this=this^e +func (F *FP8) pow(e *BIG) *FP8 { + w := NewFP8copy(F) + w.norm() + z := NewBIGcopy(e) + r := NewFP8int(1) + z.norm() + for true { + bt := z.parity() + z.fshr(1) + if bt == 1 { + r.mul(w) + } + if z.iszilch() { + break + } + w.sqr() + } + r.reduce() + return r +} */ + +/* XTR xtr_a function */ +/* +func (F *FP8) xtr_A(w *FP8, y *FP8, z *FP8) { + r := NewFP8copy(w) + t := NewFP8copy(w) + r.sub(y) + r.norm() + r.pmul(F.a) + t.add(y) + t.norm() + t.pmul(F.b) + t.times_i() + + F.copy(r) + F.add(t) + F.add(z) + + F.norm() +} +*/ +/* XTR xtr_d function */ +/* +func (F *FP8) xtr_D() { + w := NewFP8copy(F) + F.sqr() + w.conj() + w.add(w) + w.norm() + F.sub(w) + F.reduce() +} +*/ +/* r=x^n using XTR method on traces of FP24s */ +/* +func (F *FP8) xtr_pow(n *BIG) *FP8 { + a := NewFP8int(3) + b := NewFP8copy(F) + c := NewFP8copy(b) + c.xtr_D() + t := NewFP8() + r := NewFP8() + sf := NewFP8copy(F) + sf.norm() + + par := n.parity() + v := NewBIGcopy(n) + v.norm() + v.fshr(1) + if par == 0 { + v.dec(1) + v.norm() + } + + nb := v.nbits() + for i := nb - 1; i >= 0; i-- { + if v.bit(i) != 1 { + t.copy(b) + sf.conj() + c.conj() + b.xtr_A(a, sf, c) + sf.conj() + c.copy(t) + c.xtr_D() + a.xtr_D() + } else { + t.copy(a) + t.conj() + a.copy(b) + a.xtr_D() + b.xtr_A(c, sf, t) + c.xtr_D() + } + } + if par == 0 { + r.copy(c) + } else { + r.copy(b) + } + r.reduce() + return r +} +*/ +/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP24s. See Stam thesis. */ +/* +func (F *FP8) xtr_pow2(ck *FP8, ckml *FP8, ckm2l *FP8, a *BIG, b *BIG) *FP8 { + + e := NewBIGcopy(a) + d := NewBIGcopy(b) + w := NewBIGint(0) + e.norm() + d.norm() + cu := NewFP8copy(ck) // can probably be passed in w/o copying + cv := NewFP8copy(F) + cumv := NewFP8copy(ckml) + cum2v := NewFP8copy(ckm2l) + r := NewFP8() + t := NewFP8() + + f2 := 0 + for d.parity() == 0 && e.parity() == 0 { + d.fshr(1) + e.fshr(1) + f2++ + } + + for Comp(d, e) != 0 { + if Comp(d, e) > 0 { + w.copy(e) + w.imul(4) + w.norm() + if Comp(d, w) <= 0 { + w.copy(d) + d.copy(e) + e.rsub(w) + e.norm() + + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cum2v.conj() + cumv.copy(cv) + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 0 { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } else { + if e.parity() == 1 { + d.sub(e) + d.norm() + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cu.xtr_D() + cum2v.copy(cv) + cum2v.xtr_D() + cum2v.conj() + cv.copy(t) + } else { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } + } + } + } + if Comp(d, e) < 0 { + w.copy(d) + w.imul(4) + w.norm() + if Comp(e, w) <= 0 { + e.sub(d) + e.norm() + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cum2v.copy(cumv) + cumv.copy(cu) + cu.copy(t) + } else { + if e.parity() == 0 { + w.copy(d) + d.copy(e) + d.fshr(1) + e.copy(w) + t.copy(cumv) + t.xtr_D() + cumv.copy(cum2v) + cumv.conj() + cum2v.copy(t) + cum2v.conj() + t.copy(cv) + t.xtr_D() + cv.copy(cu) + cu.copy(t) + } else { + if d.parity() == 1 { + w.copy(e) + e.copy(d) + w.sub(d) + w.norm() + d.copy(w) + d.fshr(1) + t.copy(cv) + t.xtr_A(cu, cumv, cum2v) + cumv.conj() + cum2v.copy(cu) + cum2v.xtr_D() + cum2v.conj() + cu.copy(cv) + cu.xtr_D() + cv.copy(t) + } else { + d.fshr(1) + r.copy(cum2v) + r.conj() + t.copy(cumv) + t.xtr_A(cu, cv, r) + cum2v.copy(cumv) + cum2v.xtr_D() + cumv.copy(t) + cu.xtr_D() + } + } + } + } + } + r.copy(cv) + r.xtr_A(cu, cumv, cum2v) + for i := 0; i < f2; i++ { + r.xtr_D() + } + r = r.xtr_pow(d) + return r +} +*/ +/* this/=2 */ +func (F *FP8) div2() { + F.a.div2() + F.b.div2() +} + +func (F *FP8) div_i() { + u := NewFP4copy(F.a) + v := NewFP4copy(F.b) + u.div_i() + F.a.copy(v) + F.b.copy(u) + if TOWER == POSITOWER { + F.neg() + F.norm() + } +} + +/* +func (F *FP8) pow(b *BIG) { + w := NewFP8copy(F); + r := NewFP8int(1) + z := NewBIGcopy(b) + for true { + bt := z.parity() + z.shr(1) + if bt==1 { + r.mul(w) + } + if z.iszilch() {break} + w.sqr() + } + r.reduce(); + F.copy(r); +} +*/ + +/* */ +// Test for Quadratic Residue +func (F *FP8) qr(h *FP) int { + c := NewFP8copy(F) + c.conj() + c.mul(F) + return c.a.qr(h) +} + +// sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) +func (F *FP8) sqrt(h *FP) { + if F.iszilch() { + return + } + + a := NewFP4copy(F.a) + b := NewFP4() + s := NewFP4copy(F.b) + t := NewFP4copy(F.a) + hint := NewFP() + + s.sqr() + a.sqr() + s.times_i() + s.norm() + a.sub(s) + + s.copy(a) + s.norm() + + s.sqrt(h) + a.copy(t) + b.copy(t) + + a.add(s) + a.norm() + a.div2() + + b.copy(F.b) + b.div2() + qr := a.qr(hint) + + // tweak hint - multiply old hint by Norm(1/Beta)^e where Beta is irreducible polynomial + s.copy(a) + twk := NewFPbig(NewBIGints(TWK)) + twk.mul(hint) + s.div_i() + s.norm() + + a.cmove(s, 1-qr) + hint.cmove(twk, 1-qr) + + F.a.copy(a) + F.a.sqrt(hint) + s.copy(a) + s.inverse(hint) + s.mul(F.a) + F.b.copy(s) + F.b.mul(b) + t.copy(F.a) + + F.a.cmove(F.b, 1-qr) + F.b.cmove(t, 1-qr) + + sgn := F.sign() + nr := NewFP8copy(F) + nr.neg() + nr.norm() + F.cmove(nr, sgn) +} + +/* */ diff --git a/ec/bls48581/HPKE.go b/ec/bls48581/HPKE.go new file mode 100644 index 0000000..0a01e0d --- /dev/null +++ b/ec/bls48581/HPKE.go @@ -0,0 +1,327 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Hybrid Public Key Encryption */ + +/* Following https://datatracker.ietf.org/doc/draft-irtf-cfrg-hpke/?include_text=1 */ + +package bls48581 + +//import "fmt" +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +func reverse(X []byte) { + lx := len(X) + for i := 0; i < lx/2; i++ { + ch := X[i] + X[i] = X[lx-i-1] + X[lx-i-1] = ch + } +} + +func labeledExtract(SALT []byte, SUITE_ID []byte, label string, IKM []byte) []byte { + rfc := "HPKE-v1" + RFC := []byte(rfc) + LABEL := []byte(label) + var LIKM []byte + for i := 0; i < len(RFC); i++ { + LIKM = append(LIKM, RFC[i]) + } + for i := 0; i < len(SUITE_ID); i++ { + LIKM = append(LIKM, SUITE_ID[i]) + } + for i := 0; i < len(LABEL); i++ { + LIKM = append(LIKM, LABEL[i]) + } + if IKM != nil { + for i := 0; i < len(IKM); i++ { + LIKM = append(LIKM, IKM[i]) + } + } + return core.HKDF_Extract(core.MC_SHA2, HASH_TYPE, SALT, LIKM) +} + +func labeledExpand(PRK []byte, SUITE_ID []byte, label string, INFO []byte, L int) []byte { + rfc := "HPKE-v1" + RFC := []byte(rfc) + LABEL := []byte(label) + AR := core.InttoBytes(L, 2) + var LINFO []byte + for i := 0; i < len(AR); i++ { + LINFO = append(LINFO, AR[i]) + } + for i := 0; i < len(RFC); i++ { + LINFO = append(LINFO, RFC[i]) + } + for i := 0; i < len(SUITE_ID); i++ { + LINFO = append(LINFO, SUITE_ID[i]) + } + for i := 0; i < len(LABEL); i++ { + LINFO = append(LINFO, LABEL[i]) + } + if INFO != nil { + for i := 0; i < len(INFO); i++ { + LINFO = append(LINFO, INFO[i]) + } + } + + return core.HKDF_Expand(core.MC_SHA2, HASH_TYPE, L, PRK, LINFO) +} + +func extractAndExpand(config_id int, DH []byte, context []byte) []byte { + kem := config_id & 255 + txt := "KEM" + KEM_ID := core.InttoBytes(kem, 2) + KEM := []byte(txt) + var SUITE_ID []byte + for i := 0; i < len(KEM); i++ { + SUITE_ID = append(SUITE_ID, KEM[i]) + } + SUITE_ID = append(SUITE_ID, KEM_ID[0]) + SUITE_ID = append(SUITE_ID, KEM_ID[1]) + + PRK := labeledExtract(nil, SUITE_ID, "eae_prk", DH) + return labeledExpand(PRK, SUITE_ID, "shared_secret", context, HASH_TYPE) +} + +func DeriveKeyPair(config_id int, SK []byte, PK []byte, SEED []byte) bool { + counter := 0 + kem := config_id & 255 + + txt := "KEM" + KEM_ID := core.InttoBytes(kem, 2) + KEM := []byte(txt) + var SUITE_ID []byte + for i := 0; i < len(KEM); i++ { + SUITE_ID = append(SUITE_ID, KEM[i]) + } + SUITE_ID = append(SUITE_ID, KEM_ID[0]) + SUITE_ID = append(SUITE_ID, KEM_ID[1]) + + PRK := labeledExtract(nil, SUITE_ID, "dkp_prk", SEED) + var S []byte + if kem == 32 || kem == 33 { // RFC7748 + S = labeledExpand(PRK, SUITE_ID, "sk", nil, EGS) + reverse(S) + if kem == 32 { + S[EGS-1] &= 248 + S[0] &= 127 + S[0] |= 64 + } else { + S[EGS-1] &= 252 + S[0] |= 128 + } + } else { + bit_mask := 0xff + if kem == 18 { + bit_mask = 1 + } + for i := 0; i < EGS; i++ { + S = append(S, 0) + } + for !ECDH_IN_RANGE(S) && counter < 256 { + var INFO [1]byte + INFO[0] = byte(counter) + S = labeledExpand(PRK, SUITE_ID, "candidate", INFO[:], EGS) + S[0] &= byte(bit_mask) + counter++ + } + } + for i := 0; i < EGS; i++ { + SK[i] = S[i] + } + ECDH_KEY_PAIR_GENERATE(nil, SK, PK) + if kem == 32 || kem == 33 { + reverse(PK) + } + if counter < 256 { + return true + } + return false +} + +func Encap(config_id int, skE []byte, pkE []byte, pkR []byte) []byte { + DH := make([]byte, EFS) + var kemcontext []byte + kem := config_id & 255 + + if kem == 32 || kem == 33 { + reverse(pkR) + ECDH_ECPSVDP_DH(skE, pkR, DH[:], 0) + reverse(pkR) + reverse(DH[:]) + } else { + ECDH_ECPSVDP_DH(skE, pkR, DH[:], 0) + } + for i := 0; i < len(pkE); i++ { + kemcontext = append(kemcontext, pkE[i]) + } + for i := 0; i < len(pkR); i++ { + kemcontext = append(kemcontext, pkR[i]) + } + return extractAndExpand(config_id, DH[:], kemcontext) +} + +func Decap(config_id int, skR []byte, pkE []byte, pkR []byte) []byte { + DH := make([]byte, EFS) + var kemcontext []byte + kem := config_id & 255 + + if kem == 32 || kem == 33 { + reverse(pkE) + ECDH_ECPSVDP_DH(skR, pkE, DH[:], 0) + reverse(pkE) + reverse(DH[:]) + } else { + ECDH_ECPSVDP_DH(skR, pkE, DH[:], 0) + } + + for i := 0; i < len(pkE); i++ { + kemcontext = append(kemcontext, pkE[i]) + } + for i := 0; i < len(pkR); i++ { + kemcontext = append(kemcontext, pkR[i]) + } + return extractAndExpand(config_id, DH[:], kemcontext) +} + +func AuthEncap(config_id int, skE []byte, skS []byte, pkE []byte, pkR []byte, pkS []byte) []byte { + pklen := len(pkE) + DH := make([]byte, EFS) + DH1 := make([]byte, EFS) + + kemcontext := make([]byte, 3*pklen) + kem := config_id & 255 + + if kem == 32 || kem == 33 { + reverse(pkR) + ECDH_ECPSVDP_DH(skE, pkR, DH[:], 0) + ECDH_ECPSVDP_DH(skS, pkR, DH1[:], 0) + reverse(pkR) + reverse(DH[:]) + reverse(DH1[:]) + } else { + ECDH_ECPSVDP_DH(skE, pkR, DH[:], 0) + ECDH_ECPSVDP_DH(skS, pkR, DH1[:], 0) + } + ZZ := make([]byte, 2*EFS) + for i := 0; i < EFS; i++ { + ZZ[i] = DH[i] + ZZ[EFS+i] = DH1[i] + } + + for i := 0; i < pklen; i++ { + kemcontext[i] = pkE[i] + kemcontext[pklen+i] = pkR[i] + kemcontext[2*pklen+i] = pkS[i] + } + return extractAndExpand(config_id, ZZ[:], kemcontext) +} + +func AuthDecap(config_id int, skR []byte, pkE []byte, pkR []byte, pkS []byte) []byte { + pklen := len(pkE) + DH := make([]byte, EFS) + DH1 := make([]byte, EFS) + kemcontext := make([]byte, 3*pklen) + + kem := config_id & 255 + + if kem == 32 || kem == 33 { + reverse(pkE) + reverse(pkS) + ECDH_ECPSVDP_DH(skR[:], pkE, DH[:], 0) + ECDH_ECPSVDP_DH(skR[:], pkS, DH1[:], 0) + reverse(pkE) + reverse(pkS) + reverse(DH[:]) + reverse(DH1[:]) + } else { + ECDH_ECPSVDP_DH(skR[:], pkE, DH[:], 0) + ECDH_ECPSVDP_DH(skR[:], pkS, DH1[:], 0) + } + ZZ := make([]byte, 2*EFS) + for i := 0; i < EFS; i++ { + ZZ[i] = DH[i] + ZZ[EFS+i] = DH1[i] + } + + for i := 0; i < pklen; i++ { + kemcontext[i] = pkE[i] + kemcontext[pklen+i] = pkR[i] + kemcontext[2*pklen+i] = pkS[i] + } + return extractAndExpand(config_id, ZZ[:], kemcontext) +} + +/* +func printBinary(array []byte) { + for i := 0; i < len(array); i++ { + fmt.Printf("%02x", array[i]) + } + fmt.Printf("\n") +} +*/ + +func KeySchedule(config_id int, mode int, Z []byte, info []byte, psk []byte, pskID []byte) ([]byte, []byte, []byte) { + var context []byte + + kem := config_id & 255 + kdf := (config_id >> 8) & 3 + aead := (config_id >> 10) & 3 + + txt := "HPKE" + KEM := []byte(txt) + var SUITE_ID []byte + for i := 0; i < len(KEM); i++ { + SUITE_ID = append(SUITE_ID, KEM[i]) + } + num := core.InttoBytes(kem, 2) + SUITE_ID = append(SUITE_ID, num[0]) + SUITE_ID = append(SUITE_ID, num[1]) + num = core.InttoBytes(kdf, 2) + SUITE_ID = append(SUITE_ID, num[0]) + SUITE_ID = append(SUITE_ID, num[1]) + num = core.InttoBytes(aead, 2) + SUITE_ID = append(SUITE_ID, num[0]) + SUITE_ID = append(SUITE_ID, num[1]) + + ar := core.InttoBytes(mode, 1) + for i := 0; i < len(ar); i++ { + context = append(context, ar[i]) + } + + H := labeledExtract(nil, SUITE_ID, "psk_id_hash", pskID) + for i := 0; i < HASH_TYPE; i++ { + context = append(context, H[i]) + } + H = labeledExtract(nil, SUITE_ID, "info_hash", info) + for i := 0; i < HASH_TYPE; i++ { + context = append(context, H[i]) + } + //H=labeledExtract(nil,SUITE_ID,"psk_hash",psk) + //secret:=labeledExtract(H,SUITE_ID,"secret",Z) + + secret := labeledExtract(Z, SUITE_ID, "secret", psk) + + key := labeledExpand(secret, SUITE_ID, "key", context, AESKEY) + nonce := labeledExpand(secret, SUITE_ID, "base_nonce", context, 12) + exp_secret := labeledExpand(secret, SUITE_ID, "exp", context, HASH_TYPE) + + return key, nonce, exp_secret +} diff --git a/ec/bls48581/MPIN256.go b/ec/bls48581/MPIN256.go new file mode 100644 index 0000000..66ff04d --- /dev/null +++ b/ec/bls48581/MPIN256.go @@ -0,0 +1,202 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* MPIN 256-bit API Functions */ + +package bls48581 + +import "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core" + +//import "fmt" + +const MFS int = int(MODBYTES) +const MGS int = int(MODBYTES) +const BAD_PARAMS int = -11 +const INVALID_POINT int = -14 +const WRONG_ORDER int = -18 +const BAD_PIN int = -19 + +/* Configure your PIN here */ + +const MAXPIN int32 = 10000 /* PIN less than this */ +const PBLEN int32 = 14 /* Number of bits in PIN */ + +func MPIN_HASH_ID(sha int, ID []byte) []byte { + return core.GPhashit(core.MC_SHA2, sha, int(MODBYTES), 0, nil, -1, ID) + //return mhashit(sha, 0, ID) +} + +func roundup(a int, b int) int { + return (((a)-1)/(b) + 1) +} + +func MPIN_ENCODE_TO_CURVE(DST []byte, ID []byte, HCID []byte) { + q := NewBIGints(Modulus) + k := q.Nbits() + r := NewBIGints(CURVE_Order) + m := r.Nbits() + L := roundup(k+roundup(m, 2), 8) + var fd = make([]byte, L) + OKM := core.XMD_Expand(core.MC_SHA2, HASH_TYPE, L, DST, ID) + + for j := 0; j < L; j++ { + fd[j] = OKM[j] + } + dx := DBIG_fromBytes(fd) + u := NewFPbig(dx.Mod(q)) + P := ECP_map2point(u) + + P.Cfp() + P.Affine() + P.ToBytes(HCID, false) +} + +/* create random secret S */ +func MPIN_RANDOM_GENERATE(rng *core.RAND, S []byte) int { + r := NewBIGints(CURVE_Order) + s := Randtrunc(r, 16*AESKEY, rng) + s.ToBytes(S) + return 0 +} + +func MPIN_EXTRACT_PIN(CID []byte, pin int, TOKEN []byte) int { + P := ECP_fromBytes(TOKEN) + if P.Is_infinity() { + return INVALID_POINT + } + R := ECP_fromBytes(CID) + if R.Is_infinity() { + return INVALID_POINT + } + R = R.pinmul(int32(pin)%MAXPIN, PBLEN) + P.Sub(R) + P.ToBytes(TOKEN, false) + return 0 +} + +/* Implement step 2 on client side of MPin protocol */ +func MPIN_CLIENT_2(X []byte, Y []byte, SEC []byte) int { + r := NewBIGints(CURVE_Order) + P := ECP_fromBytes(SEC) + if P.Is_infinity() { + return INVALID_POINT + } + + px := FromBytes(X) + py := FromBytes(Y) + px.add(py) + px.Mod(r) + + P = G1mul(P, px) + P.Neg() + P.ToBytes(SEC, false) + return 0 +} + +func MPIN_GET_CLIENT_SECRET(S []byte, IDHTC []byte, CST []byte) int { + s := FromBytes(S) + P := ECP_fromBytes(IDHTC) + if P.Is_infinity() { + return INVALID_POINT + } + G1mul(P, s).ToBytes(CST, false) + return 0 +} + +/* Implement step 1 on client side of MPin protocol */ +func MPIN_CLIENT_1(CID []byte, rng *core.RAND, X []byte, pin int, TOKEN []byte, SEC []byte, xID []byte) int { + r := NewBIGints(CURVE_Order) + var x *BIG + if rng != nil { + x = Randtrunc(r, 16*AESKEY, rng) + x.ToBytes(X) + } else { + x = FromBytes(X) + } + + P := ECP_fromBytes(CID) + if P.Is_infinity() { + return INVALID_POINT + } + + T := ECP_fromBytes(TOKEN) + if T.Is_infinity() { + return INVALID_POINT + } + + W := P.pinmul(int32(pin)%MAXPIN, PBLEN) + T.Add(W) + + P = G1mul(P, x) + P.ToBytes(xID, false) + + T.ToBytes(SEC, false) + return 0 +} + +/* Extract Server Secret SST=S*Q where Q is fixed generator in G2 and S is master secret */ +func MPIN_GET_SERVER_SECRET(S []byte, SST []byte) int { + Q := ECP8_generator() + s := FromBytes(S) + Q = G2mul(Q, s) + Q.ToBytes(SST, false) + return 0 +} + +/* Implement step 2 of MPin protocol on server side */ +func MPIN_SERVER(HID []byte, Y []byte, SST []byte, xID []byte, mSEC []byte) int { + Q := ECP8_generator() + + sQ := ECP8_fromBytes(SST) + if sQ.Is_infinity() { + return INVALID_POINT + } + + if xID == nil { + return BAD_PARAMS + } + R := ECP_fromBytes(xID) + if R.Is_infinity() { + return INVALID_POINT + } + y := FromBytes(Y) + if HID == nil { + return BAD_PARAMS + } + P := ECP_fromBytes(HID) + if P.Is_infinity() { + return INVALID_POINT + } + + P = G1mul(P, y) + P.Add(R) + R = ECP_fromBytes(mSEC) + if R.Is_infinity() { + return INVALID_POINT + } + + var g *FP48 + g = Ate2(Q, R, sQ, P) + g = Fexp(g) + + if !g.Isunity() { + return BAD_PIN + } + return 0 +} diff --git a/ec/bls48581/PAIR8.go b/ec/bls48581/PAIR8.go new file mode 100644 index 0000000..7f6858e --- /dev/null +++ b/ec/bls48581/PAIR8.go @@ -0,0 +1,978 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* BLS Curve Pairing functions */ + +package bls48581 + +//import "fmt" + +// Point doubling for pairings +func dbl(A *ECP8, AA *FP8, BB *FP8, CC *FP8) { + CC.copy(A.getx()) //X + YY := NewFP8copy(A.gety()) //Y + BB.copy(A.getz()) //Z + AA.copy(YY) //Y + AA.mul(BB) //YZ + CC.sqr() //X^2 + YY.sqr() //Y^2 + BB.sqr() //Z^2 + + AA.add(AA) + AA.neg() + AA.norm() //-2AA + AA.times_i() + + sb := 3 * CURVE_B_I + BB.imul(sb) + CC.imul(3) + if SEXTIC_TWIST == D_TYPE { + YY.times_i() + CC.times_i() + } + if SEXTIC_TWIST == M_TYPE { + BB.times_i() + } + BB.sub(YY) + BB.norm() + + A.dbl() +} + +// Point addition for pairings +func add(A *ECP8, B *ECP8, AA *FP8, BB *FP8, CC *FP8) { + AA.copy(A.getx()) // X1 + CC.copy(A.gety()) // Y1 + T1 := NewFP8copy(A.getz()) // Z1 + BB.copy(A.getz()) // Z1 + + T1.mul(B.gety()) // T1=Z1.Y2 + BB.mul(B.getx()) // T2=Z1.X2 + + AA.sub(BB) + AA.norm() // X1=X1-Z1.X2 + CC.sub(T1) + CC.norm() // Y1=Y1-Z1.Y2 + + T1.copy(AA) // T1=X1-Z1.X2 + + if SEXTIC_TWIST == M_TYPE { + AA.times_i() + AA.norm() + } + + T1.mul(B.gety()) // T1=(X1-Z1.X2).Y2 + + BB.copy(CC) // T2=Y1-Z1.Y2 + BB.mul(B.getx()) // T2=(Y1-Z1.Y2).X2 + BB.sub(T1) + BB.norm() // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 + CC.neg() + CC.norm() // Y1=-(Y1-Z1.Y2).Xs + + A.Add(B) +} + +func line(A *ECP8, B *ECP8, Qx *FP, Qy *FP) *FP48 { + AA := NewFP8() + BB := NewFP8() + CC := NewFP8() + + var a *FP16 + var b *FP16 + var c *FP16 + + if A == B { + dbl(A, AA, BB, CC) + } else { + add(A, B, AA, BB, CC) + } + CC.tmul(Qx) + AA.tmul(Qy) + + a = NewFP16fp8s(AA, BB) + + if SEXTIC_TWIST == D_TYPE { + b = NewFP16fp8(CC) // L(0,1) | L(0,0) | L(1,0) + c = NewFP16() + } + if SEXTIC_TWIST == M_TYPE { + b = NewFP16() + c = NewFP16fp8(CC) + c.times_i() + } + + r := NewFP48fp16s(a, b, c) + r.stype = FP_SPARSER + return r +} + +/* prepare ate parameter, n=6u+2 (BN) or n=u (BLS), n3=3*n */ +func lbits(n3 *BIG, n *BIG) int { + n.copy(NewBIGints(CURVE_Bnx)) + n3.copy(n) + n3.pmul(3) + n3.norm() + return n3.nbits() +} + +/* prepare for multi-pairing */ +func Initmp() []*FP48 { + var r []*FP48 + for i := ATE_BITS - 1; i >= 0; i-- { + r = append(r, NewFP48int(1)) + } + return r +} + +/* basic Miller loop */ +func Miller(r []*FP48) *FP48 { + res := NewFP48int(1) + for i := ATE_BITS - 1; i >= 1; i-- { + res.sqr() + res.ssmul(r[i]) + r[i].zero() + } + + if SIGN_OF_X == NEGATIVEX { + res.conj() + } + res.ssmul(r[0]) + r[0].zero() + return res +} + +// Store precomputed line details in an FP8 +func pack(AA *FP8, BB *FP8, CC *FP8) *FP16 { + i := NewFP8copy(CC) + i.inverse(nil) + a := NewFP8copy(AA) + a.mul(i) + b := NewFP8copy(BB) + b.mul(i) + return NewFP16fp8s(a, b) +} + +// Unpack G2 line function details and include G1 +func unpack(T *FP16, Qx *FP, Qy *FP) *FP48 { + var a *FP16 + var b *FP16 + var c *FP16 + + a = NewFP16copy(T) + a.geta().tmul(Qy) + t := NewFP8fp(Qx) + if SEXTIC_TWIST == D_TYPE { + b = NewFP16fp8(t) + c = NewFP16() + } + if SEXTIC_TWIST == M_TYPE { + b = NewFP16() + c = NewFP16fp8(t) + c.times_i() + } + v := NewFP48fp16s(a, b, c) + v.stype = FP_SPARSEST + return v +} + +func precomp(GV *ECP8) []*FP16 { + n := NewBIG() + n3 := NewBIG() + AA := NewFP8() + BB := NewFP8() + CC := NewFP8() + var bt int + P := NewECP8() + P.Copy(GV) + + A := NewECP8() + A.Copy(P) + MP := NewECP8() + MP.Copy(P) + MP.neg() + + nb := lbits(n3, n) + var T []*FP16 + + for i := nb - 2; i >= 1; i-- { + dbl(A, AA, BB, CC) + T = append(T, pack(AA, BB, CC)) + bt = n3.bit(i) - n.bit(i) + if bt == 1 { + add(A, P, AA, BB, CC) + T = append(T, pack(AA, BB, CC)) + } + if bt == -1 { + add(A, MP, AA, BB, CC) + T = append(T, pack(AA, BB, CC)) + } + } + return T +} + +func Another_pc(r []*FP48, T []*FP16, QV *ECP) { + n := NewBIG() + n3 := NewBIG() + var lv, lv2 *FP48 + var bt, j int + + if QV.Is_infinity() { + return + } + + Q := NewECP() + Q.Copy(QV) + Q.Affine() + Qx := NewFPcopy(Q.getx()) + Qy := NewFPcopy(Q.gety()) + + nb := lbits(n3, n) + j = 0 + for i := nb - 2; i >= 1; i-- { + lv = unpack(T[j], Qx, Qy) + j += 1 + bt = n3.bit(i) - n.bit(i) + if bt == 1 { + lv2 = unpack(T[j], Qx, Qy) + j += 1 + lv.smul(lv2) + } + if bt == -1 { + lv2 = unpack(T[j], Qx, Qy) + j += 1 + lv.smul(lv2) + } + r[i].ssmul(lv) + } +} + +/* Accumulate another set of line functions for n-pairing */ +func Another(r []*FP48, P1 *ECP8, Q1 *ECP) { + n := NewBIG() + n3 := NewBIG() + var lv, lv2 *FP48 + + if Q1.Is_infinity() { + return + } + // P is needed in affine form for line function, Q for (Qx,Qy) extraction + P := NewECP8() + P.Copy(P1) + Q := NewECP() + Q.Copy(Q1) + + P.Affine() + Q.Affine() + + Qx := NewFPcopy(Q.getx()) + Qy := NewFPcopy(Q.gety()) + + A := NewECP8() + A.Copy(P) + + MP := NewECP8() + MP.Copy(P) + MP.neg() + + nb := lbits(n3, n) + + for i := nb - 2; i >= 1; i-- { + lv = line(A, A, Qx, Qy) + + bt := n3.bit(i) - n.bit(i) + if bt == 1 { + lv2 = line(A, P, Qx, Qy) + lv.smul(lv2) + } + if bt == -1 { + lv2 = line(A, MP, Qx, Qy) + lv.smul(lv2) + } + r[i].ssmul(lv) + } +} + +/* Optimal R-ate pairing */ +func Ate(P1 *ECP8, Q1 *ECP) *FP48 { + n := NewBIG() + n3 := NewBIG() + var lv, lv2 *FP48 + + if Q1.Is_infinity() { + return NewFP48int(1) + } + + P := NewECP8() + P.Copy(P1) + P.Affine() + Q := NewECP() + Q.Copy(Q1) + Q.Affine() + + Qx := NewFPcopy(Q.getx()) + Qy := NewFPcopy(Q.gety()) + + A := NewECP8() + r := NewFP48int(1) + + A.Copy(P) + NP := NewECP8() + NP.Copy(P) + NP.neg() + + nb := lbits(n3, n) + + for i := nb - 2; i >= 1; i-- { + r.sqr() + lv = line(A, A, Qx, Qy) + + bt := n3.bit(i) - n.bit(i) + if bt == 1 { + lv2 = line(A, P, Qx, Qy) + lv.smul(lv2) + } + if bt == -1 { + lv2 = line(A, NP, Qx, Qy) + lv.smul(lv2) + } + r.ssmul(lv) + } + + if SIGN_OF_X == NEGATIVEX { + r.conj() + } + + return r +} + +/* Optimal R-ate double pairing e(P,Q).e(R,S) */ +func Ate2(P1 *ECP8, Q1 *ECP, R1 *ECP8, S1 *ECP) *FP48 { + n := NewBIG() + n3 := NewBIG() + var lv, lv2 *FP48 + + if Q1.Is_infinity() { + return Ate(R1, S1) + } + if S1.Is_infinity() { + return Ate(P1, Q1) + } + + P := NewECP8() + P.Copy(P1) + P.Affine() + Q := NewECP() + Q.Copy(Q1) + Q.Affine() + R := NewECP8() + R.Copy(R1) + R.Affine() + S := NewECP() + S.Copy(S1) + S.Affine() + + Qx := NewFPcopy(Q.getx()) + Qy := NewFPcopy(Q.gety()) + Sx := NewFPcopy(S.getx()) + Sy := NewFPcopy(S.gety()) + + A := NewECP8() + B := NewECP8() + r := NewFP48int(1) + + A.Copy(P) + B.Copy(R) + NP := NewECP8() + NP.Copy(P) + NP.neg() + NR := NewECP8() + NR.Copy(R) + NR.neg() + + nb := lbits(n3, n) + + for i := nb - 2; i >= 1; i-- { + r.sqr() + lv = line(A, A, Qx, Qy) + lv2 = line(B, B, Sx, Sy) + lv.smul(lv2) + r.ssmul(lv) + bt := n3.bit(i) - n.bit(i) + if bt == 1 { + lv = line(A, P, Qx, Qy) + lv2 = line(B, R, Sx, Sy) + lv.smul(lv2) + r.ssmul(lv) + } + if bt == -1 { + lv = line(A, NP, Qx, Qy) + lv2 = line(B, NR, Sx, Sy) + lv.smul(lv2) + r.ssmul(lv) + } + } + + if SIGN_OF_X == NEGATIVEX { + r.conj() + } + + return r +} + +/* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */ +func Fexp(m *FP48) *FP48 { + f := NewFP2bigs(NewBIGints(Fra), NewBIGints(Frb)) + x := NewBIGints(CURVE_Bnx) + r := NewFP48copy(m) + // var t1, t2 *FP48 + + /* Easy part of final exp */ + lv := NewFP48copy(r) + + lv.Inverse() + r.conj() + + r.Mul(lv) + lv.Copy(r) + r.frob(f, 8) + r.Mul(lv) + + /* Hard part of final exp */ + // See https://eprint.iacr.org/2020/875.pdf + y1 := NewFP48copy(r) + y1.usqr() + y1.Mul(r) // y1=r^3 + + y0 := NewFP48copy(r.Pow(x)) + if SIGN_OF_X == NEGATIVEX { + y0.conj() + } + t0 := NewFP48copy(r) + t0.conj() + r.Copy(y0) + r.Mul(t0) + + y0.Copy(r.Pow(x)) + if SIGN_OF_X == NEGATIVEX { + y0.conj() + } + t0.Copy(r) + t0.conj() + r.Copy(y0) + r.Mul(t0) + + // ^(x+p) + y0.Copy(r.Pow(x)) + if SIGN_OF_X == NEGATIVEX { + y0.conj() + } + t0.Copy(r) + t0.frob(f, 1) + r.Copy(y0) + r.Mul(t0) + + // ^(x^2+p^2) + y0.Copy(r.Pow(x)) + y0.Copy(y0.Pow(x)) + t0.Copy(r) + t0.frob(f, 2) + r.Copy(y0) + r.Mul(t0) + + // ^(x^4+p^4) + y0.Copy(r.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + t0.Copy(r) + t0.frob(f, 4) + r.Copy(y0) + r.Mul(t0) + + // ^(x^8+p^8-1) + y0.Copy(r.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + y0.Copy(y0.Pow(x)) + t0.Copy(r) + t0.frob(f, 8) + y0.Mul(t0) + t0.Copy(r) + t0.conj() + r.Copy(y0) + r.Mul(t0) + + r.Mul(y1) + r.reduce() + + /* + // Ghamman & Fouotsa Method + + t7 := NewFP48copy(r) + t7.usqr() + + if x.parity() == 1 { + t2 = r.Pow(x) + t1 = NewFP48copy(t2) + t1.usqr() + t2 = t2.Pow(x) + } else { + t1 = t7.Pow(x) + x.fshr(1) + t2 = t1.Pow(x) + x.fshl(1) + } + + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3 := NewFP48copy(t1) + t3.conj() + t2.Mul(t3) + t2.Mul(r) + + r.Mul(t7) + + t1 = t2.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + t3.Copy(t1) + t3.frob(f, 14) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 13) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 12) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 11) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 10) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 9) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 8) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t2) + t3.conj() + t1.Mul(t3) + t3.Copy(t1) + t3.frob(f, 7) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 6) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 5) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 4) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 3) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 2) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + t3.Copy(t1) + t3.frob(f, 1) + r.Mul(t3) + t1 = t1.Pow(x) + if SIGN_OF_X == NEGATIVEX { + t1.conj() + } + + r.Mul(t1) + t2.frob(f, 15) + r.Mul(t2) + + r.reduce() + */ + return r +} + +/* GLV method */ +func glv(ee *BIG) []*BIG { + var u []*BIG + + q := NewBIGints(CURVE_Order) + x := NewBIGints(CURVE_Bnx) + x2 := smul(x, x) + x = smul(x2, x2) + x2 = smul(x, x) + bd := uint(q.nbits() - x2.nbits()) + u = append(u, NewBIGcopy(ee)) + u[0].ctmod(x2, bd) + u = append(u, NewBIGcopy(ee)) + u[1].ctdiv(x2, bd) + u[1].rsub(q) + return u +} + +/* Galbraith & Scott Method */ +func gs(ee *BIG) []*BIG { + var u []*BIG + + q := NewBIGints(CURVE_Order) + x := NewBIGints(CURVE_Bnx) + bd := uint(q.nbits() - x.nbits()) + w := NewBIGcopy(ee) + for i := 0; i < 15; i++ { + u = append(u, NewBIGcopy(w)) + u[i].ctmod(x, bd) + w.ctdiv(x, bd) + } + u = append(u, NewBIGcopy(w)) + if SIGN_OF_X == NEGATIVEX { + u[1].copy(Modneg(u[1], q)) + u[3].copy(Modneg(u[3], q)) + u[5].copy(Modneg(u[5], q)) + u[7].copy(Modneg(u[7], q)) + u[9].copy(Modneg(u[9], q)) + u[11].copy(Modneg(u[11], q)) + u[13].copy(Modneg(u[13], q)) + u[15].copy(Modneg(u[15], q)) + } + + return u +} + +/* Multiply P by e in group G1 */ +func G1mul(P *ECP, e *BIG) *ECP { + var R *ECP + q := NewBIGints(CURVE_Order) + ee := NewBIGcopy(e) + ee.Mod(q) + if USE_GLV { + R = NewECP() + R.Copy(P) + Q := NewECP() + Q.Copy(P) + Q.Affine() + + cru := NewFPbig(NewBIGints(CRu)) + t := NewBIGint(0) + u := glv(ee) + Q.getx().mul(cru) + + np := u[0].nbits() + t.copy(Modneg(u[0], q)) + nn := t.nbits() + if nn < np { + u[0].copy(t) + R.Neg() + } + + np = u[1].nbits() + t.copy(Modneg(u[1], q)) + nn = t.nbits() + if nn < np { + u[1].copy(t) + Q.Neg() + } + u[0].norm() + u[1].norm() + R = R.Mul2(u[0], Q, u[1]) + + } else { + R = P.clmul(e, q) + } + return R +} + +/* Multiply P by e in group G2 */ +func G2mul(P *ECP8, e *BIG) *ECP8 { + var R *ECP8 + q := NewBIGints(CURVE_Order) + ee := NewBIGcopy(e) + ee.Mod(q) + if USE_GS_G2 { + var Q []*ECP8 + + F := ECP8_frob_constants() + u := gs(ee) + + t := NewBIGint(0) + + Q = append(Q, NewECP8()) + Q[0].Copy(P) + for i := 1; i < 16; i++ { + Q = append(Q, NewECP8()) + Q[i].Copy(Q[i-1]) + Q[i].frob(F, 1) + } + for i := 0; i < 16; i++ { + np := u[i].nbits() + t.copy(Modneg(u[i], q)) + nn := t.nbits() + if nn < np { + u[i].copy(t) + Q[i].neg() + } + u[i].norm() + } + + R = mul16(Q, u) + + } else { + R = P.mul(e) + } + return R +} + +/* f=f^e */ +/* Note that this method requires a lot of RAM! */ +func GTpow(d *FP48, e *BIG) *FP48 { + var r *FP48 + q := NewBIGints(CURVE_Order) + ee := NewBIGcopy(e) + ee.Mod(q) + if USE_GS_GT { + var g []*FP48 + f := NewFP2bigs(NewBIGints(Fra), NewBIGints(Frb)) + t := NewBIGint(0) + + u := gs(ee) + + g = append(g, NewFP48copy(d)) + for i := 1; i < 16; i++ { + g = append(g, NewFP48()) + g[i].Copy(g[i-1]) + g[i].frob(f, 1) + } + for i := 0; i < 16; i++ { + np := u[i].nbits() + t.copy(Modneg(u[i], q)) + nn := t.nbits() + if nn < np { + u[i].copy(t) + g[i].conj() + } + u[i].norm() + } + r = pow16(g, u) + } else { + r = d.Pow(ee) + } + return r +} + +/* test G1 group membership */ +func G1member(P *ECP) bool { + if P.Is_infinity() { + return false + } + x := NewBIGints(CURVE_Bnx) + cru := NewFPbig(NewBIGints(CRu)) + W := NewECP() + W.Copy(P) + W.getx().mul(cru) + T := P.mul(x) + if P.Equals(T) { + return false + } // P is of low order + T = T.mul(x) + T = T.mul(x) + T = T.mul(x) + T = T.mul(x) + T = T.mul(x) + T = T.mul(x) + T = T.mul(x) + T.Neg() + if !W.Equals(T) { + return false + } + + // Not needed + // W.Add(P); + // T.getx().mul(cru) + // W.Add(T) + // if !W.Is_infinity() {return false} + /* + q := NewBIGints(CURVE_Order) + if P.Is_infinity() {return false} + W:=P.mul(q) + if !W.Is_infinity() {return false} */ + return true +} + +/* test G2 group membership */ +func G2member(P *ECP8) bool { + if P.Is_infinity() { + return false + } + F := ECP8_frob_constants() + x := NewBIGints(CURVE_Bnx) + W := NewECP8() + W.Copy(P) + W.frob(F, 1) + T := P.mul(x) + if SIGN_OF_X == NEGATIVEX { + T.neg() + } + /* + R:=NewECP8(); R.Copy(W) + R.frob(F,1) + W.Sub(R) + R.Copy(T) + R.frob(F,1) + W.Add(R) + */ + if !W.Equals(T) { + return false + } + return true + /* + q := NewBIGints(CURVE_Order) + if P.Is_infinity() {return false} + W:=P.mul(q) + if !W.Is_infinity() {return false} + return true */ +} + +/* Check that m is in cyclotomic sub-group */ +/* Check that m!=1, conj(m)*m==1, and m.m^{p^16}=m^{p^8} */ +func GTcyclotomic(m *FP48) bool { + if m.Isunity() { + return false + } + r := NewFP48copy(m) + r.conj() + r.Mul(m) + if !r.Isunity() { + return false + } + + f := NewFP2bigs(NewBIGints(Fra), NewBIGints(Frb)) + + r.Copy(m) + r.frob(f, 8) + w := NewFP48copy(r) + w.frob(f, 8) + w.Mul(m) + if !w.Equals(r) { + return false + } + return true +} + +/* test for full GT membership */ +func GTmember(m *FP48) bool { + if !GTcyclotomic(m) { + return false + } + f := NewFP2bigs(NewBIGints(Fra), NewBIGints(Frb)) + x := NewBIGints(CURVE_Bnx) + + r := NewFP48copy(m) + r.frob(f, 1) + t := m.Pow(x) + + if SIGN_OF_X == NEGATIVEX { + t.conj() + } + if !r.Equals(t) { + return false + } + return true + + /* + q := NewBIGints(CURVE_Order) + r := m.Pow(q) + if !r.Isunity() { + return false + } + return true */ +} diff --git a/ec/bls48581/ROM.go b/ec/bls48581/ROM.go new file mode 100644 index 0000000..7e0400a --- /dev/null +++ b/ec/bls48581/ROM.go @@ -0,0 +1,74 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/* Fixed Data in ROM - Field and Curve parameters */ + +package bls48581 + +// Base Bits= 29 +var Modulus = [...]Chunk{0x565912B, 0x16E0AA73, 0x12922B0F, 0x1FBEE434, 0xEE0A578, 0x12A898B8, 0xBDA0D9E, 0x9E8E6DB, 0x19CD3039, 0x17041566, 0x2B90EBD, 0xEA88949, 0xC0F1F39, 0x18DD9DF3, 0x1E344884, 0xADD09, 0x1D47012A, 0x9C12718, 0x1CD1DBCC, 0x501EE7F, 0x1} +var ROI = [...]Chunk{0x565912A, 0x16E0AA73, 0x12922B0F, 0x1FBEE434, 0xEE0A578, 0x12A898B8, 0xBDA0D9E, 0x9E8E6DB, 0x19CD3039, 0x17041566, 0x2B90EBD, 0xEA88949, 0xC0F1F39, 0x18DD9DF3, 0x1E344884, 0xADD09, 0x1D47012A, 0x9C12718, 0x1CD1DBCC, 0x501EE7F, 0x1} +var R2modp = [...]Chunk{0x19BCC5B0, 0x126A343E, 0xA46F6C0, 0x29B7799, 0xB758510, 0x1357043D, 0x1DC2D482, 0x115A8C75, 0x1F6CA5F6, 0x9B40365, 0x16E1C7DB, 0x1A304684, 0xA85F60F, 0x16E21141, 0x1D5AE21, 0xD9EA745, 0x1641FB69, 0x249C4AC, 0xA2B23E1, 0x14FCE472, 0x0} +var SQRTm3 = [...]Chunk{0x1D65A0A, 0x8F6FE15, 0xB6336FD, 0xC5B5452, 0x69D616D, 0x8923C1, 0x1E2B5C49, 0x4BA7957, 0x13E4CD6C, 0x14D8B5AE, 0x583BB23, 0x14076E71, 0x14343F50, 0x121BB7F6, 0xB818699, 0x11F7124B, 0x1EAABFFD, 0x4635146, 0x69D8024, 0x501EE7F, 0x1} + +const MConst Chunk = 0x39D5A7D + +var Fra = [...]Chunk{0x42AEB25, 0x1175B67F, 0x182B4FE5, 0x1683284E, 0x115ECE4D, 0x1EF92B83, 0x22B03E9, 0x6EF6A24, 0x8C41890, 0x4249F0E, 0x61F9A1, 0xC60FC53, 0x16B62F49, 0x71E57E, 0xF9E161D, 0xFA08F30, 0x1E55F606, 0x1AE6BF39, 0x140527E9, 0x1FA61B6, 0x0} +var Frb = [...]Chunk{0x42AEB25, 0x1175B67F, 0x182B4FE5, 0x1683284E, 0x115ECE4D, 0x1EF92B83, 0x22B03E9, 0x6EF6A24, 0x8C41890, 0x4249F0E, 0x61F9A1, 0xC60FC53, 0x16B62F49, 0x71E57E, 0xF9E161D, 0xFA08F30, 0x1E55F606, 0x1AE6BF39, 0x140527E9, 0x1FA61B6, 0x0} +var TWK = [...]Chunk{0x1F426953, 0x1DA19E92, 0xEE618F5, 0x159C8B24, 0xD37E160, 0x145DEFD1, 0xD2F0630, 0x1FF9915F, 0x2C4F62, 0xDA1C978, 0x51E0598, 0x4FD2A34, 0x132462ED, 0x13341DC2, 0x81D59C2, 0x19374271, 0x1D9EAEB8, 0x1ABB4E6E, 0xDEF0401, 0x74CB4A, 0x0} + +//*** rom curve parameters ***** +// Base Bits= 29 +// Ate Bits= 33 +// G2 Table size= 36 + +const CURVE_Cof_I int = 0 + +var CURVE_Cof = [...]Chunk{0x382, 0xA, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0} + +const CURVE_B_I int = 1 + +var CURVE_B = [...]Chunk{0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0} +var CURVE_Order = [...]Chunk{0xD671C01, 0x52FF37E, 0x10936846, 0x1CB328CF, 0x103C4CCB, 0x1E682B11, 0x5AA171, 0x6989924, 0x741969D, 0xB961737, 0xFEB5AF2, 0x16797C00, 0x1387A3F0, 0x6B631A, 0x13305857, 0xBC46753, 0x925E288, 0x11C37C5, 0x0, 0x0, 0x0} +var CURVE_Gx = [...]Chunk{0x115AF640, 0x1E743991, 0x79B630E, 0x9B4BA74, 0x11786CB7, 0x1ED9B458, 0x1BAF6F15, 0xBB0B246, 0x4584766, 0x14EFB7CB, 0x1154151A, 0x1F73EEA8, 0xBDBAEDF, 0x3467B0D, 0x15F83A1A, 0xC1BC7E4, 0x1F1E93F8, 0x1D795B9E, 0xB0D03CA, 0x55EB36F, 0x0} +var CURVE_Gy = [...]Chunk{0x2587A70, 0xDDAEF1F, 0x49AD5DB, 0x6F5DEF7, 0x11B2E35F, 0x1BE143B6, 0x8BD21FD, 0xB0987DE, 0x1E80F678, 0x1CC57729, 0xEDEFBFE, 0x16E41DEF, 0x1279DD41, 0x52974C8, 0xF27BFAE, 0x149114AA, 0xD1FB398, 0xFC359D1, 0x1D94C7E4, 0x19DFB489, 0x0} +var CURVE_HTPC = [...]Chunk{0x31193EC, 0x1C9F85F0, 0x1D6090C, 0x5112C88, 0x10D4620C, 0x1F255473, 0x1F5583B6, 0x4F7AABD, 0xCD0706B, 0x14B125F7, 0xECD8492, 0x4D5AF8A, 0xC755E26, 0x2D4C018, 0xB0B7761, 0x1369CD4C, 0x1FD42938, 0x782EC54, 0x17716BE5, 0x1246919A, 0x0} + +var CURVE_Bnx = [...]Chunk{0x381, 0xA, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0} +var CRu = [...]Chunk{0x1C79B90, 0x6F4D62F, 0x3977A09, 0x19B1C7F1, 0x1421A205, 0x190FBA7B, 0x16D758AA, 0x129736C1, 0x2F43166, 0x115AFDC, 0x1E9AA9CD, 0xD508D6B, 0xBED6FF4, 0x1360F2FE, 0x95960F5, 0x709E55F, 0x1F4E2096, 0x2AEEAE8, 0xB1A2DD4, 0x0, 0x0} +var CURVE_Pxaaa = [...]Chunk{0xCE8BFAB, 0x1A7E85A5, 0x85537B0, 0xF2ECC64, 0x1510317B, 0x6C0248F, 0x140C01, 0x140C25E8, 0x281A63C, 0x168D4621, 0x1BFDE6EA, 0x1DE2AD88, 0x64DB3A2, 0xDE65BEF, 0x1F1C0D13, 0x1BD7577D, 0x45A2775, 0x11C11BFD, 0x9E1C792, 0xBAC2BB3, 0x0} +var CURVE_Pxaab = [...]Chunk{0x16B47C57, 0x134D9B33, 0x1E850FC5, 0xAAD4035, 0x30FFD75, 0x1186CBCB, 0x13C30F1D, 0x1FF4C4A0, 0x214A76A, 0x15FF6F8B, 0xE50E802, 0xFE9C38, 0xF6DA123, 0x111F4A93, 0x1B660385, 0x1D164576, 0x86ABC07, 0x9034D87, 0x13889614, 0xF892E7D, 0x0} +var CURVE_Pxaba = [...]Chunk{0x55A3E6A, 0x440AB65, 0xCFC2D19, 0x1E99BDAD, 0x1D5FEA8E, 0x1EFDDC3C, 0x157C0A32, 0x1E1A54DA, 0xFFAE766, 0xDE8C921, 0x18058707, 0x156B56D0, 0x16957CCB, 0x1BE53D36, 0x1B2A6B88, 0x178E7514, 0x1853AD83, 0x70D9750, 0x663C4CD, 0x3F998E0, 0x0} +var CURVE_Pxabb = [...]Chunk{0x1B7FEAFE, 0xD3819E5, 0x2F0FC2, 0x171969D, 0xCA5231, 0x292BE10, 0x51A30C7, 0x16364F37, 0xE6EC143, 0x11F0E3BB, 0x862A57D, 0x1F17C198, 0x1B92A393, 0x1F2C10DB, 0x16B18BC, 0x17FD1EB3, 0x12954D4, 0x2E3C6C0, 0x973AD86, 0x17C44318, 0x0} +var CURVE_Pxbaa = [...]Chunk{0x13F8CCE5, 0x1CE1D0E2, 0x7532EDC, 0x16BEE8D9, 0x1AA80C65, 0xAFE0C44, 0x49D3EB5, 0x9255CB1, 0xC10B2EF, 0x40CCEAD, 0x6607E79, 0xA70CD3, 0x1F0E7C58, 0x15AB3AF, 0x1D742C59, 0xC600F8C, 0x4CAA9DD, 0x1D1E2CC7, 0x2CD644, 0x717238C, 0x0} +var CURVE_Pxbab = [...]Chunk{0xA3C093A, 0x10026C8A, 0x138CDC3C, 0x12C1221F, 0xF097FC7, 0xF8BBB09, 0x175D656A, 0x1738162B, 0x1EB57B40, 0x1AE944CB, 0x77D8E0, 0x6E8303, 0x58677BB, 0xBBD1E8D, 0xD773BC2, 0x111EF71E, 0x1E4ECDA0, 0x101F8988, 0x1FAC1CE1, 0x192D8EF2, 0x0} +var CURVE_Pxbba = [...]Chunk{0x750E057, 0xB03F30, 0x170CD539, 0x16B61C40, 0x2D63334, 0x1F219261, 0xCAAB472, 0xBDF9E68, 0x10FD0CAA, 0x9D89E76, 0x13BC47CA, 0x16F4893, 0x1908BA2C, 0x1C295B6D, 0x106CE744, 0x1CCC1BD4, 0x98908AE, 0x1F80CBD2, 0x118187B8, 0x1736F2A3, 0x0} +var CURVE_Pxbbb = [...]Chunk{0x1BC6AE34, 0x10CED007, 0x5F0FE13, 0x15E5F93D, 0x1FC44E56, 0x1EB575FC, 0x116151E6, 0x16FC561A, 0x164A7190, 0x1F94E7F9, 0x1E33F2A4, 0xE514FF3, 0xF741719, 0x3DA908E, 0xA77BEBD, 0x563CBAF, 0xC4F4AAA, 0x2941312, 0xBECAF7B, 0x104FAB84, 0x0} +var CURVE_Pyaaa = [...]Chunk{0xD2D7971, 0x1F6E9FF2, 0xB03FCC8, 0xA025562, 0x6D65904, 0x15FBBF75, 0x18F05666, 0xDB15CA2, 0xD90F733, 0x17D13BA4, 0x24188D6, 0x86BF556, 0x1B39EBFC, 0x12BBF379, 0x108E0166, 0x4972316, 0x16452F30, 0xFD24B90, 0x1B0DD6D7, 0x1D6A66A, 0x0} +var CURVE_Pyaab = [...]Chunk{0x16CD5665, 0xA38EDC9, 0x1FF1EC44, 0x16846A4B, 0xE2E588, 0x1D04BEBB, 0x1877484B, 0x11255649, 0x12C5C3D1, 0x121D8F8C, 0xBEC25AC, 0x65F97E7, 0x1D729647, 0xF37DD00, 0x108AE8C9, 0x1B856EB4, 0x11815FCA, 0xA26D329, 0x5E783FC, 0x509B8EB, 0x0} +var CURVE_Pyaba = [...]Chunk{0xA2A8474, 0x1995293, 0xEE3F79A, 0x18F88DF8, 0x52269CB, 0x9AEA8D3, 0x178BC307, 0x194652BC, 0x11515536, 0xE874820, 0x17DF5726, 0xE0A288E, 0x13A480D3, 0x16AD88CE, 0x1140C085, 0x13DE585F, 0x17036766, 0x1F210F7D, 0x17402148, 0x166D4403, 0x0} +var CURVE_Pyabb = [...]Chunk{0x841589D, 0x1109ED49, 0x194CDCC5, 0x7B17143, 0x5E578FB, 0x1ED281F7, 0xE84359E, 0xEE84EE1, 0xDCED281, 0x199FD20, 0xB226C89, 0x245A4E8, 0xB0E710E, 0x7711EEC, 0x1B4CD837, 0x563859B, 0x1BD47876, 0x144111FD, 0x1887B701, 0x15D84B48, 0x0} +var CURVE_Pybaa = [...]Chunk{0x2E50137, 0x3C18FCC, 0x13DE90FD, 0xAFFBBBF, 0x1137B088, 0x9ACA2E, 0x13D67D0C, 0x9CA256C, 0x8A1E2CA, 0x111C66E7, 0x16171DFE, 0x2530AFD, 0x159805F1, 0xEC9DAD4, 0x11506D0F, 0xB44AA9B, 0x1A5A8832, 0x148B281F, 0x88EA711, 0x1A413AB4, 0x0} +var CURVE_Pybab = [...]Chunk{0xF90BEE4, 0x776E2C6, 0x1B3CE965, 0xB3DB044, 0x12B679DA, 0xCC6553, 0xE78EABF, 0xF8301A2, 0x1F6824F4, 0x6138420, 0xA0D083A, 0x156EA09F, 0x182E2055, 0x1915AC4E, 0x159BAC59, 0x17208435, 0x1D5AD537, 0x1289E99C, 0x115CDADE, 0xFA1A06E, 0x0} +var CURVE_Pybba = [...]Chunk{0x1EB23986, 0xA0FD757, 0x6A98ACF, 0x110802FB, 0x13DCCC9E, 0x7D31CFA, 0x62D6ED0, 0x118E964C, 0x122C1FAB, 0x11D14327, 0x63D096B, 0x10334DBF, 0x15F14E4C, 0xD8320A, 0xD93F021, 0x1F1400DE, 0x1DFDD17A, 0x112E1682, 0x46F997A, 0x112CECF0, 0x0} +var CURVE_Pybbb = [...]Chunk{0x132718B6, 0x133FFE5B, 0x1A71575, 0x158CDD08, 0x13F748E5, 0x6C62559, 0x1505CC0, 0x7D8E324, 0x1E1AD033, 0x14E18F4B, 0xCE8FE39, 0x1D95352A, 0x149B6EF8, 0x728643A, 0x1C501AFA, 0x36BC0D1, 0x7E84F98, 0x9C9D2E0, 0x1FE240A7, 0x6BC4A49, 0x0} + +//var CURVE_W=[2][21]Chunk {{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}} +//var CURVE_SB=[2][2][21]Chunk {{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}},{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}}} +//var CURVE_WB=[4][21]Chunk {{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}} +//var CURVE_BB=[4][4][21]Chunk {{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}},{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}},{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}},{{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0},{0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0}}} diff --git a/ec/bls48581/core/AES.go b/ec/bls48581/core/AES.go new file mode 100644 index 0000000..5767e66 --- /dev/null +++ b/ec/bls48581/core/AES.go @@ -0,0 +1,835 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* AES Encryption */ + +package core + +//import "fmt" + +const AES_ECB int = 0 +const AES_CBC int = 1 +const AES_CFB1 int = 2 +const AES_CFB2 int = 3 +const AES_CFB4 int = 5 +const AES_OFB1 int = 14 +const AES_OFB2 int = 15 +const AES_OFB4 int = 17 +const AES_OFB8 int = 21 +const AES_OFB16 int = 29 +const AES_CTR1 int = 30 +const AES_CTR2 int = 31 +const AES_CTR4 int = 33 +const AES_CTR8 int = 37 +const AES_CTR16 int = 45 + +var aes_InCo = [...]byte{0xB, 0xD, 0x9, 0xE} /* Inverse Coefficients */ + +var aes_ptab = [...]byte{ + 1, 3, 5, 15, 17, 51, 85, 255, 26, 46, 114, 150, 161, 248, 19, 53, + 95, 225, 56, 72, 216, 115, 149, 164, 247, 2, 6, 10, 30, 34, 102, 170, + 229, 52, 92, 228, 55, 89, 235, 38, 106, 190, 217, 112, 144, 171, 230, 49, + 83, 245, 4, 12, 20, 60, 68, 204, 79, 209, 104, 184, 211, 110, 178, 205, + 76, 212, 103, 169, 224, 59, 77, 215, 98, 166, 241, 8, 24, 40, 120, 136, + 131, 158, 185, 208, 107, 189, 220, 127, 129, 152, 179, 206, 73, 219, 118, 154, + 181, 196, 87, 249, 16, 48, 80, 240, 11, 29, 39, 105, 187, 214, 97, 163, + 254, 25, 43, 125, 135, 146, 173, 236, 47, 113, 147, 174, 233, 32, 96, 160, + 251, 22, 58, 78, 210, 109, 183, 194, 93, 231, 50, 86, 250, 21, 63, 65, + 195, 94, 226, 61, 71, 201, 64, 192, 91, 237, 44, 116, 156, 191, 218, 117, + 159, 186, 213, 100, 172, 239, 42, 126, 130, 157, 188, 223, 122, 142, 137, 128, + 155, 182, 193, 88, 232, 35, 101, 175, 234, 37, 111, 177, 200, 67, 197, 84, + 252, 31, 33, 99, 165, 244, 7, 9, 27, 45, 119, 153, 176, 203, 70, 202, + 69, 207, 74, 222, 121, 139, 134, 145, 168, 227, 62, 66, 198, 81, 243, 14, + 18, 54, 90, 238, 41, 123, 141, 140, 143, 138, 133, 148, 167, 242, 13, 23, + 57, 75, 221, 124, 132, 151, 162, 253, 28, 36, 108, 180, 199, 82, 246, 1} + +var aes_ltab = [...]byte{ + 0, 255, 25, 1, 50, 2, 26, 198, 75, 199, 27, 104, 51, 238, 223, 3, + 100, 4, 224, 14, 52, 141, 129, 239, 76, 113, 8, 200, 248, 105, 28, 193, + 125, 194, 29, 181, 249, 185, 39, 106, 77, 228, 166, 114, 154, 201, 9, 120, + 101, 47, 138, 5, 33, 15, 225, 36, 18, 240, 130, 69, 53, 147, 218, 142, + 150, 143, 219, 189, 54, 208, 206, 148, 19, 92, 210, 241, 64, 70, 131, 56, + 102, 221, 253, 48, 191, 6, 139, 98, 179, 37, 226, 152, 34, 136, 145, 16, + 126, 110, 72, 195, 163, 182, 30, 66, 58, 107, 40, 84, 250, 133, 61, 186, + 43, 121, 10, 21, 155, 159, 94, 202, 78, 212, 172, 229, 243, 115, 167, 87, + 175, 88, 168, 80, 244, 234, 214, 116, 79, 174, 233, 213, 231, 230, 173, 232, + 44, 215, 117, 122, 235, 22, 11, 245, 89, 203, 95, 176, 156, 169, 81, 160, + 127, 12, 246, 111, 23, 196, 73, 236, 216, 67, 31, 45, 164, 118, 123, 183, + 204, 187, 62, 90, 251, 96, 177, 134, 59, 82, 161, 108, 170, 85, 41, 157, + 151, 178, 135, 144, 97, 190, 220, 252, 188, 149, 207, 205, 55, 63, 91, 209, + 83, 57, 132, 60, 65, 162, 109, 71, 20, 42, 158, 93, 86, 242, 211, 171, + 68, 17, 146, 217, 35, 32, 46, 137, 180, 124, 184, 38, 119, 153, 227, 165, + 103, 74, 237, 222, 197, 49, 254, 24, 13, 99, 140, 128, 192, 247, 112, 7} + +var aes_fbsub = [...]byte{ + 99, 124, 119, 123, 242, 107, 111, 197, 48, 1, 103, 43, 254, 215, 171, 118, + 202, 130, 201, 125, 250, 89, 71, 240, 173, 212, 162, 175, 156, 164, 114, 192, + 183, 253, 147, 38, 54, 63, 247, 204, 52, 165, 229, 241, 113, 216, 49, 21, + 4, 199, 35, 195, 24, 150, 5, 154, 7, 18, 128, 226, 235, 39, 178, 117, + 9, 131, 44, 26, 27, 110, 90, 160, 82, 59, 214, 179, 41, 227, 47, 132, + 83, 209, 0, 237, 32, 252, 177, 91, 106, 203, 190, 57, 74, 76, 88, 207, + 208, 239, 170, 251, 67, 77, 51, 133, 69, 249, 2, 127, 80, 60, 159, 168, + 81, 163, 64, 143, 146, 157, 56, 245, 188, 182, 218, 33, 16, 255, 243, 210, + 205, 12, 19, 236, 95, 151, 68, 23, 196, 167, 126, 61, 100, 93, 25, 115, + 96, 129, 79, 220, 34, 42, 144, 136, 70, 238, 184, 20, 222, 94, 11, 219, + 224, 50, 58, 10, 73, 6, 36, 92, 194, 211, 172, 98, 145, 149, 228, 121, + 231, 200, 55, 109, 141, 213, 78, 169, 108, 86, 244, 234, 101, 122, 174, 8, + 186, 120, 37, 46, 28, 166, 180, 198, 232, 221, 116, 31, 75, 189, 139, 138, + 112, 62, 181, 102, 72, 3, 246, 14, 97, 53, 87, 185, 134, 193, 29, 158, + 225, 248, 152, 17, 105, 217, 142, 148, 155, 30, 135, 233, 206, 85, 40, 223, + 140, 161, 137, 13, 191, 230, 66, 104, 65, 153, 45, 15, 176, 84, 187, 22} + +var aes_rbsub = [...]byte{ + 82, 9, 106, 213, 48, 54, 165, 56, 191, 64, 163, 158, 129, 243, 215, 251, + 124, 227, 57, 130, 155, 47, 255, 135, 52, 142, 67, 68, 196, 222, 233, 203, + 84, 123, 148, 50, 166, 194, 35, 61, 238, 76, 149, 11, 66, 250, 195, 78, + 8, 46, 161, 102, 40, 217, 36, 178, 118, 91, 162, 73, 109, 139, 209, 37, + 114, 248, 246, 100, 134, 104, 152, 22, 212, 164, 92, 204, 93, 101, 182, 146, + 108, 112, 72, 80, 253, 237, 185, 218, 94, 21, 70, 87, 167, 141, 157, 132, + 144, 216, 171, 0, 140, 188, 211, 10, 247, 228, 88, 5, 184, 179, 69, 6, + 208, 44, 30, 143, 202, 63, 15, 2, 193, 175, 189, 3, 1, 19, 138, 107, + 58, 145, 17, 65, 79, 103, 220, 234, 151, 242, 207, 206, 240, 180, 230, 115, + 150, 172, 116, 34, 231, 173, 53, 133, 226, 249, 55, 232, 28, 117, 223, 110, + 71, 241, 26, 113, 29, 41, 197, 137, 111, 183, 98, 14, 170, 24, 190, 27, + 252, 86, 62, 75, 198, 210, 121, 32, 154, 219, 192, 254, 120, 205, 90, 244, + 31, 221, 168, 51, 136, 7, 199, 49, 177, 18, 16, 89, 39, 128, 236, 95, + 96, 81, 127, 169, 25, 181, 74, 13, 45, 229, 122, 159, 147, 201, 156, 239, + 160, 224, 59, 77, 174, 42, 245, 176, 200, 235, 187, 60, 131, 83, 153, 97, + 23, 43, 4, 126, 186, 119, 214, 38, 225, 105, 20, 99, 85, 33, 12, 125} + +var aes_rco = [...]byte{1, 2, 4, 8, 16, 32, 64, 128, 27, 54, 108, 216, 171, 77, 154, 47} + +var aes_ftable = [...]uint32{ + 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6, 0xdf2f2ff, 0xbd6b6bd6, + 0xb16f6fde, 0x54c5c591, 0x50303060, 0x3010102, 0xa96767ce, 0x7d2b2b56, + 0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0x45caca8f, 0x9d82821f, + 0x40c9c989, 0x877d7dfa, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0xbf0f0fb, + 0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0xbf9c9c23, 0xf7a4a453, + 0x967272e4, 0x5bc0c09b, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c, + 0x5a36366c, 0x413f3f7e, 0x2f7f7f5, 0x4fcccc83, 0x5c343468, 0xf4a5a551, + 0x34e5e5d1, 0x8f1f1f9, 0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, + 0xc040408, 0x52c7c795, 0x65232346, 0x5ec3c39d, 0x28181830, 0xa1969637, + 0xf05050a, 0xb59a9a2f, 0x907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, + 0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x1b090912, 0x9e83831d, + 0x742c2c58, 0x2e1a1a34, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b, + 0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x7b292952, 0x3ee3e3dd, + 0x712f2f5e, 0x97848413, 0xf55353a6, 0x68d1d1b9, 0x0, 0x2cededc1, + 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6, 0xbe6a6ad4, 0x46cbcb8d, + 0xd9bebe67, 0x4b393972, 0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, + 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed, 0xc5434386, 0xd74d4d9a, + 0x55333366, 0x94858511, 0xcf45458a, 0x10f9f9e9, 0x6020204, 0x817f7ffe, + 0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0xf35151a2, 0xfea3a35d, + 0xc0404080, 0x8a8f8f05, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x4f5f5f1, + 0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0x30101020, 0x1affffe5, + 0xef3f3fd, 0x6dd2d2bf, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3, + 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e, 0x57c4c493, 0xf2a7a755, + 0x827e7efc, 0x473d3d7a, 0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, + 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3, 0x66222244, 0x7e2a2a54, + 0xab90903b, 0x8388880b, 0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, + 0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0x3be0e0db, 0x56323264, + 0x4e3a3a74, 0x1e0a0a14, 0xdb494992, 0xa06060c, 0x6c242448, 0xe45c5cb8, + 0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xa8919139, 0xa4959531, + 0x37e4e4d3, 0x8b7979f2, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda, + 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949, 0xb46c6cd8, 0xfa5656ac, + 0x7f4f4f3, 0x25eaeacf, 0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, + 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c, 0x241c1c38, 0xf1a6a657, + 0xc7b4b473, 0x51c6c697, 0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, + 0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0x907070e0, 0x423e3e7c, + 0xc4b5b571, 0xaa6666cc, 0xd8484890, 0x5030306, 0x1f6f6f7, 0x120e0e1c, + 0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0x91868617, 0x58c1c199, + 0x271d1d3a, 0xb99e9e27, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122, + 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433, 0xb69b9b2d, 0x221e1e3c, + 0x92878715, 0x20e9e9c9, 0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, + 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a, 0xdabfbf65, 0x31e6e6d7, + 0xc6424284, 0xb86868d0, 0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, + 0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c} + +var aes_rtable = [...]uint32{ + 0x50a7f451, 0x5365417e, 0xc3a4171a, 0x965e273a, 0xcb6bab3b, 0xf1459d1f, + 0xab58faac, 0x9303e34b, 0x55fa3020, 0xf66d76ad, 0x9176cc88, 0x254c02f5, + 0xfcd7e54f, 0xd7cb2ac5, 0x80443526, 0x8fa362b5, 0x495ab1de, 0x671bba25, + 0x980eea45, 0xe1c0fe5d, 0x2752fc3, 0x12f04c81, 0xa397468d, 0xc6f9d36b, + 0xe75f8f03, 0x959c9215, 0xeb7a6dbf, 0xda595295, 0x2d83bed4, 0xd3217458, + 0x2969e049, 0x44c8c98e, 0x6a89c275, 0x78798ef4, 0x6b3e5899, 0xdd71b927, + 0xb64fe1be, 0x17ad88f0, 0x66ac20c9, 0xb43ace7d, 0x184adf63, 0x82311ae5, + 0x60335197, 0x457f5362, 0xe07764b1, 0x84ae6bbb, 0x1ca081fe, 0x942b08f9, + 0x58684870, 0x19fd458f, 0x876cde94, 0xb7f87b52, 0x23d373ab, 0xe2024b72, + 0x578f1fe3, 0x2aab5566, 0x728ebb2, 0x3c2b52f, 0x9a7bc586, 0xa50837d3, + 0xf2872830, 0xb2a5bf23, 0xba6a0302, 0x5c8216ed, 0x2b1ccf8a, 0x92b479a7, + 0xf0f207f3, 0xa1e2694e, 0xcdf4da65, 0xd5be0506, 0x1f6234d1, 0x8afea6c4, + 0x9d532e34, 0xa055f3a2, 0x32e18a05, 0x75ebf6a4, 0x39ec830b, 0xaaef6040, + 0x69f715e, 0x51106ebd, 0xf98a213e, 0x3d06dd96, 0xae053edd, 0x46bde64d, + 0xb58d5491, 0x55dc471, 0x6fd40604, 0xff155060, 0x24fb9819, 0x97e9bdd6, + 0xcc434089, 0x779ed967, 0xbd42e8b0, 0x888b8907, 0x385b19e7, 0xdbeec879, + 0x470a7ca1, 0xe90f427c, 0xc91e84f8, 0x0, 0x83868009, 0x48ed2b32, + 0xac70111e, 0x4e725a6c, 0xfbff0efd, 0x5638850f, 0x1ed5ae3d, 0x27392d36, + 0x64d90f0a, 0x21a65c68, 0xd1545b9b, 0x3a2e3624, 0xb1670a0c, 0xfe75793, + 0xd296eeb4, 0x9e919b1b, 0x4fc5c080, 0xa220dc61, 0x694b775a, 0x161a121c, + 0xaba93e2, 0xe52aa0c0, 0x43e0223c, 0x1d171b12, 0xb0d090e, 0xadc78bf2, + 0xb9a8b62d, 0xc8a91e14, 0x8519f157, 0x4c0775af, 0xbbdd99ee, 0xfd607fa3, + 0x9f2601f7, 0xbcf5725c, 0xc53b6644, 0x347efb5b, 0x7629438b, 0xdcc623cb, + 0x68fcedb6, 0x63f1e4b8, 0xcadc31d7, 0x10856342, 0x40229713, 0x2011c684, + 0x7d244a85, 0xf83dbbd2, 0x1132f9ae, 0x6da129c7, 0x4b2f9e1d, 0xf330b2dc, + 0xec52860d, 0xd0e3c177, 0x6c16b32b, 0x99b970a9, 0xfa489411, 0x2264e947, + 0xc48cfca8, 0x1a3ff0a0, 0xd82c7d56, 0xef903322, 0xc74e4987, 0xc1d138d9, + 0xfea2ca8c, 0x360bd498, 0xcf81f5a6, 0x28de7aa5, 0x268eb7da, 0xa4bfad3f, + 0xe49d3a2c, 0xd927850, 0x9bcc5f6a, 0x62467e54, 0xc2138df6, 0xe8b8d890, + 0x5ef7392e, 0xf5afc382, 0xbe805d9f, 0x7c93d069, 0xa92dd56f, 0xb31225cf, + 0x3b99acc8, 0xa77d1810, 0x6e639ce8, 0x7bbb3bdb, 0x97826cd, 0xf418596e, + 0x1b79aec, 0xa89a4f83, 0x656e95e6, 0x7ee6ffaa, 0x8cfbc21, 0xe6e815ef, + 0xd99be7ba, 0xce366f4a, 0xd4099fea, 0xd67cb029, 0xafb2a431, 0x31233f2a, + 0x3094a5c6, 0xc066a235, 0x37bc4e74, 0xa6ca82fc, 0xb0d090e0, 0x15d8a733, + 0x4a9804f1, 0xf7daec41, 0xe50cd7f, 0x2ff69117, 0x8dd64d76, 0x4db0ef43, + 0x544daacc, 0xdf0496e4, 0xe3b5d19e, 0x1b886a4c, 0xb81f2cc1, 0x7f516546, + 0x4ea5e9d, 0x5d358c01, 0x737487fa, 0x2e410bfb, 0x5a1d67b3, 0x52d2db92, + 0x335610e9, 0x1347d66d, 0x8c61d79a, 0x7a0ca137, 0x8e14f859, 0x893c13eb, + 0xee27a9ce, 0x35c961b7, 0xede51ce1, 0x3cb1477a, 0x59dfd29c, 0x3f73f255, + 0x79ce1418, 0xbf37c773, 0xeacdf753, 0x5baafd5f, 0x146f3ddf, 0x86db4478, + 0x81f3afca, 0x3ec468b9, 0x2c342438, 0x5f40a3c2, 0x72c31d16, 0xc25e2bc, + 0x8b493c28, 0x41950dff, 0x7101a839, 0xdeb30c08, 0x9ce4b4d8, 0x90c15664, + 0x6184cb7b, 0x70b632d5, 0x745c6c48, 0x4257b8d0} + +type AES struct { + Nk int + Nr int + mode int + fkey [60]uint32 + rkey [60]uint32 + f [16]byte +} + +/* Rotates 32-bit word left by 1, 2 or 3 byte */ + +func aes_ROTL8(x uint32) uint32 { + return (((x) << 8) | ((x) >> 24)) +} + +func aes_ROTL16(x uint32) uint32 { + return (((x) << 16) | ((x) >> 16)) +} + +func aes_ROTL24(x uint32) uint32 { + return (((x) << 24) | ((x) >> 8)) +} + +func aes_pack(b [4]byte) uint32 { /* pack bytes into a 32-bit Word */ + return ((uint32(b[3]) & 0xff) << 24) | ((uint32(b[2]) & 0xff) << 16) | ((uint32(b[1]) & 0xff) << 8) | (uint32(b[0]) & 0xff) +} + +func aes_unpack(a uint32) [4]byte { /* unpack bytes from a word */ + var b = [4]byte{byte(a & 0xff), byte((a >> 8) & 0xff), byte((a >> 16) & 0xff), byte((a >> 24) & 0xff)} + return b +} + +func aes_bmul(x byte, y byte) byte { /* x.y= AntiLog(Log(x) + Log(y)) */ + + ix := int(x) & 0xff + iy := int(y) & 0xff + lx := int(aes_ltab[ix]) & 0xff + ly := int(aes_ltab[iy]) & 0xff + + if x != 0 && y != 0 { + return aes_ptab[(lx+ly)%255] + } else { + return byte(0) + } +} + +func aes_SubByte(a uint32) uint32 { + b := aes_unpack(a) + b[0] = aes_fbsub[int(b[0])] + b[1] = aes_fbsub[int(b[1])] + b[2] = aes_fbsub[int(b[2])] + b[3] = aes_fbsub[int(b[3])] + return aes_pack(b) +} + +func aes_product(x uint32, y uint32) byte { /* dot product of two 4-byte arrays */ + xb := aes_unpack(x) + yb := aes_unpack(y) + + return (aes_bmul(xb[0], yb[0]) ^ aes_bmul(xb[1], yb[1]) ^ aes_bmul(xb[2], yb[2]) ^ aes_bmul(xb[3], yb[3])) +} + +func aes_InvMixCol(x uint32) uint32 { /* matrix Multiplication */ + var b [4]byte + m := aes_pack(aes_InCo) + b[3] = aes_product(m, x) + m = aes_ROTL24(m) + b[2] = aes_product(m, x) + m = aes_ROTL24(m) + b[1] = aes_product(m, x) + m = aes_ROTL24(m) + b[0] = aes_product(m, x) + var y = aes_pack(b) + return y +} + +func aes_increment(f []byte) { + for i := 0; i < 16; i++ { + f[i]++ + if f[i] != 0 { + break + } + } +} + +/* reset cipher */ +func (A *AES) Reset(m int, iv []byte) { /* reset mode, or reset iv */ + A.mode = m + for i := 0; i < 16; i++ { + A.f[i] = 0 + } + if (A.mode != AES_ECB) && (iv != nil) { + for i := 0; i < 16; i++ { + A.f[i] = iv[i] + } + } +} + +func (A *AES) Init(m int, nk int, key []byte, iv []byte) bool { + /* Key Scheduler. Create expanded encryption key */ + var CipherKey [8]uint32 + var b [4]byte + nk /= 4 + if nk != 4 && nk != 6 && nk != 8 { + return false + } + nr := 6 + nk + A.Nk = nk + A.Nr = nr + A.Reset(m, iv) + N := 4 * (nr + 1) + + j := 0 + for i := 0; i < nk; i++ { + for k := 0; k < 4; k++ { + b[k] = key[j+k] + } + CipherKey[i] = aes_pack(b) + j += 4 + } + for i := 0; i < nk; i++ { + A.fkey[i] = CipherKey[i] + } + + j = nk + for k := 0; j < N; k++ { + A.fkey[j] = A.fkey[j-nk] ^ aes_SubByte(aes_ROTL24(A.fkey[j-1])) ^ uint32(aes_rco[k]) + if nk <= 6 { + for i := 1; i < nk && (i+j) < N; i++ { + A.fkey[i+j] = A.fkey[i+j-nk] ^ A.fkey[i+j-1] + } + } else { + i := 0 + for i = 1; i < 4 && (i+j) < N; i++ { + A.fkey[i+j] = A.fkey[i+j-nk] ^ A.fkey[i+j-1] + } + if (j + 4) < N { + A.fkey[j+4] = A.fkey[j+4-nk] ^ aes_SubByte(A.fkey[j+3]) + } + for i = 5; i < nk && (i+j) < N; i++ { + A.fkey[i+j] = A.fkey[i+j-nk] ^ A.fkey[i+j-1] + } + } + j += nk + + } + + /* now for the expanded decrypt key in reverse order */ + + for j := 0; j < 4; j++ { + A.rkey[j+N-4] = A.fkey[j] + } + for i := 4; i < N-4; i += 4 { + k := N - 4 - i + for j := 0; j < 4; j++ { + A.rkey[k+j] = aes_InvMixCol(A.fkey[i+j]) + } + } + for j := N - 4; j < N; j++ { + A.rkey[j-N+4] = A.fkey[j] + } + return true +} + +func NewAES() *AES { + var A = new(AES) + return A +} + +func (A *AES) Getreg() [16]byte { + var ir [16]byte + for i := 0; i < 16; i++ { + ir[i] = A.f[i] + } + return ir +} + +/* Encrypt a single block */ +func (A *AES) ecb_encrypt(buff []byte) { + var b [4]byte + var p [4]uint32 + var q [4]uint32 + + j := 0 + for i := 0; i < 4; i++ { + for k := 0; k < 4; k++ { + b[k] = buff[j+k] + } + p[i] = aes_pack(b) + p[i] ^= A.fkey[i] + j += 4 + } + + k := 4 + + /* State alternates between p and q */ + for i := 1; i < A.Nr; i++ { + q[0] = A.fkey[k] ^ aes_ftable[int(p[0]&0xff)] ^ aes_ROTL8(aes_ftable[int((p[1]>>8)&0xff)]) ^ aes_ROTL16(aes_ftable[int((p[2]>>16)&0xff)]) ^ aes_ROTL24(aes_ftable[int((p[3]>>24)&0xff)]) + + q[1] = A.fkey[k+1] ^ aes_ftable[int(p[1]&0xff)] ^ aes_ROTL8(aes_ftable[int((p[2]>>8)&0xff)]) ^ aes_ROTL16(aes_ftable[int((p[3]>>16)&0xff)]) ^ aes_ROTL24(aes_ftable[int((p[0]>>24)&0xff)]) + + q[2] = A.fkey[k+2] ^ aes_ftable[int(p[2]&0xff)] ^ aes_ROTL8(aes_ftable[int((p[3]>>8)&0xff)]) ^ aes_ROTL16(aes_ftable[int((p[0]>>16)&0xff)]) ^ aes_ROTL24(aes_ftable[int((p[1]>>24)&0xff)]) + + q[3] = A.fkey[k+3] ^ aes_ftable[int(p[3]&0xff)] ^ aes_ROTL8(aes_ftable[int((p[0]>>8)&0xff)]) ^ aes_ROTL16(aes_ftable[int((p[1]>>16)&0xff)]) ^ aes_ROTL24(aes_ftable[int((p[2]>>24)&0xff)]) + + k += 4 + for j = 0; j < 4; j++ { + t := p[j] + p[j] = q[j] + q[j] = t + } + } + + /* Last Round */ + + q[0] = A.fkey[k] ^ uint32(aes_fbsub[int(p[0]&0xff)]) ^ aes_ROTL8(uint32(aes_fbsub[int((p[1]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_fbsub[int((p[2]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_fbsub[int((p[3]>>24)&0xff)])) + + q[1] = A.fkey[k+1] ^ uint32(aes_fbsub[int(p[1]&0xff)]) ^ aes_ROTL8(uint32(aes_fbsub[int((p[2]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_fbsub[int((p[3]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_fbsub[int((p[0]>>24)&0xff)])) + + q[2] = A.fkey[k+2] ^ uint32(aes_fbsub[int(p[2]&0xff)]) ^ aes_ROTL8(uint32(aes_fbsub[int((p[3]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_fbsub[int((p[0]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_fbsub[int((p[1]>>24)&0xff)])) + + q[3] = A.fkey[k+3] ^ uint32(aes_fbsub[int(p[3]&0xff)]) ^ aes_ROTL8(uint32(aes_fbsub[int((p[0]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_fbsub[int((p[1]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_fbsub[int((p[2]>>24)&0xff)])) + + j = 0 + for i := 0; i < 4; i++ { + b = aes_unpack(q[i]) + for k = 0; k < 4; k++ { + buff[j+k] = b[k] + } + j += 4 + } +} + +/* Decrypt a single block */ +func (A *AES) ecb_decrypt(buff []byte) { + var b [4]byte + var p [4]uint32 + var q [4]uint32 + + j := 0 + for i := 0; i < 4; i++ { + for k := 0; k < 4; k++ { + b[k] = buff[j+k] + } + p[i] = aes_pack(b) + p[i] ^= A.rkey[i] + j += 4 + } + + k := 4 + + /* State alternates between p and q */ + for i := 1; i < A.Nr; i++ { + + q[0] = A.rkey[k] ^ aes_rtable[int(p[0]&0xff)] ^ aes_ROTL8(aes_rtable[int((p[3]>>8)&0xff)]) ^ aes_ROTL16(aes_rtable[int((p[2]>>16)&0xff)]) ^ aes_ROTL24(aes_rtable[int((p[1]>>24)&0xff)]) + + q[1] = A.rkey[k+1] ^ aes_rtable[int(p[1]&0xff)] ^ aes_ROTL8(aes_rtable[int((p[0]>>8)&0xff)]) ^ aes_ROTL16(aes_rtable[int((p[3]>>16)&0xff)]) ^ aes_ROTL24(aes_rtable[int((p[2]>>24)&0xff)]) + + q[2] = A.rkey[k+2] ^ aes_rtable[int(p[2]&0xff)] ^ aes_ROTL8(aes_rtable[int((p[1]>>8)&0xff)]) ^ aes_ROTL16(aes_rtable[int((p[0]>>16)&0xff)]) ^ aes_ROTL24(aes_rtable[int((p[3]>>24)&0xff)]) + + q[3] = A.rkey[k+3] ^ aes_rtable[int(p[3]&0xff)] ^ aes_ROTL8(aes_rtable[int((p[2]>>8)&0xff)]) ^ aes_ROTL16(aes_rtable[int((p[1]>>16)&0xff)]) ^ aes_ROTL24(aes_rtable[int((p[0]>>24)&0xff)]) + + k += 4 + for j := 0; j < 4; j++ { + t := p[j] + p[j] = q[j] + q[j] = t + } + } + + /* Last Round */ + + q[0] = A.rkey[k] ^ uint32(aes_rbsub[int(p[0]&0xff)]) ^ aes_ROTL8(uint32(aes_rbsub[int((p[3]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_rbsub[int((p[2]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_rbsub[int((p[1]>>24)&0xff)])) + + q[1] = A.rkey[k+1] ^ uint32(aes_rbsub[int(p[1]&0xff)]) ^ aes_ROTL8(uint32(aes_rbsub[int((p[0]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_rbsub[int((p[3]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_rbsub[int((p[2]>>24)&0xff)])) + + q[2] = A.rkey[k+2] ^ uint32(aes_rbsub[int(p[2]&0xff)]) ^ aes_ROTL8(uint32(aes_rbsub[int((p[1]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_rbsub[int((p[0]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_rbsub[int((p[3]>>24)&0xff)])) + + q[3] = A.rkey[k+3] ^ uint32(aes_rbsub[int((p[3])&0xff)]) ^ aes_ROTL8(uint32(aes_rbsub[int((p[2]>>8)&0xff)])) ^ aes_ROTL16(uint32(aes_rbsub[int((p[1]>>16)&0xff)])) ^ aes_ROTL24(uint32(aes_rbsub[int((p[0]>>24)&0xff)])) + + j = 0 + for i := 0; i < 4; i++ { + b = aes_unpack(q[i]) + for k := 0; k < 4; k++ { + buff[j+k] = b[k] + } + j += 4 + } +} + +/* Encrypt using selected mode of operation */ +func (A *AES) Encrypt(buff []byte) uint32 { + var st [16]byte + + // Supported Modes of Operation + + var fell_off uint32 = 0 + switch A.mode { + case AES_ECB: + A.ecb_encrypt(buff) + return 0 + case AES_CBC: + for j := 0; j < 16; j++ { + buff[j] ^= A.f[j] + } + A.ecb_encrypt(buff) + for j := 0; j < 16; j++ { + A.f[j] = buff[j] + } + return 0 + + case AES_CFB1: + fallthrough + case AES_CFB2: + fallthrough + case AES_CFB4: + bytes := A.mode - AES_CFB1 + 1 + for j := 0; j < bytes; j++ { + fell_off = (fell_off << 8) | uint32(A.f[j]) + } + for j := 0; j < 16; j++ { + st[j] = A.f[j] + } + for j := bytes; j < 16; j++ { + A.f[j-bytes] = A.f[j] + } + A.ecb_encrypt(st[:]) + for j := 0; j < bytes; j++ { + buff[j] ^= st[j] + A.f[16-bytes+j] = buff[j] + } + return fell_off + + case AES_OFB1: + fallthrough + case AES_OFB2: + fallthrough + case AES_OFB4: + fallthrough + case AES_OFB8: + fallthrough + case AES_OFB16: + + bytes := A.mode - AES_OFB1 + 1 + A.ecb_encrypt(A.f[:]) + for j := 0; j < bytes; j++ { + buff[j] ^= A.f[j] + } + return 0 + + case AES_CTR1: + fallthrough + case AES_CTR2: + fallthrough + case AES_CTR4: + fallthrough + case AES_CTR8: + fallthrough + case AES_CTR16: + bytes := A.mode - AES_CTR1 + 1 + for j := 0; j < 16; j++ { + st[j] = A.f[j] + } + A.ecb_encrypt(st[:]) + for j := 0; j < bytes; j++ { + buff[j] ^= st[j] + } + aes_increment(A.f[:]) + return 0 + + default: + return 0 + } +} + +/* Decrypt using selected mode of operation */ +func (A *AES) Decrypt(buff []byte) uint32 { + + var st [16]byte + + // Supported Modes of Operation + + var fell_off uint32 = 0 + switch A.mode { + case AES_ECB: + A.ecb_decrypt(buff) + return 0 + case AES_CBC: + for j := 0; j < 16; j++ { + st[j] = A.f[j] + A.f[j] = buff[j] + } + A.ecb_decrypt(buff) + for j := 0; j < 16; j++ { + buff[j] ^= st[j] + st[j] = 0 + } + return 0 + case AES_CFB1: + fallthrough + case AES_CFB2: + fallthrough + case AES_CFB4: + bytes := A.mode - AES_CFB1 + 1 + for j := 0; j < bytes; j++ { + fell_off = (fell_off << 8) | uint32(A.f[j]) + } + for j := 0; j < 16; j++ { + st[j] = A.f[j] + } + for j := bytes; j < 16; j++ { + A.f[j-bytes] = A.f[j] + } + A.ecb_encrypt(st[:]) + for j := 0; j < bytes; j++ { + A.f[16-bytes+j] = buff[j] + buff[j] ^= st[j] + } + return fell_off + case AES_OFB1: + fallthrough + case AES_OFB2: + fallthrough + case AES_OFB4: + fallthrough + case AES_OFB8: + fallthrough + case AES_OFB16: + bytes := A.mode - AES_OFB1 + 1 + A.ecb_encrypt(A.f[:]) + for j := 0; j < bytes; j++ { + buff[j] ^= A.f[j] + } + return 0 + + case AES_CTR1: + fallthrough + case AES_CTR2: + fallthrough + case AES_CTR4: + fallthrough + case AES_CTR8: + fallthrough + case AES_CTR16: + bytes := A.mode - AES_CTR1 + 1 + for j := 0; j < 16; j++ { + st[j] = A.f[j] + } + A.ecb_encrypt(st[:]) + for j := 0; j < bytes; j++ { + buff[j] ^= st[j] + } + aes_increment(A.f[:]) + return 0 + + default: + return 0 + } +} + +/* Clean up and delete left-overs */ +func (A *AES) End() { // clean up + for i := 0; i < 4*(A.Nr+1); i++ { + A.fkey[i] = 0 + A.rkey[i] = 0 + } + for i := 0; i < 16; i++ { + A.f[i] = 0 + } +} + +/* AES encryption/decryption. Encrypt byte array M using key K and returns ciphertext */ +func AES_CBC_IV0_ENCRYPT(K []byte, M []byte) []byte { /* AES CBC encryption, with Null IV and key K */ + /* Input is from an octet string M, output is to an octet string C */ + /* Input is padded as necessary to make up a full final block */ + a := NewAES() + fin := false + + var buff [16]byte + var C []byte + + a.Init(AES_CBC, len(K), K, nil) + + ipt := 0 //opt:=0 + var i int + for true { + for i = 0; i < 16; i++ { + if ipt < len(M) { + buff[i] = M[ipt] + ipt++ + } else { + fin = true + break + } + } + if fin { + break + } + a.Encrypt(buff[:]) + for i = 0; i < 16; i++ { + C = append(C, buff[i]) + } + } + + /* last block, filled up to i-th index */ + + padlen := 16 - i + for j := i; j < 16; j++ { + buff[j] = byte(padlen) + } + + a.Encrypt(buff[:]) + + for i = 0; i < 16; i++ { + C = append(C, buff[i]) + } + a.End() + return C +} + +/* returns plaintext if all consistent, else returns null string */ +func AES_CBC_IV0_DECRYPT(K []byte, C []byte) []byte { /* padding is removed */ + a := NewAES() + var buff [16]byte + var MM []byte + var M []byte + + var i int + ipt := 0 + opt := 0 + + a.Init(AES_CBC, len(K), K, nil) + + if len(C) == 0 { + return nil + } + ch := C[ipt] + ipt++ + + fin := false + + for true { + for i = 0; i < 16; i++ { + buff[i] = ch + if ipt >= len(C) { + fin = true + break + } else { + ch = C[ipt] + ipt++ + } + } + a.Decrypt(buff[:]) + if fin { + break + } + for i = 0; i < 16; i++ { + MM = append(MM, buff[i]) + opt++ + } + } + + a.End() + bad := false + padlen := int(buff[15]) + if i != 15 || padlen < 1 || padlen > 16 { + bad = true + } + if padlen >= 2 && padlen <= 16 { + for i = 16 - padlen; i < 16; i++ { + if buff[i] != byte(padlen) { + bad = true + } + } + } + + if !bad { + for i = 0; i < 16-padlen; i++ { + MM = append(MM, buff[i]) + opt++ + } + } + + if bad { + return nil + } + + for i = 0; i < opt; i++ { + M = append(M, MM[i]) + } + + return M +} + +/* +func main() { + var key [32]byte + var block [16]byte + var iv [16]byte + + for i:=0;i<32;i++ {key[i]=0} + key[0]=1 + for i:=0;i<16;i++ {iv[i]=byte(i)} + for i:=0;i<16;i++ {block[i]=byte(i)} + + a:=NewAES() + + a.Init(AES_CTR16,32,key[:],iv[:]) + fmt.Printf("Plain= \n") + for i:=0;i<16;i++ {fmt.Printf("%02X ", block[i]&0xff)} + fmt.Printf("\n") + + a.Encrypt(block[:]) + + fmt.Printf("Encrypt= \n") + for i:=0;i<16;i++ {fmt.Printf("%02X ", block[i]&0xff)} + fmt.Printf("\n") + + a.Reset(AES_CTR16,iv[:]) + a.Decrypt(block[:]) + + fmt.Printf("Decrypt= \n") + for i:=0;i<16;i++ {fmt.Printf("%02X ", block[i]&0xff)} + fmt.Printf("\n") + + a.End(); +} +*/ diff --git a/ec/bls48581/core/DILITHIUM.go b/ec/bls48581/core/DILITHIUM.go new file mode 100644 index 0000000..535b1a6 --- /dev/null +++ b/ec/bls48581/core/DILITHIUM.go @@ -0,0 +1,1290 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + + Arwa Alblooshi 15/12/2022 + */ +package core + +//import "fmt" + +//q = 8380417 +const DL_LGN = 8 +const DL_DEGREE = (1 << DL_LGN) +const DL_PRIME = 0x7fe001 +const DL_D = 13 +const DL_TD = (23 - DL_D) + +const DL_ONE = 0x3FFE00 // R mod Q +const DL_COMBO = 0xA3FA // ONE*inv mod Q +const DL_R2MODP = 0x2419FF // R^2 mod Q +const DL_ND = 0xFC7FDFFF // 1/(R-Q) mod R + +const DL_MAXLG = 19 +const DL_MAXK = 8 // could reduce these if not using highest security +const DL_MAXL = 7 +const DL_YBYTES = (((DL_MAXLG + 1) * DL_DEGREE) / 8) + +const DL_SK_SIZE_2 = (32*3+DL_DEGREE* (4*13+4*3+4*3)/8) +const DL_PK_SIZE_2 = ((4*DL_DEGREE*DL_TD)/8 + 32) +const DL_SIG_SIZE_2 = ((DL_DEGREE*4*(17+1))/8 + 80 + 4 + 32) + +const DL_SK_SIZE_3 = (32*3 + DL_DEGREE*(6*13+5*4+6*4)/8) +const DL_PK_SIZE_3 = ((6*DL_DEGREE*DL_TD)/8 + 32) +const DL_SIG_SIZE_3 = ((DL_DEGREE*5*(19+1))/8 + 55 + 6 + 32) + +const DL_SK_SIZE_5 = (32*3 + DL_DEGREE*(8*13+7*3+8*3)/8) +const DL_PK_SIZE_5 = ((8*DL_DEGREE*DL_TD)/8 + 32) +const DL_SIG_SIZE_5 = ((DL_DEGREE*7*(19+1))/8 + 75 + 8 + 32) + +// parameters for each security level +// tau,gamma1,gamma2,K,L,eta,lg(2*eta+1),omega + +var DL_PARAMS_2 = []int{39, 17, 88, 4, 4, 2, 3, 80} +var DL_PARAMS_3 = []int{49, 19, 32, 6, 5, 4, 4, 55} +var DL_PARAMS_5 = []int{60, 19, 32, 8, 7, 2, 3, 75} + +var DL_roots = []int32{0x3ffe00, 0x64f7, 0x581103, 0x77f504, 0x39e44, 0x740119, 0x728129, 0x71e24, 0x1bde2b, 0x23e92b, 0x7a64ae, 0x5ff480, 0x2f9a75, 0x53db0a, 0x2f7a49, 0x28e527, 0x299658, 0xfa070, 0x6f65a5, 0x36b788, 0x777d91, 0x6ecaa1, 0x27f968, 0x5fb37c, 0x5f8dd7, 0x44fae8, 0x6a84f8, 0x4ddc99, 0x1ad035, 0x7f9423, 0x3d3201, 0x445c5, 0x294a67, 0x17620, 0x2ef4cd, 0x35dec5, 0x668504, 0x49102d, 0x5927d5, 0x3bbeaf, 0x44f586, 0x516e7d, 0x368a96, 0x541e42, 0x360400, 0x7b4a4e, 0x23d69c, 0x77a55e, 0x65f23e, 0x66cad7, 0x357e1e, 0x458f5a, 0x35843f, 0x5f3618, 0x67745d, 0x38738c, 0xc63a8, 0x81b9a, 0xe8f76, 0x3b3853, 0x3b8534, 0x58dc31, 0x1f9d54, 0x552f2e, 0x43e6e6, 0x688c82, 0x47c1d0, 0x51781a, 0x69b65e, 0x3509ee, 0x2135c7, 0x67afbc, 0x6caf76, 0x1d9772, 0x419073, 0x709cf7, 0x4f3281, 0x4fb2af, 0x4870e1, 0x1efca, 0x3410f2, 0x70de86, 0x20c638, 0x296e9f, 0x5297a4, 0x47844c, 0x799a6e, 0x5a140a, 0x75a283, 0x6d2114, 0x7f863c, 0x6be9f8, 0x7a0bde, 0x1495d4, 0x1c4563, 0x6a0c63, 0x4cdbea, 0x40af0, 0x7c417, 0x2f4588, 0xad00, 0x6f16bf, 0xdcd44, 0x3c675a, 0x470bcb, 0x7fbe7f, 0x193948, 0x4e49c1, 0x24756c, 0x7ca7e0, 0xb98a1, 0x6bc809, 0x2e46c, 0x49a809, 0x3036c2, 0x639ff7, 0x5b1c94, 0x7d2ae1, 0x141305, 0x147792, 0x139e25, 0x67b0e1, 0x737945, 0x69e803, 0x51cea3, 0x44a79d, 0x488058, 0x3a97d9, 0x1fea93, 0x33ff5a, 0x2358d4, 0x3a41f8, 0x4cdf73, 0x223dfb, 0x5a8ba0, 0x498423, 0x412f5, 0x252587, 0x6d04f1, 0x359b5d, 0x4a28a1, 0x4682fd, 0x6d9b57, 0x4f25df, 0xdbe5e, 0x1c5e1a, 0xde0e6, 0xc7f5a, 0x78f83, 0x67428b, 0x7f3705, 0x77e6fd, 0x75e022, 0x503af7, 0x1f0084, 0x30ef86, 0x49997e, 0x77dcd7, 0x742593, 0x4901c3, 0x53919, 0x4610c, 0x5aad42, 0x3eb01b, 0x3472e7, 0x4ce03c, 0x1a7cc7, 0x31924, 0x2b5ee5, 0x291199, 0x585a3b, 0x134d71, 0x3de11c, 0x130984, 0x25f051, 0x185a46, 0x466519, 0x1314be, 0x283891, 0x49bb91, 0x52308a, 0x1c853f, 0x1d0b4b, 0x6fd6a7, 0x6b88bf, 0x12e11b, 0x4d3e3f, 0x6a0d30, 0x78fde5, 0x1406c7, 0x327283, 0x61ed6f, 0x6c5954, 0x1d4099, 0x590579, 0x6ae5ae, 0x16e405, 0xbdbe7, 0x221de8, 0x33f8cf, 0x779935, 0x54aa0d, 0x665ff9, 0x63b158, 0x58711c, 0x470c13, 0x910d8, 0x463e20, 0x612659, 0x251d8b, 0x2573b7, 0x7d5c90, 0x1ddd98, 0x336898, 0x2d4bb, 0x6d73a8, 0x4f4cbf, 0x27c1c, 0x18aa08, 0x2dfd71, 0xc5ca5, 0x19379a, 0x478168, 0x646c3e, 0x51813d, 0x35c539, 0x3b0115, 0x41dc0, 0x21c4f7, 0x70fbf5, 0x1a35e7, 0x7340e, 0x795d46, 0x1a4cd0, 0x645caf, 0x1d2668, 0x666e99, 0x6f0634, 0x7be5db, 0x455fdc, 0x530765, 0x5dc1b0, 0x7973de, 0x5cfd0a, 0x2cc93, 0x70f806, 0x189c2a, 0x49c5aa, 0x776a51, 0x3bcf2c, 0x7f234f, 0x6b16e0, 0x3c15ca, 0x155e68, 0x72f6b7, 0x1e29ce} +var DL_iroots = []int32{0x3ffe00, 0x7f7b0a, 0x7eafd, 0x27cefe, 0x78c1dd, 0xd5ed8, 0xbdee8, 0x7c41bd, 0x56fada, 0x5065b8, 0x2c04f7, 0x50458c, 0x1feb81, 0x57b53, 0x5bf6d6, 0x6401d6, 0x7b9a3c, 0x42ae00, 0x4bde, 0x650fcc, 0x320368, 0x155b09, 0x3ae519, 0x20522a, 0x202c85, 0x57e699, 0x111560, 0x86270, 0x492879, 0x107a5c, 0x703f91, 0x5649a9, 0x2ab0d3, 0x6042ad, 0x2703d0, 0x445acd, 0x44a7ae, 0x71508b, 0x77c467, 0x737c59, 0x476c75, 0x186ba4, 0x20a9e9, 0x4a5bc2, 0x3a50a7, 0x4a61e3, 0x19152a, 0x19edc3, 0x83aa3, 0x5c0965, 0x495b3, 0x49dc01, 0x2bc1bf, 0x49556b, 0x2e7184, 0x3aea7b, 0x442152, 0x26b82c, 0x36cfd4, 0x195afd, 0x4a013c, 0x50eb34, 0x7e69e1, 0x56959a, 0x454828, 0x375fa9, 0x3b3864, 0x2e115e, 0x15f7fe, 0xc66bc, 0x182f20, 0x6c41dc, 0x6b686f, 0x6bccfc, 0x2b520, 0x24c36d, 0x1c400a, 0x4fa93f, 0x3637f8, 0x7cfb95, 0x1417f8, 0x744760, 0x33821, 0x5b6a95, 0x319640, 0x66a6b9, 0x2182, 0x38d436, 0x4378a7, 0x7212bd, 0x10c942, 0x7f3301, 0x509a79, 0x781bea, 0x7bd511, 0x330417, 0x15d39e, 0x639a9e, 0x6b4a2d, 0x5d423, 0x13f609, 0x59c5, 0x12beed, 0xa3d7e, 0x25cbf7, 0x64593, 0x385bb5, 0x2d485d, 0x567162, 0x5f19c9, 0xf017b, 0x4bcf0f, 0x7df037, 0x376f20, 0x302d52, 0x30ad80, 0xf430a, 0x3e4f8e, 0x62488f, 0x13308b, 0x183045, 0x5eaa3a, 0x4ad613, 0x1629a3, 0x2e67e7, 0x381e31, 0x17537f, 0x3bf91b, 0x61b633, 0xce94a, 0x6a8199, 0x43ca37, 0x14c921, 0xbcb2, 0x4410d5, 0x875b0, 0x361a57, 0x6743d7, 0xee7fb, 0x7d136e, 0x22e2f7, 0x66c23, 0x221e51, 0x2cd89c, 0x3a8025, 0x3fa26, 0x10d9cd, 0x197168, 0x62b999, 0x1b8352, 0x659331, 0x682bb, 0x78abf3, 0x65aa1a, 0xee40c, 0x5e1b0a, 0x7bc241, 0x44deec, 0x4a1ac8, 0x2e5ec4, 0x1b73c3, 0x385e99, 0x66a867, 0x73835c, 0x51e290, 0x6735f9, 0x7d63e5, 0x309342, 0x126c59, 0x7d0b46, 0x4c7769, 0x620269, 0x28371, 0x5a6c4a, 0x5ac276, 0x1eb9a8, 0x39a1e1, 0x76cf29, 0x38d3ee, 0x276ee5, 0x1c2ea9, 0x198008, 0x2b35f4, 0x846cc, 0x4be732, 0x5dc219, 0x74041a, 0x68fbfc, 0x14fa53, 0x26da88, 0x629f68, 0x1386ad, 0x1df292, 0x4d6d7e, 0x6bd93a, 0x6e21c, 0x15d2d1, 0x32a1c2, 0x6cfee6, 0x145742, 0x10095a, 0x62d4b6, 0x635ac2, 0x2daf77, 0x362470, 0x57a770, 0x6ccb43, 0x397ae8, 0x6785bb, 0x59efb0, 0x6cd67d, 0x41fee5, 0x6c9290, 0x2785c6, 0x56ce68, 0x54811c, 0x7cc6dd, 0x65633a, 0x32ffc5, 0x4b6d1a, 0x412fe6, 0x2532bf, 0x7b7ef5, 0x7aa6e8, 0x36de3e, 0xbba6e, 0x8032a, 0x364683, 0x4ef07b, 0x60df7d, 0x2fa50a, 0x9ffdf, 0x7f904, 0xa8fc, 0x189d76, 0x78507e, 0x7360a7, 0x71ff1b, 0x6381e7, 0x7221a3, 0x30ba22, 0x1244aa, 0x395d04, 0x35b760, 0x4a44a4, 0x12db10, 0x5aba7a, 0x7bcd0c, 0x365bde, 0x255461, 0x5da206, 0x33008e, 0x459e09, 0x5c872d, 0x4be0a7, 0x5ff56e} + +func DL_round(a int32, b int32) int32 { + return (a + b/2) / b +} + +// constant time absolute vaue +func DL_nabs(x int32) int32 { + mask := (x >> 31) + return (x + mask)^mask +} + +// Montgomery stuff +func DL_redc(T uint64) int32 { + m := uint32(T) * (uint32(DL_ND)) + return int32((uint64(m)*DL_PRIME + T) >> 32) +} + +func DL_nres(x uint32) int32 { + return DL_redc(uint64(x)*DL_R2MODP) +} + +func DL_modmul(a uint32, b uint32) int32 { + return DL_redc(uint64(a)*uint64(b)) +} + +//make all elements +ve +func DL_poly_pos(p []int32) { + for i := 0; i < DL_DEGREE; i++ { + p[i] += (p[i] >> 31)&DL_PRIME + } +} + +// NTT code + +// Important! +// DL_nres(x); DL_ntt(x) +// DL_nres(y); DL_ntt(y) +// z=x*y +// DL_intt(z); +// DL_redc(z); + +// is equivalent to (note that DL_nres() and DL_redc() cancel out) + +// DL_ntt(x); +// DL_nres(y); DL_ntt(y); +// z=x*y +// DL_intt(z) + +// is equivalent to + +// DL_ntt(x) +// DL_ntt(y) +// z=x*y +// DL_intt(z) +// DL_nres(z) + +// In all cases z ends up in normal (non-Montgomery) form! +// So the conversion to Montgomery form can be "pushed" through the calculation. + +// Here DL_intt(z) <- DL_intt(z);DL_nres(z); +// Combining is more efficient +// note that DL_ntt() and DL_intt() are not mutually inverse + +/* NTT code */ +/* Cooley-Tukey NTT */ +/* Excess of 2 allowed on input - coefficients must be < 2*PRIME */ + +func DL_ntt(x []int32) { + + var start int + len := DL_DEGREE/2 + + var S, V int32 + var q int32 = DL_PRIME + + //Make positive + DL_poly_pos(x) + m := 1 + for m < DL_DEGREE { + start = 0 + for i := 0; i < m; i++ { + S = DL_roots[m+i] + for j := start; j < start+len; j++ { + V = DL_modmul(uint32(x[j+len]), uint32(S)) + x[j+len] = x[j] + 2 * q - V + x[j] = x[j] + V + } + start += 2 * len + } + len /= 2 + m *= 2 + } +} + +// Gentleman-Sande INTT +// Excess of 2 allowed on input - coefficients must be < 2*PRIME +// Output fully reduced +const NTTL = 1 + +func DL_intt(x []int32) { + var k,lim int + t := 1 + var S,U,V,W int32 + var q int32 = DL_PRIME + m := DL_DEGREE/2 + n := DL_LGN + for m >= 1 { + lim = NTTL >> n + n-- + k = 0 + for i := 0; i < m; i++ { + S = DL_iroots[m+i] + for j := k; j < k+t; j++ { + if NTTL > 1 { + if m < NTTL && j < k+lim { + U = DL_modmul(uint32(x[j]), DL_ONE) + V = DL_modmul(uint32(x[j+t]), DL_ONE) + } else { + U = x[j] + V = x[j+t] + } + } else { + U = x[j] + V = x[j+t] + } + x[j] = U + V + W = U + (DL_DEGREE/NTTL)*q - V + x[j+t] = DL_modmul(uint32(W), uint32(S)) + //T := int64(W)*int64(S) + //var M int64 = (T*DL_ND) & 0xffffffff + //R := int((M * int64(DL_PRIME+T)) >> 32) + //fmt.Printf("x,W,S= %d %d %d %x %x %d\n",x[j+t],W,S,T,M,R) + } + k += 2 * t + } + t *= 2 + m /= 2 + } + //fmt.Printf("\nx[0]= %d\n",x[0]) + //fmt.Printf("x[1]= %d\n",x[1]) + for j := 0; j < DL_DEGREE; j++ { + //fully reduce, DL_nres combined with 1/DEGREE + x[j] = DL_modmul(uint32(x[j]), DL_COMBO) + x[j] -= q + x[j] += (x[j] >> 31)&q + } +} + +func DL_nres_it(p []int32) { + for i := 0; i < DL_DEGREE; i++ { + p[i] = DL_nres(uint32(p[i])) + } +} + +func DL_redc_it(p []int32) { + for i := 0; i < DL_DEGREE; i++ { + p[i] = DL_redc(uint64(p[i])) + } +} + +//copy polynomial +func DL_poly_copy(p1 []int32, p2 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = p2[i] + } +} + +//copy from small polynomial +func DL_poly_scopy(p1 []int32, p2 []int8) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = int32(p2[i]) + } +} + +//copy from medium polynomial +func DL_poly_mcopy(p1 []int32, p2 []int16) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = int32(p2[i]) + } +} + +func DL_poly_zero(p1 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = 0 + } +} + +func DL_poly_negate(p1 []int32, p2 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = DL_PRIME - p2[i] + } +} + +func DL_poly_mul(p1 []int32, p2 []int32, p3 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = DL_modmul(uint32(p2[i]), uint32(p3[i])) + } +} + +func DL_poly_add(p1 []int32, p2 []int32, p3 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = p2[i] + p3[i] + } +} + +func DL_poly_sub(p1 []int32, p2 []int32, p3 []int32) { + for i := 0; i < DL_DEGREE; i++ { + p1[i] = p2[i] + DL_PRIME - p3[i] + } +} + +//reduce inputs that are already < 2q +func DL_poly_soft_reduce(poly []int32) { + var e int32 + for i := 0; i < DL_DEGREE; i++ { + e = poly[i] - DL_PRIME + poly[i] = e + ((e >> 31)&DL_PRIME) + + } +} + +//fully reduces modulo q +func DL_poly_hard_reduce(poly []int32) { + var e int32 + for i := 0; i < DL_DEGREE; i++ { + e = DL_modmul(uint32(poly[i]), DL_ONE) //reduces to < 2q + e = e - DL_PRIME + poly[i] = e + ((e >> 31)&DL_PRIME) //finishes it off + } +} + +//Generate A[i][j] from rho +func DL_ExpandAij(rho []byte, Aij []int32, i int, j int) { + sh := NewSHA3(SHA3_SHAKE128) + var cf int32 + //var b0, b1, b2 uint32 + var buff [4*DL_DEGREE]byte // should be plenty + + for m := 0; m < 32; m++ { + sh.Process(rho[m]) + } + sh.Process(byte(j & 0xFF)) + sh.Process(byte(i & 0xff)) + sh.Shake(buff[:], 4*DL_DEGREE) + m := 0 + n := 0 + for m < DL_DEGREE { + b0 := uint32(buff[n]&0xff) + n++ + b1 := uint32(buff[n]&0xff) + n++ + b2 := uint32(buff[n]&0xff) + n++ + cf = int32(((b2 & 0x7f) << 16) + (b1 << 8) + b0) + if cf >= DL_PRIME { + continue + } + Aij[m] = cf + m++ + } +} + +// array t has ab active bits per word +// extract bytes from array of words +// if max!=0 then -max<=t[i]<=+max +func DL_nextbyte32(ab int, max int, t []int32, position []int) byte { + ptr := position[0] // index in array + bts := position[1] // bit index in word + left := ab - bts // number of bits left in this word + i := 0 + k := ptr % 256 + var r int32 + var w int32 = t[k] + + if max != 0 { + w = int32(max) - w + } + r = w >> bts + for left < 8 { + i++ + w = t[k+i] + if max != 0 { + w = int32(max) - w + } + r |= w << left + left += ab + } + bts += 8 + for bts >= ab { + bts -= ab + ptr++ + } + position[0] = ptr + position[1] = bts + + return byte(r & 0xff) +} + +// array t has ab active bits per word +// extract dense bytes from array of words +// if max!=0 then -max<=t[i]<=+max +func DL_nextbyte16(ab int, max int, t []int16, position []int) byte { + ptr := position[0] // index in array + bts := position[1] // bit index in word + left := ab - bts // number of bits left in this word + i := 0 + k := ptr % 256 + var r int32 + var w int32 = int32(t[k]) + if max != 0 { + w = int32(max) - w + } + r = w >> bts + for left < 8 { + i++ + w = int32(t[k+i]) + if max != 0 { + w = int32(max) - w + } + r |= w << left + left += ab + } + bts += 8 + for bts >= ab { + bts -= ab + ptr++ + } + position[0] = ptr + position[1] = bts + + return byte(r & 0xff) +} + +// array t has ab active bits per word +// extract dense bytes from array of words +// if max!=0 then -max<=t[i]<=+max +func DL_nextbyte8(ab int, max int, t []int8, position []int) byte { + ptr := position[0] // index in array + bts := position[1] // bit index in word + left := ab - bts // number of bits left in this word + i := 0 + k := ptr % 256 + var r int32 + var w int32 = int32(t[k]) + if max != 0 { + w = int32(max) - w + } + r = w >> bts + for left < 8 { + i++ + w = int32(t[k+i]) + if max != 0 { + w = int32(max) - w + } + r |= w << left + left += ab + } + bts += 8 + for bts >= ab { + bts -= ab + ptr++ + } + position[0] = ptr + position[1] = bts + + return byte(r&0xff) +} + +// extract ab bits into word from dense byte stream +func DL_nextword(ab int, max int, t []byte, position []int) int32 { + ptr := position[0] // index in array + bts := position[1] // bit index in word + r := int32(t[ptr]>>bts) + mask := int32((1<= 8 { + bts -= 8 + ptr++ + } + w = r&mask + if max != 0 { + w = int32(max) - w + } + position[0] = ptr + position[1] = bts + return w +} + +//pack public key +func DL_pack_pk(params []int, pk []byte, rho []byte, t1 [][DL_DEGREE]int16) int { + var pos [2]int + pos[0] = 0; pos[1] = 0 + ck := params[3] + for i := 0; i < 32; i++ { + pk[i] = rho[i] + } + n := 32 + for j := 0; j < ck; j++ { + for i := 0; i < (DL_DEGREE*DL_TD)/8; i++ { + pk[n] = DL_nextbyte16(DL_TD, 0, t1[j][:], pos[:]) + n++ + } + } + return n +} + +//unpack public key +func DL_unpack_pk(params []int, rho []byte, t1 [][DL_DEGREE]int16, pk []byte) { + var pos [2]int + pos[0] = 32; pos[1] = 0 + ck := params[3] + for i := 0; i < 32; i++ { + rho[i] = pk[i] + } + for j := 0; j < ck; j++ { + for i := 0; i < DL_DEGREE; i++ { + t1[j][i] = int16(DL_nextword(DL_TD, 0, pk, pos[:])) + } + } +} + +// secret key of size 32*3+DEGREE*(K*D+L*LG2ETA1+K*LG2ETA1)/8 +func DL_pack_sk(params []int, sk []byte, rho []byte, bK []byte, tr []byte, s1 [][DL_DEGREE]int8, s2 [][DL_DEGREE]int8, t0 [][DL_DEGREE]int16) int { + n := 32 + ck := params[3] + el := params[4] + eta := params[5] + lg2eta1 := params[6] + + for i := 0; i < 32; i++ { + sk[i] = rho[i] + } + for i := 0; i < 32; i++ { + sk[n] = bK[i] + n++ + } + for i := 0; i < 32; i++ { + sk[n] = tr[i] + n++ + } + + var pos [2]int + pos[0] = 0; pos[1] = 0 + + for j := 0; j < el; j++ { + for i := 0; i < (DL_DEGREE*lg2eta1)/8; i++ { + sk[n] = DL_nextbyte8(lg2eta1, eta, s1[j][:], pos[:]) + n++ + } + } + pos[0] = 0; pos[1] = 0 + for j := 0; j < ck; j++ { + for i := 0; i < (DL_DEGREE*lg2eta1)/8; i++ { + sk[n] = DL_nextbyte8(lg2eta1, eta, s2[j][:], pos[:]) + n++ + } + } + pos[0] = 0; pos[1] = 0 + for j := 0; j < ck; j++ { + for i := 0; i < (DL_DEGREE*DL_D)/8; i++ { + sk[n] = DL_nextbyte16(DL_D, (1 << (DL_D - 1)), t0[j][:], pos[:]) + n++ + } + } + return n +} + +func DL_unpack_sk(params []int, rho []byte, bK []byte, tr []byte, s1 [][DL_DEGREE]int8, s2 [][DL_DEGREE]int8, t0 [][DL_DEGREE]int16, sk []byte) { + n := 32 + ck := params[3] + el := params[4] + eta := params[5] + lg2eta1 := params[6] + + for i := 0; i < 32; i++ { + rho[i] = sk[i] + } + for i := 0; i < 32; i++ { + bK[i] = sk[n] + n++ + } + for i := 0; i < 32; i++ { + tr[i] = sk[n] + n++ + } + + var pos [2]int + pos[0] = n; pos[1] = 0 + for j := 0; j < el; j++ { + for i := 0; i < DL_DEGREE; i++ { + s1[j][i] = int8(DL_nextword(lg2eta1, eta, sk, pos[:])) + } + } + //fmt.Printf("lg2eta1 = %d eta= %d\n",lg2eta1,eta) + //fmt.Printf("s1[0][0]= %d sk[0] = %d\n",s1[0][0],sk[n]) + for j := 0; j < ck; j++ { + for i := 0; i < DL_DEGREE; i++ { + s2[j][i] = int8(DL_nextword(lg2eta1, eta, sk, pos[:])) + } + } + for j := 0; j < ck; j++ { + for i := 0; i < DL_DEGREE; i++ { + t0[j][i] = int16(DL_nextword(DL_D, (1 << (DL_D - 1)), sk, pos[:])) + } + } +} + +// pack signature - change z +func DL_pack_sig(params []int, sig []byte, z [][DL_DEGREE]int32, ct []byte, h []byte) int { + lg := params[1] + gamma1 := 1 << lg + ck := params[3] + el := params[4] + omega := params[7] + + var t int32 + + for i := 0; i < 32; i++ { + sig[i] = ct[i] + } + + n := 32 + var pos [2]int + pos[0] = 0; pos[1] = 0 + //pre-process z + for i := 0; i < el; i++ { + for m := 0; m < DL_DEGREE; m++ { + t = z[i][m] + if t > DL_PRIME/2 { + t -= DL_PRIME + } + t = int32(gamma1) - t + z[i][m] = t + } + } + for j := 0; j < el; j++ { + for i := 0; i < (DL_DEGREE*(lg+1))/8; i++ { + sig[n] = DL_nextbyte32(lg+1, 0, z[j][:], pos[:]) + n++ + } + } + for i := 0; i < omega+ck; i++ { + sig[n] = h[i] + n++ + } + return n +} + +func DL_unpack_sig(params []int, z [][DL_DEGREE]int32, ct []byte, h []byte, sig []byte) { + lg := params[1] + gamma1 := 1 << lg + ck := params[3] + el := params[4] + omega := params[7] + var t int32 + m := 32 + (el*DL_DEGREE*(lg+1))/8 + + for i := 0; i < 32; i++ { + ct[i] = sig[i] + } + + var pos [2]int + pos[0] = 32; pos[1] = 0 + for j := 0; j < el; j++ { + for i := 0; i < DL_DEGREE; i++ { + t = DL_nextword(lg+1, 0, sig, pos[:]) + t = int32(gamma1)-t + if t < 0 { + t += DL_PRIME + } + z[j][i] = t + } + } + for i := 0; i < omega+ck; i++ { + h[i] = sig[m] + m++ + } +} + +// rejection sampling in range -ETA to +ETA +func DL_sample_Sn(params []int, rhod []byte, s []int8, n int) { + eta := int8(params[5]) + lg2eta1 := params[6] + sh := NewSHA3(SHA3_SHAKE256) + var buff [272]byte + + for m := 0; m < 64; m++ { + sh.Process(rhod[m]) + } + sh.Process(byte(n & 0xff)) + sh.Process(byte((n >> 8) & 0xff)) + sh.Shake(buff[:], 272) + + var pos [2]int + pos[0] = 0; pos[1] = 0 + for m := 0; m < DL_DEGREE; m++ { + for next := true; next; next = s[m] > 2*eta { + s[m] = int8(DL_nextword(lg2eta1, 0, buff[:], pos[:])) + } + s[m] = int8(eta - s[m]) + } +} + +//uniform random sampling +func DL_sample_Y(params []int, k int, rhod []byte, y [][DL_DEGREE]int32) { + lg := params[1] + gamma1 := 1 << lg + el := params[4] + var ki int + var w, t int32 + var buff [DL_YBYTES]byte + + for i := 0; i < el; i++ { + sh := NewSHA3(SHA3_SHAKE256) + for j := 0; j < 64; j++ { + sh.Process(rhod[j]) + } + ki = k + i + sh.Process(byte(ki & 0xff)) + sh.Process(byte(ki >> 8)) + sh.Shake(buff[:], DL_YBYTES) + + var pos [2]int + pos[0] = 0; pos[1] = 0 + for m := 0; m < DL_DEGREE; m++ { + //take in LG+1 bits at a time + w = DL_nextword(lg+1, 0, buff[:], pos[:]) + w = int32(gamma1) - w + t = w >> 31 + y[i][m] = w + (DL_PRIME & t) + } + } +} + +//CRH(rho,t1) +func DL_CRH1(params []int, H []byte, rho []byte, t1 [][DL_DEGREE]int16) { + var pos [2]int + pos[0] = 0; pos[1] = 0 + ck := params[3] + sh := NewSHA3(SHA3_SHAKE256) + //fmt.Printf("rho[1]= %d\n",rho[1]) + for i := 0; i < 32; i++ { + sh.Process(rho[i]) + } + for j := 0; j < ck; j++ { + //fmt.Printf("X t1[j][0]= %d\n",t1[j][0]) + //fmt.Printf("Y t1[j][1]= %d\n",t1[j][1]) + //fmt.Printf("Z t1[j][2]= %d\n",t1[j][2]) + for i := 0; i < (DL_DEGREE*DL_TD)/8; i++ { + nxt := DL_nextbyte16(DL_TD, 0, t1[j][:], pos[:]) + /* if i==0 && j==0 { + //fmt.Printf(" nxt= %d",nxt) + } + */ + sh.Process(nxt) + } + } + sh.Shake(H, 32) + //fmt.Printf("H[0]= %d\n",H[0]) +} + +//CRH(tr,M) +func DL_CRH2(H []byte, tr []byte, mess []byte, mlen int) { + sh := NewSHA3(SHA3_SHAKE256) + for i := 0; i < 32; i++ { + sh.Process(tr[i]) + } + for i := 0; i < mlen; i++ { + sh.Process(mess[i]) + } + sh.Shake(H, 64) +} + +//CRH(K,mu) +func DL_CRH3(H []byte, bK []byte, mu []byte) { + sh := NewSHA3(SHA3_SHAKE256) + for i := 0; i < 32; i++ { + sh.Process(bK[i]) + } + for i := 0; i < 64; i++ { + sh.Process(mu[i]) + } + sh.Shake(H, 64) +} + +//H(mu,w1) +func DL_H4(params []int, CT []byte, mu []byte, w1 [][DL_DEGREE]int8) { + var pos [2]int + pos[0] = 0; pos[1] = 0 + ck := params[3] + dv := params[2] + w1b := 4 + if dv == 88 { + w1b = 6 + } + + sh := NewSHA3(SHA3_SHAKE256) + for i := 0; i < 64; i++ { + sh.Process(mu[i]) + } + for j := 0; j < ck; j++ { + for i := 0; i < (DL_DEGREE*w1b)/8; i++ { + sh.Process(DL_nextbyte8(w1b, 0, w1[j][:], pos[:])) + } + } + sh.Shake(CT, 32) +} + +func DL_SampleInBall(params []int, ct []byte, c []int32) { + tau := params[0] + var signs [8]byte + var buff [136]byte + sh := NewSHA3(SHA3_SHAKE256) + + for i := 0; i < 32; i++ { + sh.Process(ct[i]) + } + sh.Shake(buff[:], 136) + + for i := 0; i < 8; i++ { + signs[i] = buff[i] + } + + k := 8 + b := 0 + DL_poly_zero(c) + var sn int = int(signs[0]) + n := 1 + var j int + + for i := DL_DEGREE - tau; i < DL_DEGREE; i++ { + for next := true; next; next = j > i { + j = int(buff[k]) + k++ + } + c[i] = c[j] + c[j] = 1 - 2*(int32(sn&1)) + sn >>= 1 + b++ + if b == 8 { + sn = int(signs[n]) + n++ + b = 0 + } + } +} + +func DL_Power2Round(t []int32, t0 []int16, t1 []int16) { + var w, d, r int32 + for m := 0; m < DL_DEGREE; m++ { + w = t[m] + d = 1 << DL_D + r = (w + d/2 - 1) >> DL_D + w -= r << DL_D + t1[m] = int16(r) + t0[m] = int16(w) + } +} + +// ALPHA = (Q-1)/16 - borrowed from dilithium ref implementation +func DL_decompose_lo(params []int, a int32) int32 { + var gamma2 int + dv := params[2] + var a0, a1 int32 + a1 = (a + 127) >> 7 + if dv == 32 { + a1 = (a1*1025 + (1 << 21)) >> 22 + a1 &= 15 + gamma2 = (DL_PRIME - 1) / 32 + } else { //88 + a1 = (a1*11275 + (1 << 23)) >> 24 + a1 ^= ((43 - a1) >> 31) & a1 + gamma2 = (DL_PRIME - 1) / 88 + } + + a0 = a - a1 * 2 * int32(gamma2) + a0 -= (((DL_PRIME-1)/2 - a0) >> 31) & DL_PRIME + a0 += (a0 >> 31) & DL_PRIME + + return a0 +} + +// ALPHA = (Q-1)/16 +func DL_decompose_hi(params []int, a int32) int8 { + dv := params[2] + var a1 int32 = (a + 127) >> 7 + + if dv == 32 { + a1 = (a1*1025 + (1 << 21)) >> 22 + a1 &= 15 + } else { + a1 = (a1*11275 + (1 << 23)) >> 24 + a1 ^= ((43 - a1) >> 31) & a1 + } + return int8(a1) +} + +func DL_lobits(params []int, r0 []int32, r []int32) { + for m := 0; m < DL_DEGREE; m++ { + r0[m] = DL_decompose_lo(params, r[m]) + } +} + +func DL_hibits(params []int, r1 []int8, r []int32) { + for m := 0; m < DL_DEGREE; m++ { + r1[m] = DL_decompose_hi(params, r[m]) + } +} + +// before h initialised to zeros, hptr=0 +// after new hptr returned and h[OMEGA+i]= hptr +func DL_MakePartialHint(params []int, h []byte, hptr int, z []int32, r []int32) int { + var a0, a1 int8 + var rz int32 + omega := params[7] + for m := 0; m < DL_DEGREE; m++ { + a0 = DL_decompose_hi(params, r[m]) + rz = r[m] + z[m] + rz -= DL_PRIME + rz = rz + ((rz >> 31) & DL_PRIME) + a1 = DL_decompose_hi(params, rz) + if a0 != a1 { + if hptr >= omega { + return omega + 1 + } + h[hptr] = byte(m) & 0xff + hptr++ + } + } + return hptr +} + +func DL_UsePartialHint(params []int, r []int8, h []byte, hptr int, i int, w []int32) int { + dv := int8(params[2]) + omega := params[7] + md := int8(dv / 2) + var a0 int32 + var a1 int8 + for m := 0; m < DL_DEGREE; m++ { + a1 = DL_decompose_hi(params, w[m]) + if m == int(h[hptr]) && hptr < int(h[omega+i]) { + hptr++ + a0 = DL_decompose_lo(params, w[m]) + if a0 <= DL_PRIME/2 { + a1++ + if a1 >= md { + a1 -= md + } + } else { + a1-- + if a1 < 0 { + a1 += md + } + } + } + r[m] = a1 + } + return hptr +} + +func DL_infinity_norm(w []int32) int32 { + var az int32 + var n int32 + n = 0 + for m := 0; m < DL_DEGREE; m++ { + az = w[m] + if az > (DL_PRIME/2) { + az = DL_PRIME - az + } + if az > n { + n = az + } + } + return n +} + +//Dilithium API +func DL_keypair(params []int, tau []byte, sk []byte, pk []byte) { + var buff [128]byte + var rho [32]byte + var rhod [64]byte + var bK [32]byte + var tr [32]byte // 320 bytes + var Aij [DL_DEGREE]int32 // 1024 bytes + var w [DL_DEGREE]int32 // work space 1024 bytes + var r [DL_DEGREE]int32 // work space 1024 bytes total = 12352 + + ck := params[3] + el := params[4] + + s1 := make([][DL_DEGREE]int8, el) // 1280 bytes + s2 := make([][DL_DEGREE]int8, ck) // 1536 bytes + t0 := make([][DL_DEGREE]int16, ck) // 3072 bytes + t1 := make([][DL_DEGREE]int16, ck) // 3072 bytes + + sh := NewSHA3(SHA3_SHAKE256) + + for i := 0; i < 32; i++ { + sh.Process(tau[i]) + } + sh.Shake(buff[:], 128) + + for i := 0; i < 32; i++ { + rho[i] = buff[i] + bK[i] = buff[i+96] + } + + for i := 0; i < 64; i++ { + rhod[i] = buff[32+i] + } + //fmt.Printf("rhod[0]= %d\n", rhod[0]) + + for i := 0; i < el; i++ { + DL_sample_Sn(params, rhod[:], s1[i][:], i) + } + //fmt.Printf("s1[0][0]= %d\n",s1[0][0]) + + for i := 0; i < ck; i++ { + DL_sample_Sn(params, rhod[:], s2[i][:], el+i) + //fmt.Printf("s2[0][0]= %d\n",s2[0][0]) + DL_poly_zero(r[:]) + for j := 0; j < el; j++ { + DL_poly_scopy(w[:], s1[j][:]) + DL_ntt(w[:]) + DL_ExpandAij(rho[:], Aij[:], i, j) //This is bottleneck + DL_poly_mul(w[:], w[:], Aij[:]) + DL_poly_add(r[:], r[:], w[:]) + //DL_poly_soft_reduce(r[:]) // be lazy + } + DL_poly_hard_reduce(r[:]) + /*for k:=0; k= gamma1-beta { //seems to be always true + badone = true; + break; + } + } + if badone { + continue + } + // Calculate Ay=w-c.s2 and r0=DL_lobits(w-c.s2) + nh = 0 + for i := 0; i < omega+ck; i++ { + hint[i] = 0 + } + for i := 0; i < ck; i++ { + DL_poly_scopy(w[:], s2[i][:]) + DL_ntt(w[:]) + DL_poly_mul(w[:], w[:], c[:]) + + DL_intt(w[:]) + DL_poly_sub(Ay[i][:], Ay[i][:], w[:]) + DL_poly_soft_reduce(Ay[i][:]) // Ay=w-cs2 + DL_lobits(params, w[:], Ay[i][:]) // r0 + if DL_infinity_norm(w[:]) >= gamma2-beta { + badone = true + break + } + + DL_poly_mcopy(w[:], t0[i][:]) + DL_ntt(w[:]) + DL_poly_mul(w[:], w[:], c[:]) + + DL_intt(w[:]) + DL_poly_negate(r[:], w[:]) // -ct0 + if DL_infinity_norm(r[:]) >= gamma2 { + badone = true + break + } + DL_poly_sub(Ay[i][:], Ay[i][:], r[:]) + DL_poly_soft_reduce(Ay[i][:]) + + nh = DL_MakePartialHint(params, hint[:], nh, r[:], Ay[i][:]) + if nh > omega { + badone = true + break + } + hint[omega+i] = byte(nh) + } + if badone { + continue + } + break + } + //fmt.Printf("y[0][0] = %d y[0][1] = %d\n",y[0][0],y[0][1]) + DL_pack_sig(params, sig, y[:], ct[:], hint[:]) + return k + 1 +} + +func DL_verify(params []int, pk []byte, M []byte, sig []byte) bool { + var rho [32]byte + var mu [64]byte + var ct [32]byte + var cct [32]byte + var tr [32]byte // 192 bytes + var hint [100]byte + + var Aij [DL_DEGREE]int32 // 1024 bytes + var c [DL_DEGREE]int32 // 1024 bytes + var w [DL_DEGREE]int32 // work space // 1024 bytes + var r [DL_DEGREE]int32 // work space // 1024 bytes total=14077 bytes + + ck := params[3] + el := params[4] + + z := make([][DL_DEGREE]int32, el) + t1 := make([][DL_DEGREE]int16, ck) + w1d := make([][DL_DEGREE]int8, ck) + + tau := params[0] + lg := params[1] + gamma1 := int32(1<= gamma1-beta { + return false + } + DL_ntt(z[i][:]) // convert to ntt form + } + + DL_CRH1(params, tr[:], rho[:], t1) + DL_CRH2(mu[:], tr[:], M, len(M)) + DL_SampleInBall(params, ct[:], c[:]) + DL_ntt(c[:]) + + // Calculate Az + hints := 0 + for i := 0; i < ck; i++ { + DL_poly_zero(r[:]) + for j := 0; j < el; j++ { + //Note : no NTTs in here + DL_poly_copy(w[:], z[j][:]) + DL_ExpandAij(rho[:], Aij[:], i, j) + DL_poly_mul(w[:], w[:], Aij[:]) + DL_poly_add(r[:], r[:], w[:]) + //DL_poly_soft_reduce(r[:]) // be lazy + } + DL_poly_hard_reduce(r[:]) + + // Calculate Az-ct1.s^d + for m := 0; m < DL_DEGREE; m++ { + w[m] = int32(t1[i][m])< omega { + return false + } + } + + DL_H4(params, cct[:], mu[:], w1d) + + for i := 0; i < 32; i++ { + if ct[i] != cct[i] { + return false + } + } + return true +} + +func DL_keypair_2(tau []byte, sk []byte, pk []byte) { + DL_keypair(DL_PARAMS_2[:], tau, sk, pk) +} + +func DL_signature_2(sk []byte, M []byte, sig []byte) int { + return DL_signature(DL_PARAMS_2[:], sk, M, sig) +} + +func DL_verify_2(pk []byte, M []byte, sig []byte) bool { + return DL_verify(DL_PARAMS_2[:], pk, M, sig) +} + +func DL_keypair_3(tau []byte, sk []byte, pk []byte) { + DL_keypair(DL_PARAMS_3[:], tau, sk, pk) +} + +func DL_signature_3(sk []byte, M []byte, sig []byte) int { + return DL_signature(DL_PARAMS_3[:], sk, M, sig) +} + +func DL_verify_3(pk []byte, M []byte, sig []byte) bool { + return DL_verify(DL_PARAMS_3[:], pk, M, sig) +} + +func DL_keypair_5(tau []byte, sk []byte, pk []byte) { + DL_keypair(DL_PARAMS_5[:], tau, sk, pk) +} + +func DL_signature_5(sk []byte, M []byte, sig []byte) int { + return DL_signature(DL_PARAMS_5[:], sk, M, sig) +} + +func DL_verify_5(pk []byte, M []byte, sig []byte) bool { + return DL_verify(DL_PARAMS_5[:], pk, M, sig) +} diff --git a/ec/bls48581/core/GCM.go b/ec/bls48581/core/GCM.go new file mode 100644 index 0000000..f519f98 --- /dev/null +++ b/ec/bls48581/core/GCM.go @@ -0,0 +1,457 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* +* Implementation of the AES-GCM Encryption/Authentication +* +* Some restrictions.. +* 1. Only for use with AES +* 2. Returned tag is always 128-bits. Truncate at your own risk. +* 3. The order of function calls must follow some rules +* +* Typical sequence of calls.. +* 1. call GCM_init +* 2. call GCM_add_header any number of times, as long as length of header is multiple of 16 bytes (block size) +* 3. call GCM_add_header one last time with any length of header +* 4. call GCM_add_cipher any number of times, as long as length of cipher/plaintext is multiple of 16 bytes +* 5. call GCM_add_cipher one last time with any length of cipher/plaintext +* 6. call GCM_finish to extract the tag. +* +* See http://www.mindspring.com/~dmcgrew/gcm-nist-6.pdf + */ + +package core + +import ( + // "fmt" + "strconv" +) + +const gcm_NB int = 4 +const GCM_ACCEPTING_HEADER int = 0 +const GCM_ACCEPTING_CIPHER int = 1 +const GCM_NOT_ACCEPTING_MORE int = 2 +const GCM_FINISHED int = 3 +const GCM_ENCRYPTING int = 0 +const GCM_DECRYPTING int = 1 + +type GCM struct { + table [128][4]uint32 /* 2k bytes */ + stateX [16]byte + Y_0 [16]byte + counter int + lenA [2]uint32 + lenC [2]uint32 + status int + a *AES +} + +func gcm_pack(b [4]byte) uint32 { /* pack bytes into a 32-bit Word */ + return ((uint32(b[0]) & 0xff) << 24) | ((uint32(b[1]) & 0xff) << 16) | ((uint32(b[2]) & 0xff) << 8) | (uint32(b[3]) & 0xff) +} + +func gcm_unpack(a uint32) [4]byte { /* unpack bytes from a word */ + var b = [4]byte{byte((a >> 24) & 0xff), byte((a >> 16) & 0xff), byte((a >> 8) & 0xff), byte(a & 0xff)} + return b +} + +func (G *GCM) precompute(H []byte) { + var b [4]byte + j := 0 + for i := 0; i < gcm_NB; i++ { + b[0] = H[j] + b[1] = H[j+1] + b[2] = H[j+2] + b[3] = H[j+3] + G.table[0][i] = gcm_pack(b) + j += 4 + } + for i := 1; i < 128; i++ { + c := uint32(0) + for j := 0; j < gcm_NB; j++ { + G.table[i][j] = c | (G.table[i-1][j])>>1 + c = G.table[i-1][j] << 31 + } + if c != 0 { + G.table[i][0] ^= 0xE1000000 + } /* irreducible polynomial */ + } +} + +func (G *GCM) gf2mul() { /* gf2m mul - Z=H*X mod 2^128 */ + var P [4]uint32 + + for i := 0; i < 4; i++ { + P[i] = 0 + } + j := uint(8) + m := 0 + for i := 0; i < 128; i++ { + j-- + c := uint32((G.stateX[m] >> j) & 1) + c = ^c + 1 + for k := 0; k < gcm_NB; k++ { + P[k] ^= (G.table[i][k] & c) + } + if j == 0 { + j = 8 + m++ + if m == 16 { + break + } + } + } + j = 0 + for i := 0; i < gcm_NB; i++ { + b := gcm_unpack(P[i]) + G.stateX[j] = b[0] + G.stateX[j+1] = b[1] + G.stateX[j+2] = b[2] + G.stateX[j+3] = b[3] + j += 4 + } +} + +func (G *GCM) wrap() { /* Finish off GHASH */ + var F [4]uint32 + var L [16]byte + + /* convert lengths from bytes to bits */ + F[0] = (G.lenA[0] << 3) | (G.lenA[1]&0xE0000000)>>29 + F[1] = G.lenA[1] << 3 + F[2] = (G.lenC[0] << 3) | (G.lenC[1]&0xE0000000)>>29 + F[3] = G.lenC[1] << 3 + j := 0 + for i := 0; i < gcm_NB; i++ { + b := gcm_unpack(F[i]) + L[j] = b[0] + L[j+1] = b[1] + L[j+2] = b[2] + L[j+3] = b[3] + j += 4 + } + for i := 0; i < 16; i++ { + G.stateX[i] ^= L[i] + } + G.gf2mul() +} + +func (G *GCM) ghash(plain []byte, len int) bool { + if G.status == GCM_ACCEPTING_HEADER { + G.status = GCM_ACCEPTING_CIPHER + } + if G.status != GCM_ACCEPTING_CIPHER { + return false + } + + j := 0 + for j < len { + for i := 0; i < 16 && j < len; i++ { + G.stateX[i] ^= plain[j] + j++ + G.lenC[1]++ + if G.lenC[1] == 0 { + G.lenC[0]++ + } + } + G.gf2mul() + } + if len%16 != 0 { + G.status = GCM_NOT_ACCEPTING_MORE + } + return true +} + +/* Initialize GCM mode */ +func (G *GCM) Init(nk int, key []byte, niv int, iv []byte) { /* iv size niv is usually 12 bytes (96 bits). AES key size nk can be 16,24 or 32 bytes */ + var H [16]byte + + for i := 0; i < 16; i++ { + H[i] = 0 + G.stateX[i] = 0 + } + + G.a = new(AES) + + G.a.Init(AES_ECB, nk, key, iv) + G.a.ecb_encrypt(H[:]) /* E(K,0) */ + G.precompute(H[:]) + + G.lenA[0] = 0 + G.lenC[0] = 0 + G.lenA[1] = 0 + G.lenC[1] = 0 + if niv == 12 { + for i := 0; i < 12; i++ { + G.a.f[i] = iv[i] + } + b := gcm_unpack(uint32(1)) + G.a.f[12] = b[0] + G.a.f[13] = b[1] + G.a.f[14] = b[2] + G.a.f[15] = b[3] /* initialise IV */ + for i := 0; i < 16; i++ { + G.Y_0[i] = G.a.f[i] + } + } else { + G.status = GCM_ACCEPTING_CIPHER + G.ghash(iv, niv) /* GHASH(H,0,IV) */ + G.wrap() + for i := 0; i < 16; i++ { + G.a.f[i] = G.stateX[i] + G.Y_0[i] = G.a.f[i] + G.stateX[i] = 0 + } + G.lenA[0] = 0 + G.lenC[0] = 0 + G.lenA[1] = 0 + G.lenC[1] = 0 + } + G.status = GCM_ACCEPTING_HEADER +} + +/* Add Header data - included but not encrypted */ +func (G *GCM) Add_header(header []byte, len int) bool { /* Add some header. Won't be encrypted, but will be authenticated. len is length of header */ + if G.status != GCM_ACCEPTING_HEADER { + return false + } + + j := 0 + for j < len { + for i := 0; i < 16 && j < len; i++ { + G.stateX[i] ^= header[j] + j++ + G.lenA[1]++ + if G.lenA[1] == 0 { + G.lenA[0]++ + } + } + G.gf2mul() + } + if len%16 != 0 { + G.status = GCM_ACCEPTING_CIPHER + } + + return true +} + +/* Add Plaintext - included and encrypted */ +func (G *GCM) Add_plain(plain []byte, len int) []byte { + var B [16]byte + var b [4]byte + + cipher := make([]byte, len) + var counter uint32 = 0 + if G.status == GCM_ACCEPTING_HEADER { + G.status = GCM_ACCEPTING_CIPHER + } + if G.status != GCM_ACCEPTING_CIPHER { + return nil + } + + j := 0 + for j < len { + + b[0] = G.a.f[12] + b[1] = G.a.f[13] + b[2] = G.a.f[14] + b[3] = G.a.f[15] + counter = gcm_pack(b) + counter++ + b = gcm_unpack(counter) + G.a.f[12] = b[0] + G.a.f[13] = b[1] + G.a.f[14] = b[2] + G.a.f[15] = b[3] /* increment counter */ + for i := 0; i < 16; i++ { + B[i] = G.a.f[i] + } + G.a.ecb_encrypt(B[:]) /* encrypt it */ + + for i := 0; i < 16 && j < len; i++ { + cipher[j] = (plain[j] ^ B[i]) + G.stateX[i] ^= cipher[j] + j++ + G.lenC[1]++ + if G.lenC[1] == 0 { + G.lenC[0]++ + } + } + G.gf2mul() + } + if len%16 != 0 { + G.status = GCM_NOT_ACCEPTING_MORE + } + return cipher +} + +/* Add Ciphertext - decrypts to plaintext */ +func (G *GCM) Add_cipher(cipher []byte, len int) []byte { + var B [16]byte + var b [4]byte + + plain := make([]byte, len) + var counter uint32 = 0 + + if G.status == GCM_ACCEPTING_HEADER { + G.status = GCM_ACCEPTING_CIPHER + } + if G.status != GCM_ACCEPTING_CIPHER { + return nil + } + + j := 0 + for j < len { + b[0] = G.a.f[12] + b[1] = G.a.f[13] + b[2] = G.a.f[14] + b[3] = G.a.f[15] + counter = gcm_pack(b) + counter++ + b = gcm_unpack(counter) + G.a.f[12] = b[0] + G.a.f[13] = b[1] + G.a.f[14] = b[2] + G.a.f[15] = b[3] /* increment counter */ + for i := 0; i < 16; i++ { + B[i] = G.a.f[i] + } + G.a.ecb_encrypt(B[:]) /* encrypt it */ + for i := 0; i < 16 && j < len; i++ { + oc := cipher[j] + plain[j] = (cipher[j] ^ B[i]) + G.stateX[i] ^= oc + j++ + G.lenC[1]++ + if G.lenC[1] == 0 { + G.lenC[0]++ + } + } + G.gf2mul() + } + if len%16 != 0 { + G.status = GCM_NOT_ACCEPTING_MORE + } + return plain +} + +/* Finish and extract Tag */ +func (G *GCM) Finish(extract bool) []byte { /* Finish off GHASH and extract tag (MAC) */ + var tag []byte + + G.wrap() + /* extract tag */ + if extract { + G.a.ecb_encrypt(G.Y_0[:]) /* E(K,Y0) */ + for i := 0; i < 16; i++ { + G.Y_0[i] ^= G.stateX[i] + } + for i := 0; i < 16; i++ { + tag = append(tag, G.Y_0[i]) + G.Y_0[i] = 0 + G.stateX[i] = 0 + } + } + G.status = GCM_FINISHED + G.a.End() + return tag +} + +func hex2bytes(s string) []byte { + lgh := len(s) + data := make([]byte, lgh/2) + + for i := 0; i < lgh; i += 2 { + a, _ := strconv.ParseInt(s[i:i+2], 16, 32) + data[i/2] = byte(a) + } + return data +} + +func GCM_ENCRYPT(K []byte, IV []byte, H []byte, P []byte) ([]byte, []byte) { + g := new(GCM) + g.Init(len(K), K, len(IV), IV) + g.Add_header(H, len(H)) + C := g.Add_plain(P, len(P)) + T := g.Finish(true) + return C, T +} + +func GCM_DECRYPT(K []byte, IV []byte, H []byte, C []byte) ([]byte, []byte) { + g := new(GCM) + g.Init(len(K), K, len(IV), IV) + g.Add_header(H, len(H)) + P := g.Add_cipher(C, len(C)) + T := g.Finish(true) + return P, T +} + +/* +func main() { + + KT:="feffe9928665731c6d6a8f9467308308" + MT:="d9313225f88406e5a55909c5aff5269a86a7a9531534f7da2e4c303d8a318a721c3c0c95956809532fcf0e2449a6b525b16aedf5aa0de657ba637b39" + HT:="feedfacedeadbeeffeedfacedeadbeefabaddad2" + + NT:="9313225df88406e555909c5aff5269aa6a7a9538534f7da1e4c303d2a318a728c3c0c95156809539fcf0e2429a6b525416aedbf5a0de6a57a637b39b"; +// Tag should be 619cc5aefffe0bfa462af43c1699d050 + + g:=new(GCM) + + M:=hex2bytes(MT) + H:=hex2bytes(HT) + N:=hex2bytes(NT) + K:=hex2bytes(KT) + + lenM:=len(M) + lenH:=len(H) + lenK:=len(K) + lenIV:=len(N) + + fmt.Printf("Plaintext=\n"); + for i:=0;i> n) | ((x) << (32 - n))) +} + +func hash256_R(n uint32, x uint32) uint32 { + return ((x) >> n) +} + +func hash256_Ch(x, y, z uint32) uint32 { + return ((x & y) ^ (^(x) & z)) +} + +func hash256_Maj(x, y, z uint32) uint32 { + return ((x & y) ^ (x & z) ^ (y & z)) +} + +func hash256_Sig0(x uint32) uint32 { + return (hash256_S(2, x) ^ hash256_S(13, x) ^ hash256_S(22, x)) +} + +func hash256_Sig1(x uint32) uint32 { + return (hash256_S(6, x) ^ hash256_S(11, x) ^ hash256_S(25, x)) +} + +func hash256_theta0(x uint32) uint32 { + return (hash256_S(7, x) ^ hash256_S(18, x) ^ hash256_R(3, x)) +} + +func hash256_theta1(x uint32) uint32 { + return (hash256_S(17, x) ^ hash256_S(19, x) ^ hash256_R(10, x)) +} + +func (H *HASH256) transform() { /* basic transformation step */ + for j := 16; j < 64; j++ { + H.w[j] = hash256_theta1(H.w[j-2]) + H.w[j-7] + hash256_theta0(H.w[j-15]) + H.w[j-16] + } + a := H.h[0] + b := H.h[1] + c := H.h[2] + d := H.h[3] + e := H.h[4] + f := H.h[5] + g := H.h[6] + hh := H.h[7] + for j := 0; j < 64; j++ { /* 64 times - mush it up */ + t1 := hh + hash256_Sig1(e) + hash256_Ch(e, f, g) + hash256_K[j] + H.w[j] + t2 := hash256_Sig0(a) + hash256_Maj(a, b, c) + hh = g + g = f + f = e + e = d + t1 + d = c + c = b + b = a + a = t1 + t2 + } + H.h[0] += a + H.h[1] += b + H.h[2] += c + H.h[3] += d + H.h[4] += e + H.h[5] += f + H.h[6] += g + H.h[7] += hh +} + +/* Initialise Hash function */ +func (H *HASH256) Init() { /* initialise */ + for i := 0; i < 64; i++ { + H.w[i] = 0 + } + H.length[0] = 0 + H.length[1] = 0 + H.h[0] = hash256_H0 + H.h[1] = hash256_H1 + H.h[2] = hash256_H2 + H.h[3] = hash256_H3 + H.h[4] = hash256_H4 + H.h[5] = hash256_H5 + H.h[6] = hash256_H6 + H.h[7] = hash256_H7 +} + +func NewHASH256() *HASH256 { + H := new(HASH256) + H.Init() + return H +} + +func NewHASH256copy(HC *HASH256) *HASH256 { + H := new(HASH256) + for i := 0; i < 64; i++ { + H.w[i] = HC.w[i] + } + for i := 0; i < 8; i++ { + H.h[i] = HC.h[i] + } + H.length[0] = HC.length[0] + H.length[1] = HC.length[1] + return H +} + +/* process a single byte */ +func (H *HASH256) Process(byt byte) { /* process the next message byte */ + cnt := (H.length[0] / 32) % 16 + + H.w[cnt] <<= 8 + H.w[cnt] |= uint32(byt & 0xFF) + H.length[0] += 8 + if H.length[0] == 0 { + H.length[1]++ + H.length[0] = 0 + } + if (H.length[0] % 512) == 0 { + H.transform() + } +} + +/* process an array of bytes */ +func (H *HASH256) Process_array(b []byte) { + for i := 0; i < len(b); i++ { + H.Process((b[i])) + } +} + +/* process a 32-bit integer */ +func (H *HASH256) Process_num(n int32) { + H.Process(byte((n >> 24) & 0xff)) + H.Process(byte((n >> 16) & 0xff)) + H.Process(byte((n >> 8) & 0xff)) + H.Process(byte(n & 0xff)) +} + +/* Generate 32-byte Hash */ +func (H *HASH256) Hash() []byte { /* pad message and finish - supply digest */ + var digest [32]byte + len0 := H.length[0] + len1 := H.length[1] + H.Process(0x80) + for (H.length[0] % 512) != 448 { + H.Process(0) + } + H.w[14] = len1 + H.w[15] = len0 + H.transform() + for i := 0; i < 32; i++ { /* convert to bytes */ + digest[i] = byte((H.h[i/4] >> uint(8*(3-i%4))) & 0xff) + } + H.Init() + return digest[0:32] +} + +func (H *HASH256) Continuing_Hash() []byte { + sh := NewHASH256copy(H) + return sh.Hash() +} + +/* test program: should produce digest */ + +//248d6a61 d20638b8 e5c02693 0c3e6039 a33ce459 64ff2167 f6ecedd4 19db06c1 +/* +func main() { + + test := []byte("abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq") + sh:=NewHASH256() + + for i:=0;i> n) | ((x) << (64 - n))) +} + +func hash384_R(n uint64, x uint64) uint64 { + return ((x) >> n) +} + +func hash384_Ch(x, y, z uint64) uint64 { + return ((x & y) ^ (^(x) & z)) +} + +func hash384_Maj(x, y, z uint64) uint64 { + return ((x & y) ^ (x & z) ^ (y & z)) +} + +func hash384_Sig0(x uint64) uint64 { + return (hash384_S(28, x) ^ hash384_S(34, x) ^ hash384_S(39, x)) +} + +func hash384_Sig1(x uint64) uint64 { + return (hash384_S(14, x) ^ hash384_S(18, x) ^ hash384_S(41, x)) +} + +func hash384_theta0(x uint64) uint64 { + return (hash384_S(1, x) ^ hash384_S(8, x) ^ hash384_R(7, x)) +} + +func hash384_theta1(x uint64) uint64 { + return (hash384_S(19, x) ^ hash384_S(61, x) ^ hash384_R(6, x)) +} + +func (H *HASH384) transform() { /* basic transformation step */ + for j := 16; j < 80; j++ { + H.w[j] = hash384_theta1(H.w[j-2]) + H.w[j-7] + hash384_theta0(H.w[j-15]) + H.w[j-16] + } + a := H.h[0] + b := H.h[1] + c := H.h[2] + d := H.h[3] + e := H.h[4] + f := H.h[5] + g := H.h[6] + hh := H.h[7] + for j := 0; j < 80; j++ { /* 80 times - mush it up */ + t1 := hh + hash384_Sig1(e) + hash384_Ch(e, f, g) + hash384_K[j] + H.w[j] + t2 := hash384_Sig0(a) + hash384_Maj(a, b, c) + hh = g + g = f + f = e + e = d + t1 + d = c + c = b + b = a + a = t1 + t2 + } + H.h[0] += a + H.h[1] += b + H.h[2] += c + H.h[3] += d + H.h[4] += e + H.h[5] += f + H.h[6] += g + H.h[7] += hh +} + +/* Initialise Hash function */ +func (H *HASH384) Init() { /* initialise */ + for i := 0; i < 80; i++ { + H.w[i] = 0 + } + H.length[0] = 0 + H.length[1] = 0 + H.h[0] = hash384_H0 + H.h[1] = hash384_H1 + H.h[2] = hash384_H2 + H.h[3] = hash384_H3 + H.h[4] = hash384_H4 + H.h[5] = hash384_H5 + H.h[6] = hash384_H6 + H.h[7] = hash384_H7 +} + +func NewHASH384() *HASH384 { + H := new(HASH384) + H.Init() + return H +} + +func NewHASH384copy(HC *HASH384) *HASH384 { + H := new(HASH384) + for i := 0; i < 80; i++ { + H.w[i] = HC.w[i] + } + for i := 0; i < 8; i++ { + H.h[i] = HC.h[i] + } + H.length[0] = HC.length[0] + H.length[1] = HC.length[1] + return H +} + +/* process a single byte */ +func (H *HASH384) Process(byt byte) { /* process the next message byte */ + cnt := (H.length[0] / 64) % 16 + + H.w[cnt] <<= 8 + H.w[cnt] |= uint64(byt & 0xFF) + H.length[0] += 8 + if H.length[0] == 0 { + H.length[1]++ + H.length[0] = 0 + } + if (H.length[0] % 1024) == 0 { + H.transform() + } +} + +/* process an array of bytes */ +func (H *HASH384) Process_array(b []byte) { + for i := 0; i < len(b); i++ { + H.Process((b[i])) + } +} + +/* process a 32-bit integer */ +func (H *HASH384) Process_num(n int32) { + H.Process(byte((n >> 24) & 0xff)) + H.Process(byte((n >> 16) & 0xff)) + H.Process(byte((n >> 8) & 0xff)) + H.Process(byte(n & 0xff)) +} + +/* Generate 32-byte Hash */ +func (H *HASH384) Hash() []byte { /* pad message and finish - supply digest */ + var digest [48]byte + len0 := H.length[0] + len1 := H.length[1] + H.Process(0x80) + for (H.length[0] % 1024) != 896 { + H.Process(0) + } + H.w[14] = len1 + H.w[15] = len0 + H.transform() + for i := 0; i < 48; i++ { /* convert to bytes */ + digest[i] = byte((H.h[i/8] >> uint(8*(7-i%8))) & 0xff) + } + H.Init() + return digest[0:48] +} + +func (H *HASH384) Continuing_Hash() []byte { + sh := NewHASH384copy(H) + return sh.Hash() +} + +/* test program: should produce digest */ + +//09330c33f71147e8 3d192fc782cd1b47 53111b173b3b05d2 2fa08086e3b0f712 fcc7c71a557e2db9 66c3e9fa91746039 +/* +func main() { + + test := []byte("abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu") + sh:=NewHASH384() + + for i:=0;i> n) | ((x) << (64 - n))) +} + +func hash512_R(n uint64, x uint64) uint64 { + return ((x) >> n) +} + +func hash512_Ch(x, y, z uint64) uint64 { + return ((x & y) ^ (^(x) & z)) +} + +func hash512_Maj(x, y, z uint64) uint64 { + return ((x & y) ^ (x & z) ^ (y & z)) +} + +func hash512_Sig0(x uint64) uint64 { + return (hash512_S(28, x) ^ hash512_S(34, x) ^ hash512_S(39, x)) +} + +func hash512_Sig1(x uint64) uint64 { + return (hash512_S(14, x) ^ hash512_S(18, x) ^ hash512_S(41, x)) +} + +func hash512_theta0(x uint64) uint64 { + return (hash512_S(1, x) ^ hash512_S(8, x) ^ hash512_R(7, x)) +} + +func hash512_theta1(x uint64) uint64 { + return (hash512_S(19, x) ^ hash512_S(61, x) ^ hash512_R(6, x)) +} + +func (H *HASH512) transform() { /* basic transformation step */ + for j := 16; j < 80; j++ { + H.w[j] = hash512_theta1(H.w[j-2]) + H.w[j-7] + hash512_theta0(H.w[j-15]) + H.w[j-16] + } + a := H.h[0] + b := H.h[1] + c := H.h[2] + d := H.h[3] + e := H.h[4] + f := H.h[5] + g := H.h[6] + hh := H.h[7] + for j := 0; j < 80; j++ { /* 80 times - mush it up */ + t1 := hh + hash512_Sig1(e) + hash512_Ch(e, f, g) + hash512_K[j] + H.w[j] + t2 := hash512_Sig0(a) + hash512_Maj(a, b, c) + hh = g + g = f + f = e + e = d + t1 + d = c + c = b + b = a + a = t1 + t2 + } + H.h[0] += a + H.h[1] += b + H.h[2] += c + H.h[3] += d + H.h[4] += e + H.h[5] += f + H.h[6] += g + H.h[7] += hh +} + +/* Initialise Hash function */ +func (H *HASH512) Init() { /* initialise */ + for i := 0; i < 80; i++ { + H.w[i] = 0 + } + H.length[0] = 0 + H.length[1] = 0 + H.h[0] = hash512_H0 + H.h[1] = hash512_H1 + H.h[2] = hash512_H2 + H.h[3] = hash512_H3 + H.h[4] = hash512_H4 + H.h[5] = hash512_H5 + H.h[6] = hash512_H6 + H.h[7] = hash512_H7 +} + +func NewHASH512() *HASH512 { + H := new(HASH512) + H.Init() + return H +} + +func NewHASH512copy(HC *HASH512) *HASH512 { + H := new(HASH512) + for i := 0; i < 80; i++ { + H.w[i] = HC.w[i] + } + for i := 0; i < 8; i++ { + H.h[i] = HC.h[i] + } + H.length[0] = HC.length[0] + H.length[1] = HC.length[1] + return H +} + +/* process a single byte */ +func (H *HASH512) Process(byt byte) { /* process the next message byte */ + cnt := (H.length[0] / 64) % 16 + + H.w[cnt] <<= 8 + H.w[cnt] |= uint64(byt & 0xFF) + H.length[0] += 8 + if H.length[0] == 0 { + H.length[1]++ + H.length[0] = 0 + } + if (H.length[0] % 1024) == 0 { + H.transform() + } +} + +/* process an array of bytes */ +func (H *HASH512) Process_array(b []byte) { + for i := 0; i < len(b); i++ { + H.Process((b[i])) + } +} + +/* process a 32-bit integer */ +func (H *HASH512) Process_num(n int32) { + H.Process(byte((n >> 24) & 0xff)) + H.Process(byte((n >> 16) & 0xff)) + H.Process(byte((n >> 8) & 0xff)) + H.Process(byte(n & 0xff)) +} + +/* Generate 64-byte Hash */ +func (H *HASH512) Hash() []byte { /* pad message and finish - supply digest */ + var digest [64]byte + len0 := H.length[0] + len1 := H.length[1] + H.Process(0x80) + for (H.length[0] % 1024) != 896 { + H.Process(0) + } + H.w[14] = len1 + H.w[15] = len0 + H.transform() + for i := 0; i < 64; i++ { /* convert to bytes */ + digest[i] = byte((H.h[i/8] >> uint(8*(7-i%8))) & 0xff) + } + H.Init() + return digest[0:64] +} + +func (H *HASH512) Continuing_Hash() []byte { + sh := NewHASH512copy(H) + return sh.Hash() +} + +/* test program: should produce digest */ + +//8e959b75dae313da 8cf4f72814fc143f 8f7779c6eb9f7fa1 7299aeadb6889018 501d289e4900f7e4 331b99dec4b5433a c7d329eeb6dd2654 5e96e55b874be909 +/* +func main() { + + test := []byte("abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu") + sh:=NewHASH512() + + for i:=0;i 0 && i > 0 { + i-- + b[i] = byte(n & 0xff) + n /= 256 + } + return b +} + +/* general purpose hashing of Byte array|integer|Byte array. Output of length olen, padded with leading zeros if required */ + +func GPhashit(hash int, hlen int, olen int, zpad int, A []byte, n int32, B []byte) []byte { + var R []byte + if hash == MC_SHA2 { + if hlen == SHA256 { + H := NewHASH256() + for i := 0; i < zpad; i++ { + H.Process(0) + } + if A != nil { + H.Process_array(A) + } + if n >= 0 { + H.Process_num(int32(n)) + } + if B != nil { + H.Process_array(B) + } + R = H.Hash() + } + if hlen == SHA384 { + H := NewHASH384() + for i := 0; i < zpad; i++ { + H.Process(0) + } + if A != nil { + H.Process_array(A) + } + if n >= 0 { + H.Process_num(int32(n)) + } + if B != nil { + H.Process_array(B) + } + R = H.Hash() + } + if hlen == SHA512 { + H := NewHASH512() + for i := 0; i < zpad; i++ { + H.Process(0) + } + if A != nil { + H.Process_array(A) + } + if n >= 0 { + H.Process_num(int32(n)) + } + if B != nil { + H.Process_array(B) + } + R = H.Hash() + } + } + if hash == MC_SHA3 { + H := NewSHA3(hlen) + for i := 0; i < zpad; i++ { + H.Process(0) + } + if A != nil { + H.Process_array(A) + } + if n >= 0 { + H.Process_num(int32(n)) + } + if B != nil { + H.Process_array(B) + } + R = H.Hash() + } + + if R == nil { + return nil + } + + if olen == 0 { + return R + } + var W []byte + for i := 0; i < olen; i++ { + W = append(W, 0) + } + if olen <= hlen { + for i := 0; i < olen; i++ { + W[i] = R[i] + } + } else { + for i := 0; i < hlen; i++ { + W[i+olen-hlen] = R[i] + } + for i := 0; i < olen-hlen; i++ { + W[i] = 0 + } + } + return W +} + +/* Simple hashing of byte array */ +func SPhashit(hash int, hlen int, A []byte) []byte { + return GPhashit(hash, hlen, 0, 0, A, -1, nil) +} + +/* Key Derivation Function */ +/* Input octet Z */ +/* Output key of length olen */ + +func KDF2(hash int, sha int, Z []byte, P []byte, olen int) []byte { + /* NOTE: the parameter olen is the length of the output k in bytes */ + hlen := sha + var K []byte + k := 0 + + for i := 0; i < olen; i++ { + K = append(K, 0) + } + + cthreshold := olen / hlen + if olen%hlen != 0 { + cthreshold++ + } + + for counter := 1; counter <= cthreshold; counter++ { + B := GPhashit(hash, sha, 0, 0, Z, int32(counter), P) + if k+hlen > olen { + for i := 0; i < olen%hlen; i++ { + K[k] = B[i] + k++ + } + } else { + for i := 0; i < hlen; i++ { + K[k] = B[i] + k++ + } + } + } + return K +} + +/* Password based Key Derivation Function */ +/* Input password p, salt s, and repeat count */ +/* Output key of length olen */ +func PBKDF2(hash int, sha int, Pass []byte, Salt []byte, rep int, olen int) []byte { + d := olen / sha + if olen%sha != 0 { + d++ + } + + var F []byte + var U []byte + var S []byte + var K []byte + + for i := 0; i < sha; i++ { + F = append(F, 0) + U = append(U, 0) + } + + for i := 1; i <= d; i++ { + for j := 0; j < len(Salt); j++ { + S = append(S, Salt[j]) + } + N := InttoBytes(i, 4) + for j := 0; j < 4; j++ { + S = append(S, N[j]) + } + + HMAC(MC_SHA2, sha, F[:], sha, S, Pass) + + for j := 0; j < sha; j++ { + U[j] = F[j] + } + for j := 2; j <= rep; j++ { + HMAC(MC_SHA2, sha, U[:], sha, U[:], Pass) + for k := 0; k < sha; k++ { + F[k] ^= U[k] + } + } + for j := 0; j < sha; j++ { + K = append(K, F[j]) + } + } + var key []byte + for i := 0; i < olen; i++ { + key = append(key, K[i]) + } + return key +} + +func blksize(hash int, sha int) int { + b := 0 + if hash == MC_SHA2 { + b = 64 + if sha > 32 { + b = 128 + } + } + if hash == MC_SHA3 { + b = 200 - 2*sha + } + return b +} + +/* Calculate HMAC of m using key k. HMAC is tag of length olen (which is length of tag) */ +func HMAC(hash int, sha int, tag []byte, olen int, K []byte, M []byte) int { + /* Input is from an octet m * + * olen is requested output length in bytes. k is the key * + * The output is the calculated tag */ + var B []byte + + b := blksize(hash, sha) + if b == 0 { + return 0 + } + + var K0 [200]byte + //olen := len(tag) + + for i := 0; i < b; i++ { + K0[i] = 0 + } + + if len(K) > b { + B = SPhashit(hash, sha, K) + for i := 0; i < sha; i++ { + K0[i] = B[i] + } + } else { + for i := 0; i < len(K); i++ { + K0[i] = K[i] + } + } + + for i := 0; i < b; i++ { + K0[i] ^= 0x36 + } + B = GPhashit(hash, sha, 0, 0, K0[0:b], -1, M) + + for i := 0; i < b; i++ { + K0[i] ^= 0x6a + } + B = GPhashit(hash, sha, olen, 0, K0[0:b], -1, B) + + for i := 0; i < olen; i++ { + tag[i] = B[i] + } + + return 1 +} + +func HKDF_Extract(hash int, hlen int, SALT []byte, IKM []byte) []byte { + var PRK []byte + for i := 0; i < hlen; i++ { + PRK = append(PRK, 0) + } + if SALT == nil { + var H []byte + for i := 0; i < hlen; i++ { + H = append(H, 0) + } + HMAC(hash, hlen, PRK, hlen, H, IKM) + } else { + HMAC(hash, hlen, PRK, hlen, SALT, IKM) + } + return PRK +} + +func HKDF_Expand(hash int, hlen int, olen int, PRK []byte, INFO []byte) []byte { + n := olen / hlen + flen := olen % hlen + + var OKM []byte + var T []byte + var K [64]byte + + for i := 1; i <= n; i++ { + for j := 0; j < len(INFO); j++ { + T = append(T, INFO[j]) + } + T = append(T, byte(i)) + HMAC(hash, hlen, K[:], hlen, PRK, T) + T = nil + for j := 0; j < hlen; j++ { + OKM = append(OKM, K[j]) + T = append(T, K[j]) + } + } + if flen > 0 { + for j := 0; j < len(INFO); j++ { + T = append(T, INFO[j]) + } + T = append(T, byte(n+1)) + HMAC(hash, hlen, K[:], flen, PRK, T) + for j := 0; j < flen; j++ { + OKM = append(OKM, K[j]) + } + } + return OKM +} + +func ceil(a int, b int) int { + return (((a)-1)/(b) + 1) +} + +func XOF_Expand(hlen int, olen int, DST []byte, MSG []byte) []byte { + var OKM = make([]byte, olen) + H := NewSHA3(hlen) + for i := 0; i < len(MSG); i++ { + H.Process(MSG[i]) + } + H.Process(byte((olen >> 8) & 0xff)) + H.Process(byte(olen & 0xff)) + + for i := 0; i < len(DST); i++ { + H.Process(DST[i]) + } + H.Process(byte(len(DST) & 0xff)) + + H.Shake(OKM[:], olen) + return OKM +} + +func xmd_Expand_Short_DST(hash int, hlen int, olen int, DST []byte, MSG []byte) []byte { + var OKM = make([]byte, olen) + var TMP = make([]byte, len(DST)+4) + + ell := ceil(olen, hlen) + blk := blksize(hash, hlen) + TMP[0] = byte((olen >> 8) & 0xff) + TMP[1] = byte(olen & 0xff) + TMP[2] = byte(0) + + for j := 0; j < len(DST); j++ { + TMP[3+j] = DST[j] + } + TMP[3+len(DST)] = byte(len(DST) & 0xff) + var H0 = GPhashit(hash, hlen, 0, blk, MSG, -1, TMP) + + var H1 = make([]byte, hlen) + var TMP2 = make([]byte, len(DST)+2) + + k := 0 + for i := 1; i <= ell; i++ { + for j := 0; j < hlen; j++ { + H1[j] ^= H0[j] + } + TMP2[0] = byte(i) + + for j := 0; j < len(DST); j++ { + TMP2[1+j] = DST[j] + } + TMP2[1+len(DST)] = byte(len(DST) & 0xff) + + H1 = GPhashit(hash, hlen, 0, 0, H1, -1, TMP2) + for j := 0; j < hlen && k < olen; j++ { + OKM[k] = H1[j] + k++ + } + } + return OKM +} + +func XMD_Expand(hash int, hlen int, olen int, DST []byte, MSG []byte) []byte { + var R []byte + OS := []byte("H2C-OVERSIZE-DST-") + if len(DST)>=256 { + W := GPhashit(hash, hlen, 0, 0, OS, -1, DST) + R=xmd_Expand_Short_DST(hash,hlen,olen,W,MSG) + } else { + R=xmd_Expand_Short_DST(hash,hlen,olen,DST,MSG) + } + return R; +} + +/* Mask Generation Function */ + +func MGF1(sha int, Z []byte, olen int, K []byte) { + hlen := sha + + var k int = 0 + for i := 0; i < len(K); i++ { + K[i] = 0 + } + + cthreshold := olen / hlen + if olen%hlen != 0 { + cthreshold++ + } + for counter := 0; counter < cthreshold; counter++ { + B := GPhashit(MC_SHA2, sha, 0, 0, Z, int32(counter), nil) + //B := hashit(sha, Z, counter) + + if k+hlen > olen { + for i := 0; i < olen%hlen; i++ { + K[k] = B[i] + k++ + } + } else { + for i := 0; i < hlen; i++ { + K[k] = B[i] + k++ + } + } + } +} + +func MGF1XOR(sha int, Z []byte, olen int, K []byte) { + hlen := sha + + var k int = 0 + + cthreshold := olen / hlen + if olen%hlen != 0 { + cthreshold++ + } + for counter := 0; counter < cthreshold; counter++ { + B := GPhashit(MC_SHA2, sha, 0, 0, Z, int32(counter), nil) + //B := hashit(sha, Z, counter) + + if k+hlen > olen { + for i := 0; i < olen%hlen; i++ { + K[k] ^= B[i] + k++ + } + } else { + for i := 0; i < hlen; i++ { + K[k] ^= B[i] + k++ + } + } + } +} + +/* SHAXXX identifier strings */ +var SHA256ID = [...]byte{0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20} +var SHA384ID = [...]byte{0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30} +var SHA512ID = [...]byte{0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40} + +func RSA_PKCS15(sha int, m []byte, w []byte, RFS int) bool { + olen := RFS + hlen := sha + idlen := 19 + + if olen < idlen+hlen+10 { + return false + } + H := SPhashit(MC_SHA2, sha, m) + //H := hashit(sha, m, -1) + + for i := 0; i < len(w); i++ { + w[i] = 0 + } + i := 0 + w[i] = 0 + i++ + w[i] = 1 + i++ + for j := 0; j < olen-idlen-hlen-3; j++ { + w[i] = 0xff + i++ + } + w[i] = 0 + i++ + + if hlen == SHA256 { + for j := 0; j < idlen; j++ { + w[i] = SHA256ID[j] + i++ + } + } + if hlen == SHA384 { + for j := 0; j < idlen; j++ { + w[i] = SHA384ID[j] + i++ + } + } + if hlen == SHA512 { + for j := 0; j < idlen; j++ { + w[i] = SHA512ID[j] + i++ + } + } + for j := 0; j < hlen; j++ { + w[i] = H[j] + i++ + } + + return true +} + +/* SHAXXX identifier strings */ +var SHA256IDb = [...]byte{0x30, 0x2f, 0x30, 0x0b, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x04, 0x20} +var SHA384IDb = [...]byte{0x30, 0x3f, 0x30, 0x0b, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x04, 0x30} +var SHA512IDb = [...]byte{0x30, 0x4f, 0x30, 0x0b, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x04, 0x40} + +func RSA_PKCS15b(sha int, m []byte, w []byte, RFS int) bool { + olen := RFS + hlen := sha + idlen := 17 + + if olen < idlen+hlen+10 { + return false + } + H := SPhashit(MC_SHA2,sha,m) + //H := hashit(sha, m, -1) + + for i := 0; i < len(w); i++ { + w[i] = 0 + } + i := 0 + w[i] = 0 + i++ + w[i] = 1 + i++ + for j := 0; j < olen-idlen-hlen-3; j++ { + w[i] = 0xff + i++ + } + w[i] = 0 + i++ + + if hlen == SHA256 { + for j := 0; j < idlen; j++ { + w[i] = SHA256IDb[j] + i++ + } + } + if hlen == SHA384 { + for j := 0; j < idlen; j++ { + w[i] = SHA384IDb[j] + i++ + } + } + if hlen == SHA512 { + for j := 0; j < idlen; j++ { + w[i] = SHA512IDb[j] + i++ + } + } + for j := 0; j < hlen; j++ { + w[i] = H[j] + i++ + } + return true +} + + +func RSA_PSS_ENCODE(sha int, m []byte, rng *RAND, RFS int) []byte { + emlen := RFS + embits := 8*emlen - 1 + + hlen := sha + SALT := make([]byte, hlen) + for i := 0; i < hlen; i++ { + SALT[i] = rng.GetByte() + } + mask := byte(0xff >> (8*emlen - embits)) + + H := SPhashit(MC_SHA2, sha, m) + if emlen < hlen+hlen+2 { + return nil + } + + MD := make([]byte, 8+hlen+hlen) + for i := 0; i < 8; i++ { + MD[i] = 0 + } + for i := 0; i < hlen; i++ { + MD[8+i] = H[i] + } + for i := 0; i < hlen; i++ { + MD[8+hlen+i] = SALT[i] + } + H = SPhashit(MC_SHA2, sha, MD) + f := make([]byte, RFS) + for i := 0; i < emlen-hlen-hlen-2; i++ { + f[i] = 0 + } + f[emlen-hlen-hlen-2] = 0x1 + for i := 0; i < hlen; i++ { + f[emlen+i-hlen-hlen-1] = SALT[i] + } + + MGF1XOR(sha, H, emlen-hlen-1, f) + f[0] &= mask + for i := 0; i < hlen; i++ { + f[emlen+i-hlen-1] = H[i] + } + f[emlen-1] = byte(0xbc) + return f +} + +func RSA_PSS_VERIFY(sha int, m []byte, f []byte) bool { + emlen := len(f) + embits := 8*emlen - 1 + hlen := sha + SALT := make([]byte, hlen) + mask := byte(0xff >> (8*emlen - embits)) + + HMASK := SPhashit(MC_SHA2, sha, m) + if emlen < hlen+hlen+2 { + return false + } + if f[emlen-1] != byte(0xbc) { + return false + } + if (f[0] & (^mask)) != 0 { + return false + } + DB := make([]byte, emlen-hlen-1) + for i := 0; i < emlen-hlen-1; i++ { + DB[i] = f[i] + } + H := make([]byte, hlen) + for i := 0; i < hlen; i++ { + H[i] = f[emlen+i-hlen-1] + } + MGF1XOR(sha, H, emlen-hlen-1, DB) + DB[0] &= mask + k := byte(0) + for i := 0; i < emlen-hlen-hlen-2; i++ { + k |= DB[i] + } + if k != 0 { + return false + } + if DB[emlen-hlen-hlen-2] != 0x01 { + return false + } + + for i := 0; i < hlen; i++ { + SALT[i] = DB[emlen+i-hlen-hlen-1] + } + MD := make([]byte, 8+hlen+hlen) + for i := 0; i < 8; i++ { + MD[i] = 0 + } + for i := 0; i < hlen; i++ { + MD[8+i] = HMASK[i] + } + for i := 0; i < hlen; i++ { + MD[8+hlen+i] = SALT[i] + } + HMASK = SPhashit(MC_SHA2, sha, MD) + k = 0 + for i := 0; i < hlen; i++ { + k |= (H[i] - HMASK[i]) + } + if k != 0 { + return false + } + return true +} + +/* OAEP Message Encoding for Encryption */ +func RSA_OAEP_ENCODE(sha int, m []byte, rng *RAND, p []byte, RFS int) []byte { + olen := RFS - 1 + mlen := len(m) + //var f [RFS]byte + f := make([]byte, RFS) + + hlen := sha + + SEED := make([]byte, hlen) + + seedlen := hlen + if mlen > olen-hlen-seedlen-1 { + return nil + } + + DBMASK := make([]byte, olen-seedlen) + + h := SPhashit(MC_SHA2, sha, p) + //h := hashit(sha, p, -1) + + for i := 0; i < hlen; i++ { + f[i] = h[i] + } + + slen := olen - mlen - hlen - seedlen - 1 + + for i := 0; i < slen; i++ { + f[hlen+i] = 0 + } + f[hlen+slen] = 1 + for i := 0; i < mlen; i++ { + f[hlen+slen+1+i] = m[i] + } + + for i := 0; i < seedlen; i++ { + SEED[i] = rng.GetByte() + } + MGF1(sha, SEED, olen-seedlen, DBMASK) + + for i := 0; i < olen-seedlen; i++ { + DBMASK[i] ^= f[i] + } + + MGF1(sha, DBMASK, seedlen, f[:]) + + for i := 0; i < seedlen; i++ { + f[i] ^= SEED[i] + } + + for i := 0; i < olen-seedlen; i++ { + f[i+seedlen] = DBMASK[i] + } + + /* pad to length RFS */ + d := 1 + for i := RFS - 1; i >= d; i-- { + f[i] = f[i-d] + } + for i := d - 1; i >= 0; i-- { + f[i] = 0 + } + return f[:] +} + +/* OAEP Message Decoding for Decryption */ +func RSA_OAEP_DECODE(sha int, p []byte, f []byte, RFS int) []byte { + olen := RFS - 1 + + hlen := sha + SEED := make([]byte, hlen) + seedlen := hlen + CHASH := make([]byte, hlen) + + if olen < seedlen+hlen+1 { + return nil + } + DBMASK := make([]byte, olen-seedlen) + for i := 0; i < olen-seedlen; i++ { + DBMASK[i] = 0 + } + + if len(f) < RFS { + d := RFS - len(f) + for i := RFS - 1; i >= d; i-- { + f[i] = f[i-d] + } + for i := d - 1; i >= 0; i-- { + f[i] = 0 + } + } + + h := SPhashit(MC_SHA2, sha, p) + //h := hashit(sha, p, -1) + for i := 0; i < hlen; i++ { + CHASH[i] = h[i] + } + + x := f[0] + + for i := seedlen; i < olen; i++ { + DBMASK[i-seedlen] = f[i+1] + } + + MGF1(sha, DBMASK, seedlen, SEED) + for i := 0; i < seedlen; i++ { + SEED[i] ^= f[i+1] + } + MGF1(sha, SEED, olen-seedlen, f) + for i := 0; i < olen-seedlen; i++ { + DBMASK[i] ^= f[i] + } + + comp := 0 + for i := 0; i < hlen; i++ { + comp |= int(CHASH[i] ^ DBMASK[i]) + //if CHASH[i] != DBMASK[i] { + // comp = false + //} + } + m:=olen-seedlen-hlen + for i := 0; i < m; i++ { + DBMASK[i] = DBMASK[i+hlen] + } + + for i := 0; i < hlen; i++ { + SEED[i] = 0 + CHASH[i] = 0 + } + + k:=0 + t:=0 + for i:=0;i= m { + return nil + } + if DBMASK[k] != 0 { + break + } + } + t := DBMASK[k] */ + + if comp!=0 || x != 0 || t != 0x01 { + for i := 0; i < olen-seedlen; i++ { + DBMASK[i] = 0 + } + return nil + } + + var r = make([]byte, m-k-1) + + for i := 0; i < m-k-1; i++ { + r[i] = DBMASK[i+k+1] + } + + for i := 0; i < olen-seedlen; i++ { + DBMASK[i] = 0 + } + + return r +} + +/* + + + MSG := []byte("abc") + DST := []byte("P256_XMD:SHA-256_SSWU_RO_TESTGEN") + + OKM := core.XOF_Expand(core.SHA3_SHAKE128,48,DST,MSG) + fmt.Printf("OKM= "); printBinary(OKM[:]) + + OKM = core.XMD_Expand(core.MC_SHA2,32,48,DST,MSG) + fmt.Printf("OKM= "); printBinary(OKM[:]) + + + +func main() { + var ikm []byte + var salt []byte + var info []byte + + for i:=0;i<22;i++ {ikm=append(ikm,0x0b)} + for i:=0;i<13;i++ {salt=append(salt,byte(i))} + for i:=0;i<10;i++ {info=append(info,byte(0xf0+i))} + + prk:=core.HKDF_Extract(core.MC_SHA2,32,salt,ikm) + fmt.Printf("PRK= ") + for i := 0; i < len(prk); i++ { + fmt.Printf("%02x", prk[i]) + } + + okm:=core.HKDF_Expand(core.MC_SHA2,32,42,prk,info) + fmt.Printf("\nOKM= ") + for i := 0; i < len(okm); i++ { + fmt.Printf("%02x", okm[i]) + } + +} +*/ diff --git a/ec/bls48581/core/KYBER.go b/ec/bls48581/core/KYBER.go new file mode 100644 index 0000000..bda1708 --- /dev/null +++ b/ec/bls48581/core/KYBER.go @@ -0,0 +1,796 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* Kyber API */ + +package core + +//import "fmt" + +const KY_LGN uint = 8 +const KY_DEGREE int = (1 << KY_LGN); +const KY_PRIME int32 = 0xD01 + +const KY_ONE int32 = 0x549 // R mod Q +const KY_QINV int32 = 62209 // q^(-1) mod 2^16 + +const KYBER_SECRET_CPA_SIZE_512 int = (2*(KY_DEGREE*3)/2) +const KYBER_PUBLIC_SIZE_512 int = (32+2*(KY_DEGREE*3)/2) +const KYBER_CIPHERTEXT_SIZE_512 int = ((10*2+4)*KY_DEGREE/8) +const KYBER_SECRET_CCA_SIZE_512 int = (KYBER_SECRET_CPA_SIZE_512+KYBER_PUBLIC_SIZE_512+64) +const KYBER_SHARED_SECRET_512 int = 32 + +const KYBER_SECRET_CPA_SIZE_768 int = (3*(KY_DEGREE*3)/2) +const KYBER_PUBLIC_SIZE_768 int = (32+3*(KY_DEGREE*3)/2) +const KYBER_CIPHERTEXT_SIZE_768 int = ((10*3+4)*KY_DEGREE/8) +const KYBER_SECRET_CCA_SIZE_768 int = (KYBER_SECRET_CPA_SIZE_768+KYBER_PUBLIC_SIZE_768+64) +const KYBER_SHARED_SECRET_768 int = 32 + +const KYBER_SECRET_CPA_SIZE_1024 int = (4*(KY_DEGREE*3)/2) +const KYBER_PUBLIC_SIZE_1024 int = (32+4*(KY_DEGREE*3)/2) +const KYBER_CIPHERTEXT_SIZE_1024 int = ((11*4+5)*KY_DEGREE/8) +const KYBER_SECRET_CCA_SIZE_1024 int = (KYBER_SECRET_CPA_SIZE_1024+KYBER_PUBLIC_SIZE_1024+64) +const KYBER_SHARED_SECRET_1024 int = 32 + +const KY_MAXK = 4; + +// parameters for each security level +// K,eta1,eta2,du,dv,shared secret +var PARAMS_512 = [6]int{2,3,2,10,4,32} +var PARAMS_768 = [6]int{3,2,2,10,4,32} +var PARAMS_1024 = [6]int{4,2,2,11,5,32} + +/* Translated from public domain reference implementation code - taken from https://github.com/pq-crystals/kyber */ +var ZETAS = [256]int16{ + -1044, -758, -359, -1517, 1493, 1422, 287, 202, + -171, 622, 1577, 182, 962, -1202, -1474, 1468, + 573, -1325, 264, 383, -829, 1458, -1602, -130, + -681, 1017, 732, 608, -1542, 411, -205, -1571, + 1223, 652, -552, 1015, -1293, 1491, -282, -1544, + 516, -8, -320, -666, -1618, -1162, 126, 1469, + -853, -90, -271, 830, 107, -1421, -247, -951, + -398, 961, -1508, -725, 448, -1065, 677, -1275, + -1103, 430, 555, 843, -1251, 871, 1550, 105, + 422, 587, 177, -235, -291, -460, 1574, 1653, + -246, 778, 1159, -147, -777, 1483, -602, 1119, + -1590, 644, -872, 349, 418, 329, -156, -75, + 817, 1097, 603, 610, 1322, -1285, -1465, 384, + -1215, -136, 1218, -1335, -874, 220, -1187, -1659, + -1185, -1530, -1278, 794, -1510, -854, -870, 478, + -108, -308, 996, 991, 958, -1460, 1522, 1628} + +func montgomery_reduce(a int32) int16 { + t := int16(a*KY_QINV) + t = int16((a - int32(t)*KY_PRIME) >> 16) + return t +} + +func barrett_reduce(a int16) int16 { + v := int16(((int32(1)<<26) + KY_PRIME/2)/KY_PRIME) + vv := int32(v) + aa := int32(a) + t := int16((vv*aa + 0x2000000) >> 26); + t *= int16(KY_PRIME) + return int16(a - t); +} + +func fqmul(a int16, b int16) int16 { + return montgomery_reduce(int32(a)*int32(b)); +} + +func ntt(r []int16) { + var j int + k := 1 + for len := 128; len >= 2; len >>= 1 { + for start := 0; start < 256; start = j + len { + zeta := ZETAS[k]; k+=1 + for j = start; j < start + len; j++ { + t := fqmul(zeta, r[j + len]) + r[j + len] = r[j] - t + r[j] = r[j] + t + } + } + } +} + +func invntt(r []int16) { + var j int + f := int16(1441) // mont^2/128 + k := 127 + for len := 2; len <= 128; len <<= 1 { + for start := 0; start < 256; start = j + len { + zeta := ZETAS[k]; k-=1 + for j = start; j < start + len; j++ { + t := r[j] + r[j] = barrett_reduce(t + r[j + len]) + r[j + len] = (r[j + len] - t) + r[j + len] = fqmul(zeta, r[j + len]) + } + } + } + + for j := 0; j < 256; j++ { + r[j] = fqmul(r[j], f) + } +} + +func basemul(index int,r []int16, a []int16, b []int16,zeta int16) { + i:=index + j:=index+1 + r[i] = fqmul(a[j], b[j]) + r[i] = fqmul(r[i], zeta) + r[i] += fqmul(a[i], b[i]) + r[j] = fqmul(a[i], b[j]) + r[j] += fqmul(a[j], b[i]) +} + +func poly_reduce(r []int16) { + for i:=0;i>bt)&1) +} + +// centered binomial distribution +func cbd(bts []byte,eta int,f []int16) { + for i:=0;i>bts) + mask:=int16((1<=8{ + bts-=8 + ptr++ + } + w:=int16(r&mask) + position[0]=ptr + position[1]=bts + return w +} + +// array t has ab active bits per word +// extract bytes from array of words +// if max!=0 then -max<=t[i]<=+max +func nextbyte16(ab int,t []int16,position []int) byte { + ptr:=position[0] // index in array + bts:=position[1] // bit index in byte + + left:=ab-bts // number of bits left in this word + i:=0 + k:=ptr%256 + + w:=t[k]; w+=(w>>15)&int16(KY_PRIME) + r:=int16(w>>bts); + for left<8 { + i++ + w=t[k+i]; w+=(w>>15)&int16(KY_PRIME) + r|=w<=ab { + bts-=ab; + ptr++; + } + position[0]=ptr + position[1]=bts + return byte(r&0xff); +} + +// encode polynomial vector of length len with coefficients of length L, into packed bytes +func encode(t []int16,pos []int,L int,pack []byte,pptr int) { + k:=(KY_DEGREE*L)/8 // compressed length + for n:=0;n>15)&int16(KY_PRIME) + t[i]= int16(((twod*int32(t[i])+KY_PRIME/2)/KY_PRIME)&(twod-1)) + } +} + +// decompress polynomial coefficents in place, for polynomial vector of length len +func decompress(t []int16,d int) { + twod1:=int32(1<<(d-1)) + for i:=0;i>d) + } +} + +// input entropy, output key pair +func cpa_keypair(params [6]int,tau []byte,sk []byte,pk []byte) { + sh := NewSHA3(SHA3_HASH512) + var rho [32]byte + var sigma [33]byte + var buff [256]byte + + ck:=params[0] + var r [KY_DEGREE]int16 + var w [KY_DEGREE]int16 + var Aij [KY_DEGREE]int16 + + var s= make([][KY_DEGREE]int16, ck) + var e= make([][KY_DEGREE]int16, ck) + var p= make([][KY_DEGREE]int16, ck) + + eta1:=params[1] + public_key_size:=32+ck*(KY_DEGREE*3)/2 +// secret_cpa_key_size:=ck*(KY_DEGREE*3)/2 + + for i:=0;i<32;i++ { + sh.Process(tau[i]) + } + bf := sh.Hash(); + for i:=0;i<32;i++ { + rho[i]=bf[i] + sigma[i]=bf[i+32] + } + sigma[32]=0 // N + +// create s + for i:=0;i SHA -> PRNG internal state -> SHA -> random numbers + * Slow - but secure + * + * See ftp://ftp.rsasecurity.com/pub/pdfs/bull-1.pdf for a justification + */ + +/* Marsaglia & Zaman Random number generator constants */ + +package core + +//import "fmt" + +const rand_NK int = 21 +const rand_NJ int = 6 +const rand_NV int = 8 + +type RAND struct { + ira [rand_NK]uint32 /* random number... */ + rndptr int + borrow uint32 + pool_ptr int + pool [32]byte +} + +/* Terminate and clean up */ +func (R *RAND) Clean() { /* kill internal state */ + R.pool_ptr = 0 + R.rndptr = 0 + for i := 0; i < 32; i++ { + R.pool[i] = 0 + } + for i := 0; i < rand_NK; i++ { + R.ira[i] = 0 + } + R.borrow = 0 +} + +func NewRAND() *RAND { + R := new(RAND) + R.Clean() + return R +} + +func (R *RAND) sbrand() uint32 { /* Marsaglia & Zaman random number generator */ + R.rndptr++ + if R.rndptr < rand_NK { + return R.ira[R.rndptr] + } + R.rndptr = 0 + k := rand_NK - rand_NJ + for i := 0; i < rand_NK; i++ { /* calculate next NK values */ + if k == rand_NK { + k = 0 + } + t := R.ira[k] + pdiff := t - R.ira[i] - R.borrow + if pdiff < t { + R.borrow = 0 + } + if pdiff > t { + R.borrow = 1 + } + R.ira[i] = pdiff + k++ + } + + return R.ira[0] +} + +func (R *RAND) sirand(seed uint32) { + var m uint32 = 1 + R.borrow = 0 + R.rndptr = 0 + R.ira[0] ^= seed + for i := 1; i < rand_NK; i++ { /* fill initialisation vector */ + in := (rand_NV * i) % rand_NK + R.ira[in] ^= m /* note XOR */ + t := m + m = seed - m + seed = t + } + for i := 0; i < 10000; i++ { + R.sbrand() + } /* "warm-up" & stir the generator */ +} + +func (R *RAND) fill_pool() { + sh := NewHASH256() + for i := 0; i < 128; i++ { + sh.Process(byte(R.sbrand() & 0xff)) + } + W := sh.Hash() + for i := 0; i < 32; i++ { + R.pool[i] = W[i] + } + R.pool_ptr = 0 +} + +func pack(b [4]byte) uint32 { /* pack 4 bytes into a 32-bit Word */ + return (((uint32(b[3])) & 0xff) << 24) | ((uint32(b[2]) & 0xff) << 16) | ((uint32(b[1]) & 0xff) << 8) | (uint32(b[0]) & 0xff) +} + +/* Initialize RNG with some real entropy from some external source */ +func (R *RAND) Seed(rawlen int, raw []byte) { /* initialise from at least 128 byte string of raw random entropy */ + var b [4]byte + sh := NewHASH256() + R.pool_ptr = 0 + + for i := 0; i < rand_NK; i++ { + R.ira[i] = 0 + } + if rawlen > 0 { + for i := 0; i < rawlen; i++ { + sh.Process(raw[i]) + } + digest := sh.Hash() + + /* initialise PRNG from distilled randomness */ + + for i := 0; i < 8; i++ { + b[0] = digest[4*i] + b[1] = digest[4*i+1] + b[2] = digest[4*i+2] + b[3] = digest[4*i+3] + R.sirand(pack(b)) + } + } + R.fill_pool() +} + +/* get random byte */ +func (R *RAND) GetByte() byte { + r := R.pool[R.pool_ptr] + R.pool_ptr++ + if R.pool_ptr >= 32 { + R.fill_pool() + } + return byte(r & 0xff) +} + +/* test main program */ +/* +func main() { + var raw [100]byte + rng:=NewRAND() + + rng.Clean() + for i:=0;i<100;i++ {raw[i]=byte(i)} + + rng.Seed(100,raw[:]) + + for i:=0;i<1000;i++ { + fmt.Printf("%03d ",rng.GetByte()) + } +} +*/ diff --git a/ec/bls48581/core/SHA3.go b/ec/bls48581/core/SHA3.go new file mode 100644 index 0000000..f157a21 --- /dev/null +++ b/ec/bls48581/core/SHA3.go @@ -0,0 +1,302 @@ +/* + * Copyright (c) 2012-2020 MIRACL UK Ltd. + * + * This file is part of MIRACL Core + * (see https://github.com/miracl/core). + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * Implementation of the Secure Hashing Algorithm (SHA-384) + * + * Generates a 384 bit message digest. It should be impossible to come + * come up with two messages that hash to the same value ("collision free"). + * + * For use with byte-oriented messages only. + */ + +//package main + +package core + +//import "fmt" + +const SHA3_HASH224 int = 28 +const SHA3_HASH256 int = 32 +const SHA3_HASH384 int = 48 +const SHA3_HASH512 int = 64 +const SHA3_SHAKE128 int = 16 +const SHA3_SHAKE256 int = 32 + +const sha3_ROUNDS int = 24 + +var sha3_RC = [24]uint64{ + 0x0000000000000001, 0x0000000000008082, 0x800000000000808A, 0x8000000080008000, + 0x000000000000808B, 0x0000000080000001, 0x8000000080008081, 0x8000000000008009, + 0x000000000000008A, 0x0000000000000088, 0x0000000080008009, 0x000000008000000A, + 0x000000008000808B, 0x800000000000008B, 0x8000000000008089, 0x8000000000008003, + 0x8000000000008002, 0x8000000000000080, 0x000000000000800A, 0x800000008000000A, + 0x8000000080008081, 0x8000000000008080, 0x0000000080000001, 0x8000000080008008} + +type SHA3 struct { + length uint64 + rate int + len int + s [5][5]uint64 +} + +/* functions */ + +func sha3_ROTL(x uint64, n uint64) uint64 { + return (((x) << n) | ((x) >> (64 - n))) +} + +func (H *SHA3) transform() { /* basic transformation step */ + + var c [5]uint64 + var d [5]uint64 + var b [5][5]uint64 + + for k := 0; k < sha3_ROUNDS; k++ { + c[0] = H.s[0][0] ^ H.s[0][1] ^ H.s[0][2] ^ H.s[0][3] ^ H.s[0][4] + c[1] = H.s[1][0] ^ H.s[1][1] ^ H.s[1][2] ^ H.s[1][3] ^ H.s[1][4] + c[2] = H.s[2][0] ^ H.s[2][1] ^ H.s[2][2] ^ H.s[2][3] ^ H.s[2][4] + c[3] = H.s[3][0] ^ H.s[3][1] ^ H.s[3][2] ^ H.s[3][3] ^ H.s[3][4] + c[4] = H.s[4][0] ^ H.s[4][1] ^ H.s[4][2] ^ H.s[4][3] ^ H.s[4][4] + + d[0] = c[4] ^ sha3_ROTL(c[1], 1) + d[1] = c[0] ^ sha3_ROTL(c[2], 1) + d[2] = c[1] ^ sha3_ROTL(c[3], 1) + d[3] = c[2] ^ sha3_ROTL(c[4], 1) + d[4] = c[3] ^ sha3_ROTL(c[0], 1) + + for i := 0; i < 5; i++ { + for j := 0; j < 5; j++ { + H.s[i][j] ^= d[i] + } + } + + b[0][0] = H.s[0][0] + b[1][3] = sha3_ROTL(H.s[0][1], 36) + b[2][1] = sha3_ROTL(H.s[0][2], 3) + b[3][4] = sha3_ROTL(H.s[0][3], 41) + b[4][2] = sha3_ROTL(H.s[0][4], 18) + + b[0][2] = sha3_ROTL(H.s[1][0], 1) + b[1][0] = sha3_ROTL(H.s[1][1], 44) + b[2][3] = sha3_ROTL(H.s[1][2], 10) + b[3][1] = sha3_ROTL(H.s[1][3], 45) + b[4][4] = sha3_ROTL(H.s[1][4], 2) + + b[0][4] = sha3_ROTL(H.s[2][0], 62) + b[1][2] = sha3_ROTL(H.s[2][1], 6) + b[2][0] = sha3_ROTL(H.s[2][2], 43) + b[3][3] = sha3_ROTL(H.s[2][3], 15) + b[4][1] = sha3_ROTL(H.s[2][4], 61) + + b[0][1] = sha3_ROTL(H.s[3][0], 28) + b[1][4] = sha3_ROTL(H.s[3][1], 55) + b[2][2] = sha3_ROTL(H.s[3][2], 25) + b[3][0] = sha3_ROTL(H.s[3][3], 21) + b[4][3] = sha3_ROTL(H.s[3][4], 56) + + b[0][3] = sha3_ROTL(H.s[4][0], 27) + b[1][1] = sha3_ROTL(H.s[4][1], 20) + b[2][4] = sha3_ROTL(H.s[4][2], 39) + b[3][2] = sha3_ROTL(H.s[4][3], 8) + b[4][0] = sha3_ROTL(H.s[4][4], 14) + + for i := 0; i < 5; i++ { + for j := 0; j < 5; j++ { + H.s[i][j] = b[i][j] ^ (^b[(i+1)%5][j] & b[(i+2)%5][j]) + } + } + + H.s[0][0] ^= sha3_RC[k] + } +} + +/* Initialise Hash function */ +func (H *SHA3) Init(olen int) { + for i := 0; i < 5; i++ { + for j := 0; j < 5; j++ { + H.s[i][j] = 0 + } + } + H.length = 0 + H.len = olen + H.rate = 200 - 2*olen +} + +func NewSHA3(olen int) *SHA3 { + H := new(SHA3) + H.Init(olen) + return H +} + +func NewSHA3copy(HC *SHA3) *SHA3 { + H := new(SHA3) + for i := 0; i < 5; i++ { + for j := 0; j < 5; j++ { + H.s[i][j] = HC.s[i][j] + } + } + H.length = HC.length + H.len = HC.len + H.rate = HC.rate + return H +} + +/* process a single byte */ +func (H *SHA3) Process(byt byte) { /* process the next message byte */ + cnt := int(H.length % uint64(H.rate)) + b := cnt % 8 + cnt /= 8 + i := cnt % 5 + j := cnt / 5 + H.s[i][j] ^= uint64(byt&0xff) << uint(8*b) + H.length++ + if int(H.length%uint64(H.rate)) == 0 { + H.transform() + } +} + +/* process an array of bytes */ +func (H *SHA3) Process_array(b []byte) { + for i := 0; i < len(b); i++ { + H.Process((b[i])) + } +} + +/* process a 32-bit integer */ +func (H *SHA3) Process_num(n int32) { + H.Process(byte((n >> 24) & 0xff)) + H.Process(byte((n >> 16) & 0xff)) + H.Process(byte((n >> 8) & 0xff)) + H.Process(byte(n & 0xff)) +} + +/* squeeze the sponge */ +func (H *SHA3) Squeeze(buff []byte, olen int) { + // olen:=len(buff) + done := false + m := 0 + /* extract by columns */ + for { + for j := 0; j < 5; j++ { + for i := 0; i < 5; i++ { + el := H.s[i][j] + for k := 0; k < 8; k++ { + buff[m] = byte(el & 0xff) + m++ + if m >= olen || (m%H.rate) == 0 { + done = true + break + } + el >>= 8 + } + if done { + break + } + } + if done { + break + } + } + if m >= olen { + break + } + done = false + H.transform() + + } +} + +/* Generate Hash */ +func (H *SHA3) Hash() []byte { /* generate a SHA3 hash of appropriate size */ + var digest [64]byte + q := H.rate - int(H.length%uint64(H.rate)) + if q == 1 { + H.Process(0x86) + } else { + H.Process(0x06) + for int(H.length%uint64(H.rate)) != (H.rate - 1) { + H.Process(0x00) + } + H.Process(0x80) + } + H.Squeeze(digest[:], H.len) + return digest[0:H.len] +} + +func (H *SHA3) Continuing_Hash() []byte { + sh := NewSHA3copy(H) + return sh.Hash() +} + +func (H *SHA3) Shake(hash []byte, olen int) { /* generate a SHA3 hash of appropriate size */ + q := H.rate - int(H.length%uint64(H.rate)) + if q == 1 { + H.Process(0x9f) + } else { + H.Process(0x1f) + for int(H.length%uint64(H.rate)) != H.rate-1 { + H.Process(0x00) + } + H.Process(0x80) + } + H.Squeeze(hash, olen) +} + +func (H *SHA3) Continuing_Shake(hash []byte, olen int) { + sh := NewSHA3copy(H) + sh.Shake(hash, olen) +} + +/* test program: should produce digest */ +//916f6061fe879741ca6469b43971dfdb28b1a32dc36cb3254e812be27aad1d18 +//afebb2ef542e6579c50cad06d2e578f9f8dd6881d7dc824d26360feebf18a4fa73e3261122948efcfd492e74e82e2189ed0fb440d187f382270cb455f21dd185 +//98be04516c04cc73593fef3ed0352ea9f6443942d6950e29a372a681c3deaf4535423709b02843948684e029010badcc0acd8303fc85fdad3eabf4f78cae165635f57afd28810fc2 + +/* +func main() { + + test := []byte("abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu") + var digest [172]byte + + sh:=NewSHA3(SHA3_HASH256) + for i:=0;i= 256 || nsr < 2 || nsr >= 256 { + S.ID = 0 + S.NSR = 0 + S.B = nil + return S + } + S.ID = byte(id) + S.NSR = byte(nsr) + m := len(M) + S.B = make([]byte, m) + rng := NewRAND() + rng.Clean() + rng.Seed(len(R), R) + for j := 0; j < m; j++ { + x := byte(S.ID) + S.B[j] = M[j] + for n := 1; n < nsr; n++ { + S.B[j] = add(S.B[j], mul(rng.GetByte(), x)) + x = mul(x, S.ID) + } + } + return S +} + +/* recover M from shares */ +func Recover(S []*SHARE) []byte { + m := len(S[0].B) + nsr := int(S[0].NSR) + if nsr != len(S) { + return nil + } + for i := 1; i < nsr; i++ { + if int(S[i].NSR) != nsr || len(S[i].B) != m { + return nil + } + } + x := make([]byte, nsr) + y := make([]byte, nsr) + + M := make([]byte, m) + for j := 0; j < m; j++ { + for i := 0; i < nsr; i++ { + x[i] = S[i].ID + y[i] = S[i].B[j] + } + M[j] = interpolate(nsr, x, y) + } + return M +} diff --git a/feldman/feldman.go b/feldman/feldman.go new file mode 100644 index 0000000..664aeea --- /dev/null +++ b/feldman/feldman.go @@ -0,0 +1,540 @@ +package feldman + +import ( + "bytes" + "crypto/rand" + "crypto/sha256" + "fmt" + + "source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581" +) + +// This will not be used in the initial ceremony, but will be used in a end of ceremony event +type FeldmanECP struct { + threshold int + total int + id int + fragsForCounterparties map[int][]byte + fragsFromCounterparties map[int]*bls48581.BIG + zkpok *bls48581.BIG + secret *bls48581.BIG + scalar *bls48581.BIG + publicKey *bls48581.ECP + point *bls48581.ECP + randomCommitmentPoint *bls48581.ECP + round FeldmanRound + zkcommitsFromCounterparties map[int][]byte + pointsFromCounterparties map[int]*bls48581.ECP +} + +type FeldmanReveal struct { + Point []byte + RandomCommitmentPoint []byte + ZKPoK []byte +} + +type FeldmanECP8 struct { + threshold int + total int + id int + fragsForCounterparties map[int][]byte + fragsFromCounterparties map[int]*bls48581.BIG + zkpok *bls48581.BIG + secret *bls48581.BIG + scalar *bls48581.BIG + publicKey *bls48581.ECP8 + point *bls48581.ECP8 + randomCommitmentPoint *bls48581.ECP8 + round FeldmanRound + zkcommitsFromCounterparties map[int][]byte + pointsFromCounterparties map[int]*bls48581.ECP8 +} + +type FeldmanRound int + +const ( + FELDMAN_ROUND_UNINITIALIZED = FeldmanRound(0) + FELDMAN_ROUND_INITIALIZED = FeldmanRound(1) + FELDMAN_ROUND_COMMITTED = FeldmanRound(2) + FELDMAN_ROUND_REVEALED = FeldmanRound(3) + FELDMAN_ROUND_RECONSTRUCTED = FeldmanRound(4) +) + +func NewFeldmanECP(threshold, total, id int, secret *bls48581.BIG) (*FeldmanECP, error) { + return &FeldmanECP{ + threshold: threshold, + total: total, + id: id, + fragsForCounterparties: make(map[int][]byte), + fragsFromCounterparties: make(map[int]*bls48581.BIG), + zkpok: nil, + secret: secret, + scalar: nil, + publicKey: bls48581.ECP_generator(), + point: bls48581.ECP_generator(), + round: FELDMAN_ROUND_UNINITIALIZED, + zkcommitsFromCounterparties: make(map[int][]byte), + pointsFromCounterparties: make(map[int]*bls48581.ECP), + }, nil +} + +func NewFeldmanECP8(threshold, total, id int, secret *bls48581.BIG) (*FeldmanECP8, error) { + return &FeldmanECP8{ + threshold: threshold, + total: total, + id: id, + fragsForCounterparties: make(map[int][]byte), + fragsFromCounterparties: make(map[int]*bls48581.BIG), + zkpok: nil, + secret: secret, + scalar: nil, + publicKey: bls48581.ECP8_generator(), + point: bls48581.ECP8_generator(), + round: FELDMAN_ROUND_UNINITIALIZED, + zkcommitsFromCounterparties: make(map[int][]byte), + pointsFromCounterparties: make(map[int]*bls48581.ECP8), + }, nil +} + +func (f *FeldmanECP) SamplePolynomial() { + coeffs := append([]*bls48581.BIG{}, f.secret) + + for i := 0; i < f.threshold-1; i++ { + secretBytes := make([]byte, int(bls48581.MODBYTES)) + rand.Read(secretBytes) + secret := bls48581.FromBytes(secretBytes) + coeffs = append(coeffs, secret) + } + + for i := 1; i <= f.total; i++ { + result := coeffs[len(coeffs)-1] + + for j := len(coeffs) - 2; j >= 0; j-- { + result = bls48581.Modadd( + coeffs[j], + bls48581.Modmul( + result, + bls48581.NewBIGint(i), + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + } + + if i == f.id { + f.scalar = result + } else { + fragBytes := make([]byte, int(bls48581.MODBYTES)) + result.ToBytes(fragBytes) + f.fragsForCounterparties[i] = fragBytes + } + } + + f.round = FELDMAN_ROUND_INITIALIZED +} + +func (f *FeldmanECP) Scalar() *bls48581.BIG { + return f.scalar +} + +func (f *FeldmanECP) GetPolyFrags() map[int][]byte { + return f.fragsForCounterparties +} + +func (f *FeldmanECP) SetPolyFragForParty(id int, frag []byte) []byte { + f.fragsFromCounterparties[id] = bls48581.FromBytes(frag) + + if len(f.fragsFromCounterparties) == f.total-1 { + for _, v := range f.fragsFromCounterparties { + f.scalar = bls48581.Modadd(f.scalar, v, bls48581.NewBIGints(bls48581.CURVE_Order)) + } + + f.point = f.point.Mul(f.scalar) + + randCommitmentBytes := make([]byte, int(bls48581.MODBYTES)) + rand.Read(randCommitmentBytes) + randCommitment := bls48581.FromBytes(randCommitmentBytes) + f.randomCommitmentPoint = f.publicKey.Mul(randCommitment) + + publicPointBytes := make([]byte, bls48581.MODBYTES+1) + randCommitmentPointBytes := make([]byte, bls48581.MODBYTES+1) + f.point.ToBytes(publicPointBytes, true) + f.randomCommitmentPoint.ToBytes(randCommitmentPointBytes, true) + + challenge := sha256.Sum256(append(append([]byte{}, publicPointBytes...), randCommitmentPointBytes...)) + challengeBig := bls48581.FromBytes(challenge[:]) + challengeBig.Mod(bls48581.NewBIGints(bls48581.CURVE_Order)) + + f.zkpok = bls48581.Modadd( + bls48581.Modmul( + f.scalar, + challengeBig, + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + randCommitment, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + + zkpokBytes := make([]byte, int(bls48581.MODBYTES)) + f.zkpok.ToBytes(zkpokBytes) + zkcommit := sha256.Sum256(append(append([]byte{}, randCommitmentPointBytes...), zkpokBytes...)) + + f.round = FELDMAN_ROUND_COMMITTED + return zkcommit[:] + } + + return []byte{} +} + +func (f *FeldmanECP) ReceiveCommitments(id int, zkcommit []byte) *FeldmanReveal { + f.zkcommitsFromCounterparties[id] = zkcommit + + if len(f.zkcommitsFromCounterparties) == f.total-1 { + publicPointBytes := make([]byte, bls48581.MODBYTES+1) + randCommitmentPointBytes := make([]byte, bls48581.MODBYTES+1) + f.point.ToBytes(publicPointBytes, true) + f.randomCommitmentPoint.ToBytes(randCommitmentPointBytes, true) + f.round = FELDMAN_ROUND_REVEALED + zkpokBytes := make([]byte, int(bls48581.MODBYTES)) + f.zkpok.ToBytes(zkpokBytes) + + return &FeldmanReveal{ + Point: publicPointBytes, + RandomCommitmentPoint: randCommitmentPointBytes, + ZKPoK: zkpokBytes, + } + } + + return nil +} + +func (f *FeldmanECP) Recombine(id int, reveal *FeldmanReveal) { + counterpartyPoint := bls48581.ECP_fromBytes(reveal.Point) + if counterpartyPoint.Equals(bls48581.ECP_generator()) { + fmt.Printf("invalid point from %d", id) + return + } + + counterpartyRandomCommitmentPoint := bls48581.ECP_fromBytes(reveal.RandomCommitmentPoint) + if counterpartyRandomCommitmentPoint.Equals(bls48581.ECP_generator()) { + fmt.Printf("invalid commitment point from %d", id) + return + } + + counterpartyZKPoK := bls48581.FromBytes(reveal.ZKPoK) + counterpartyZKCommit := f.zkcommitsFromCounterparties[id] + + challenge := sha256.Sum256(append(append([]byte{}, reveal.Point...), reveal.RandomCommitmentPoint...)) + challengeBig := bls48581.FromBytes(challenge[:]) + challengeBig.Mod(bls48581.NewBIGints(bls48581.CURVE_Order)) + + proof := f.publicKey.Mul(counterpartyZKPoK) + counterpartyRandomCommitmentPoint.Add(counterpartyPoint.Mul(challengeBig)) + + if !proof.Equals(counterpartyRandomCommitmentPoint) { + fmt.Printf("invalid proof from %d", id) + return + } + + verifier := sha256.Sum256(append(append([]byte{}, reveal.RandomCommitmentPoint...), reveal.ZKPoK...)) + if !bytes.Equal(counterpartyZKCommit, verifier[:]) { + fmt.Printf("%d changed zkpok after commit", id) + return + } + + f.pointsFromCounterparties[id] = counterpartyPoint + + if len(f.pointsFromCounterparties) == f.total-1 { + f.pointsFromCounterparties[f.id] = f.point + + for i := 1; i <= f.total-f.threshold; i++ { + reconstructedSum := bls48581.ECP_generator() + + for j := i; j <= f.threshold+i; j++ { + coefficientNumerator := bls48581.NewBIGint(1) + coefficientDenominator := bls48581.NewBIGint(1) + + for k := i; k <= f.threshold+i; k++ { + if j != k { + k := bls48581.NewBIGint(k) + + coefficientNumerator = bls48581.Modmul( + coefficientNumerator, + k, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + kj := bls48581.Modadd( + k, + bls48581.NewBIGints(bls48581.CURVE_Order).Minus(bls48581.NewBIGint(j)), + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + coefficientDenominator = bls48581.Modmul( + coefficientDenominator, + kj, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + } + } + + coefficientDenominator.Invmodp(bls48581.NewBIGints(bls48581.CURVE_Order)) + + reconstructedFragment := f.pointsFromCounterparties[j].Mul( + bls48581.Modmul( + coefficientNumerator, + coefficientDenominator, + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + ) + + if reconstructedSum.Equals(bls48581.ECP_generator()) { + reconstructedSum = reconstructedFragment + } else { + reconstructedSum.Add(reconstructedFragment) + } + } + + if f.publicKey.Equals(bls48581.ECP_generator()) { + f.publicKey = reconstructedSum + } else if !f.publicKey.Equals(reconstructedSum) { + fmt.Println("key mismatch") + fmt.Println(f.publicKey.ToString()) + fmt.Println(reconstructedSum.ToString()) + return + } + } + f.round = FELDMAN_ROUND_RECONSTRUCTED + } +} + +func (f *FeldmanECP) PublicKey() *bls48581.ECP { + key := bls48581.NewECP() + key.Copy(f.publicKey) + return key +} + +func (f *FeldmanECP) PublicKeyBytes() []byte { + publicKeyBytes := make([]byte, bls48581.MODBYTES+1) + f.publicKey.ToBytes(publicKeyBytes, true) + return publicKeyBytes +} + +func (f *FeldmanECP8) SamplePolynomial() { + coeffs := append([]*bls48581.BIG{}, f.secret) + + for i := 0; i < f.threshold-1; i++ { + secretBytes := make([]byte, int(bls48581.MODBYTES)) + rand.Read(secretBytes) + secret := bls48581.FromBytes(secretBytes) + coeffs = append(coeffs, secret) + } + + for i := 1; i <= f.total; i++ { + result := coeffs[len(coeffs)-1] + + for j := len(coeffs) - 2; j >= 0; j-- { + result = bls48581.Modadd( + coeffs[j], + bls48581.Modmul( + result, + bls48581.NewBIGint(i), + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + } + + if i == f.id { + f.scalar = result + } else { + fragBytes := make([]byte, int(bls48581.MODBYTES)) + result.ToBytes(fragBytes) + f.fragsForCounterparties[i] = fragBytes + } + } + + f.round = FELDMAN_ROUND_INITIALIZED +} + +func (f *FeldmanECP8) GetPolyFrags() map[int][]byte { + return f.fragsForCounterparties +} + +func (f *FeldmanECP8) SetPolyFragForParty(id int, frag []byte) []byte { + f.fragsFromCounterparties[id] = bls48581.FromBytes(frag) + + if len(f.fragsFromCounterparties) == f.total-1 { + for _, v := range f.fragsFromCounterparties { + f.scalar = bls48581.Modadd(f.scalar, v, bls48581.NewBIGints(bls48581.CURVE_Order)) + } + + f.point = f.point.Mul(f.scalar) + + randCommitmentBytes := make([]byte, int(bls48581.MODBYTES)) + rand.Read(randCommitmentBytes) + randCommitment := bls48581.FromBytes(randCommitmentBytes) + f.randomCommitmentPoint = f.publicKey.Mul(randCommitment) + + publicPointBytes := make([]byte, bls48581.MODBYTES*8+1) + randCommitmentPointBytes := make([]byte, bls48581.MODBYTES*8+1) + f.point.ToBytes(publicPointBytes, true) + f.randomCommitmentPoint.ToBytes(randCommitmentPointBytes, true) + + challenge := sha256.Sum256(append(append([]byte{}, publicPointBytes...), randCommitmentPointBytes...)) + challengeBig := bls48581.FromBytes(challenge[:]) + challengeBig.Mod(bls48581.NewBIGints(bls48581.CURVE_Order)) + + f.zkpok = bls48581.Modadd( + bls48581.Modmul( + f.scalar, + challengeBig, + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + randCommitment, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + + zkpokBytes := make([]byte, int(bls48581.MODBYTES)) + f.zkpok.ToBytes(zkpokBytes) + zkcommit := sha256.Sum256(append(append([]byte{}, randCommitmentPointBytes...), zkpokBytes...)) + + f.round = FELDMAN_ROUND_COMMITTED + return zkcommit[:] + } + + return []byte{} +} + +func (f *FeldmanECP8) Scalar() *bls48581.BIG { + return f.scalar +} + +func (f *FeldmanECP8) ReceiveCommitments(id int, zkcommit []byte) *FeldmanReveal { + f.zkcommitsFromCounterparties[id] = zkcommit + + if len(f.zkcommitsFromCounterparties) == f.total-1 { + publicPointBytes := make([]byte, bls48581.MODBYTES*8+1) + randCommitmentPointBytes := make([]byte, bls48581.MODBYTES*8+1) + f.point.ToBytes(publicPointBytes, true) + f.randomCommitmentPoint.ToBytes(randCommitmentPointBytes, true) + f.round = FELDMAN_ROUND_REVEALED + zkpokBytes := make([]byte, int(bls48581.MODBYTES)) + f.zkpok.ToBytes(zkpokBytes) + + return &FeldmanReveal{ + Point: publicPointBytes, + RandomCommitmentPoint: randCommitmentPointBytes, + ZKPoK: zkpokBytes, + } + } + + return nil +} + +func (f *FeldmanECP8) Recombine(id int, reveal *FeldmanReveal) { + counterpartyPoint := bls48581.ECP8_fromBytes(reveal.Point) + if counterpartyPoint.Equals(bls48581.ECP8_generator()) { + fmt.Printf("invalid point from %d", id) + return + } + + counterpartyRandomCommitmentPoint := bls48581.ECP8_fromBytes(reveal.RandomCommitmentPoint) + if counterpartyRandomCommitmentPoint.Equals(bls48581.ECP8_generator()) { + fmt.Printf("invalid commitment point from %d", id) + return + } + + counterpartyZKPoK := bls48581.FromBytes(reveal.ZKPoK) + counterpartyZKCommit := f.zkcommitsFromCounterparties[id] + + challenge := sha256.Sum256(append(append([]byte{}, reveal.Point...), reveal.RandomCommitmentPoint...)) + challengeBig := bls48581.FromBytes(challenge[:]) + challengeBig.Mod(bls48581.NewBIGints(bls48581.CURVE_Order)) + + proof := f.publicKey.Mul(counterpartyZKPoK) + counterpartyRandomCommitmentPoint.Add(counterpartyPoint.Mul(challengeBig)) + + if !proof.Equals(counterpartyRandomCommitmentPoint) { + fmt.Printf("invalid proof from %d", id) + return + } + + verifier := sha256.Sum256(append(append([]byte{}, reveal.RandomCommitmentPoint...), reveal.ZKPoK...)) + if !bytes.Equal(counterpartyZKCommit, verifier[:]) { + fmt.Printf("%d changed zkpok after commit", id) + return + } + + f.pointsFromCounterparties[id] = counterpartyPoint + + if len(f.pointsFromCounterparties) == f.total-1 { + f.pointsFromCounterparties[f.id] = f.point + for i := 1; i <= f.total-f.threshold; i++ { + reconstructedSum := bls48581.ECP8_generator() + + for j := i; j <= f.threshold+i; j++ { + coefficientNumerator := bls48581.NewBIGint(1) + coefficientDenominator := bls48581.NewBIGint(1) + + for k := i; k <= f.threshold+i; k++ { + if j != k { + k := bls48581.NewBIGint(k) + + coefficientNumerator = bls48581.Modmul( + coefficientNumerator, + k, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + kj := bls48581.Modadd( + k, + bls48581.NewBIGints(bls48581.CURVE_Order).Minus(bls48581.NewBIGint(j)), + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + coefficientDenominator = bls48581.Modmul( + coefficientDenominator, + kj, + bls48581.NewBIGints(bls48581.CURVE_Order), + ) + } + } + + coefficientDenominator.Invmodp(bls48581.NewBIGints(bls48581.CURVE_Order)) + + reconstructedFragment := f.pointsFromCounterparties[j].Mul( + bls48581.Modmul( + coefficientNumerator, + coefficientDenominator, + bls48581.NewBIGints(bls48581.CURVE_Order), + ), + ) + + if reconstructedSum.Equals(bls48581.ECP8_generator()) { + reconstructedSum = reconstructedFragment + } else { + reconstructedSum.Add(reconstructedFragment) + } + } + + if f.publicKey.Equals(bls48581.ECP8_generator()) { + f.publicKey = reconstructedSum + } else if !f.publicKey.Equals(reconstructedSum) { + fmt.Println("key mismatch") + fmt.Println(f.publicKey.ToString()) + fmt.Println(reconstructedSum.ToString()) + return + } + } + f.round = FELDMAN_ROUND_RECONSTRUCTED + } +} + +func (f *FeldmanECP8) PublicKey() *bls48581.ECP8 { + key := bls48581.NewECP8() + key.Copy(f.publicKey) + return key +} + +func (f *FeldmanECP8) PublicKeyBytes() []byte { + publicKeyBytes := make([]byte, bls48581.MODBYTES*8+1) + f.publicKey.ToBytes(publicKeyBytes, true) + return publicKeyBytes +} diff --git a/go.mod b/go.mod new file mode 100644 index 0000000..3d2a0fb --- /dev/null +++ b/go.mod @@ -0,0 +1,7 @@ +module source.quilibrium.com/quilibrium/ceremonyclient + +go 1.18 + +require github.com/cloudflare/circl v1.3.2 + +require golang.org/x/sys v0.6.0 // indirect diff --git a/go.sum b/go.sum new file mode 100644 index 0000000..22b0783 --- /dev/null +++ b/go.sum @@ -0,0 +1,4 @@ +github.com/cloudflare/circl v1.3.2 h1:VWp8dY3yH69fdM7lM6A1+NhhVoDu9vqK0jOgmkQHFWk= +github.com/cloudflare/circl v1.3.2/go.mod h1:+CauBF6R70Jqcyl8N2hC8pAXYbWkGIezuSbuGLtRhnw= +golang.org/x/sys v0.6.0 h1:MVltZSvRTcU2ljQOhs94SXPftV6DCNnZViHeQps87pQ= +golang.org/x/sys v0.6.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= diff --git a/main.go b/main.go new file mode 100644 index 0000000..35905b6 --- /dev/null +++ b/main.go @@ -0,0 +1,71 @@ +package main + +import ( + "fmt" + "time" +) + +var HOST string = "https://ceremony.quilibrium.com:8443/" + +func main() { + PrintLogo() + PrintVersion() + + fmt.Println("Checking sequencer...") + state := GetSequencerState() + for state != SEQUENCER_ACCEPTING { + fmt.Println("Sequencer currently not accepting new contributions, waiting...") + time.Sleep(30 * time.Second) + state = GetSequencerState() + } + + JoinLobby() + batchSize := uint(32) + for batch := uint(0); batch < 65536/batchSize; batch++ { + Bootstrap(batch, batchSize) + fmt.Printf("batch: %d\n", batch) + } + fmt.Println("New Pubkey: ") + fmt.Println(bcj.PotPubKey) + ContributeAndGetVoucher() +} + +func PrintLogo() { + fmt.Println(" %#########") + fmt.Println(" #############################") + fmt.Println(" ########################################&") + fmt.Println(" ###############################################") + fmt.Println(" &#####################% %######################") + fmt.Println(" ################# #################") + fmt.Println(" ############### ###############") + fmt.Println(" ############# ##############") + fmt.Println(" ############# ############&") + fmt.Println(" ############ ############") + fmt.Println(" ########### ########## &###########") + fmt.Println(" ########### ############## ###########") + fmt.Println(" ########### ############## ##########&") + fmt.Println(" ########## ############## ##########") + fmt.Println("%########## ########## ##########") + fmt.Println("##########& ##########") + fmt.Println("########## &#########") + fmt.Println("##########& ####### ####### ##########") + fmt.Println(" ########## &######################### ##########") + fmt.Println(" ########## ##############% ############## &##########") + fmt.Println(" %########## &############## ############### ##########") + fmt.Println(" ########### ############### ##############% ###########") + fmt.Println(" ###########& ########## ############### ########") + fmt.Println(" ############ ##### ##############% ####") + fmt.Println(" ############ ###############") + fmt.Println(" ############## ##############%") + fmt.Println(" ############### ###############") + fmt.Println(" #################& ##############%") + fmt.Println(" #########################&&&############# ###############") + fmt.Println(" ########################################% ############") + fmt.Println(" ####################################### ########") + fmt.Println(" ############################# ##") +} + +func PrintVersion() { + fmt.Println(" ") + fmt.Println(" Quilibrium Ceremony Client - CLI - v1.0.0") +} diff --git a/quil_voucher.hex b/quil_voucher.hex new file mode 100644 index 0000000..0ace8bd --- /dev/null +++ b/quil_voucher.hex @@ -0,0 +1 @@ +654990bfacd0d2702f318089f73b838c64f79b0369840bdff6e1f6b8c3aa2698585c61a0e35794afb9365a4f5ed9c841a62eb9f35d29aa50486780552dd2293cb865905d120047905b98f55bb96a8e2b1e960807a3a0f5b236b7819799a64f7c0a52f8c754dc5086373bb0ce2702ebfba900 \ No newline at end of file