ceremonyclient/nekryptology/pkg/verenc/camshoup/proof_enc.go

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2023-07-05 05:32:28 +00:00
//
// Copyright Coinbase, Inc. All Rights Reserved.
//
// SPDX-License-Identifier: Apache-2.0
//
package camshoup
import (
"fmt"
"math/big"
"git.sr.ht/~sircmpwn/go-bare"
"source.quilibrium.com/quilibrium/monorepo/nekryptology/internal"
mod "source.quilibrium.com/quilibrium/monorepo/nekryptology/pkg/core"
)
// ProofVerEnc is a proof of verifiable encryption for a discrete log
type ProofVerEnc struct {
challenge, r *big.Int
m []*big.Int
}
type proofMarshal struct {
M [][]byte `bare:"m"`
R []byte `bare:"r"`
Challenge []byte `bare:"challenge"`
}
func (pf ProofVerEnc) MarshalBinary() ([]byte, error) {
tv := new(proofMarshal)
tv.R = pf.r.Bytes()
tv.Challenge = pf.challenge.Bytes()
tv.M = make([][]byte, len(pf.m))
for i, m := range pf.m {
tv.M[i] = m.Bytes()
}
return bare.Marshal(tv)
}
func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error {
tv := new(proofMarshal)
err := bare.Unmarshal(data, tv)
if err != nil {
return err
}
pf.r = new(big.Int).SetBytes(tv.R)
pf.challenge = new(big.Int).SetBytes(tv.Challenge)
pf.m = make([]*big.Int, len(tv.M))
for i, m := range tv.M {
pf.m[i] = new(big.Int).SetBytes(m)
}
return nil
}
// EncryptAndProve is a NIZK where the ciphertext and commitments are computed (t values).
// The blindings are generated as part of calling this function
// Return ciphertext and proof created during encryption.
// "The protocol" from section 5.2 in <https://shoup.net/papers/verenc.pdf>
// Not using t = g^m*h^s as the idemix protocol does not use it.
// Guess is that since the knowledge of m is proved in the credential attribute proving protocol.
// Use this function if the proof is by itself and not part of a bigger composite proof.
func (ek EncryptionKey) EncryptAndProve(nonce []byte, msgs []*big.Int) (*CipherText, *ProofVerEnc, error) {
var err error
blindings := make([]*big.Int, len(msgs))
for i := 0; i < len(blindings); i++ {
blindings[i], err = ek.group.RandForEncrypt()
if err != nil {
return nil, nil, err
}
}
return ek.EncryptAndProveBlindings(nonce, msgs, blindings)
}
// EncryptAndProveBlindings is a NIZK where the ciphertext and commitments are computed (t values).
// The blindings are generated prior to calling this function
// Return ciphertext and proof created during encryption.
// "The protocol" from section 5.2 in <https://shoup.net/papers/verenc.pdf>
// Not using t = g^m*h^s as the idemix protocol does not use it.
// Guess is that since the knowledge of m is proved in the credential attribute proving protocol.
// Use this function if the proof will be part of more proofs.
func (ek EncryptionKey) EncryptAndProveBlindings(nonce []byte, msgs []*big.Int, blindings []*big.Int) (*CipherText, *ProofVerEnc, error) {
if len(msgs) != len(blindings) {
return nil, nil, fmt.Errorf("number of messages %d != number of blindings %d", len(msgs), len(blindings))
}
if len(msgs) > len(ek.y1) {
return nil, nil, fmt.Errorf("number of messages %d is more than supported by this key %d", len(msgs), len(ek.y1))
}
for i, b := range blindings {
if b == nil {
return nil, nil, internal.ErrNilArguments
}
if msgs[i] == nil {
return nil, nil, internal.ErrNilArguments
}
if b.Cmp(mod.Zero) == 0 {
return nil, nil, internal.ErrZeroValue
}
}
r, err := ek.group.RandForEncrypt()
if err != nil {
return nil, nil, err
}
rBlinding, err := ek.group.RandForEncrypt()
if err != nil {
return nil, nil, err
}
ciphertext, err := ek.encryptWithR(nonce, msgs, r)
if err != nil {
return nil, nil, err
}
hs, err := ek.group.Hash(ciphertext.u, ciphertext.e, nonce)
if err != nil {
return nil, nil, err
}
ciphertextTValues, err := ek.ciphertextTestValues(rBlinding, hs, blindings)
if err != nil {
return nil, nil, err
}
challenge, err := ek.fiatShamir(nonce, ciphertext, ciphertextTValues)
if err != nil {
return nil, nil, err
}
// generate the schnorr proofs
rHat := ek.schnorr(rBlinding, challenge, r)
mHat := make([]*big.Int, len(msgs))
for i, m := range msgs {
mHat[i] = ek.schnorr(blindings[i], challenge, m)
}
return ciphertext, &ProofVerEnc{
challenge: challenge,
r: rHat,
m: mHat,
}, nil
}
// ciphertextTestValues computes commitments for the ciphertext when proving encryption is correct
func (ek EncryptionKey) ciphertextTestValues(r, hash *big.Int, msgs []*big.Int) (*CipherText, error) {
twoR := new(big.Int).Lsh(r, 1)
twoMsgs := make([]*big.Int, len(msgs))
for i, m := range msgs {
twoMsgs[i] = new(big.Int).Lsh(m, 1)
}
u := ek.computeU(twoR)
e := ek.computeE(twoMsgs, twoR)
v := ek.computeV(twoR, hash, false)
return &CipherText{u, v, e}, nil
}
// fiatShamir computes h(n, g, Y2, Y3, Y1, C.U, C.V, C.E, CT.U, CT.V, CT.E)
func (ek EncryptionKey) fiatShamir(nonce []byte, ciphertext *CipherText, ciphertextTValues *CipherText) (*big.Int, error) {
hValues := make([][]byte, len(ciphertext.e)+len(ciphertextTValues.e)+len(ek.y1)+9)
hValues[0] = ek.group.n.Bytes()
hValues[1] = ek.group.g.Bytes()
hValues[2] = ek.y2.Bytes()
hValues[3] = ek.y3.Bytes()
offset := 4
for _, y := range ek.y1 {
hValues[offset] = y.Bytes()
offset++
}
hValues[offset] = ciphertext.u.Bytes()
offset++
for _, n := range ciphertext.e {
hValues[offset] = n.Bytes()
offset++
}
hValues[offset] = ciphertext.v.Bytes()
offset++
hValues[offset] = ciphertextTValues.u.Bytes()
offset++
for _, n := range ciphertextTValues.e {
hValues[offset] = n.Bytes()
offset++
}
hValues[offset] = ciphertextTValues.v.Bytes()
hValues[len(hValues)-1] = nonce
h, err := internal.Hash([]byte("Coinbase Hash 1.0"), hValues...)
if err != nil {
return nil, err
}
return new(big.Int).SetBytes(h), nil
}
// schnorr computes tilde - challenge * value mod n^2
func (ek EncryptionKey) schnorr(tilde, challenge, value *big.Int) *big.Int {
r := ek.group.Mul(challenge, value)
t := new(big.Int).Sub(tilde, r)
return t
}
// VerifyEncryptProof a Proof of Verifiable Encryption
// See section 6.2.19 in <https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf>
func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error {
if ciphertext == nil || proof == nil {
return internal.ErrNilArguments
}
if proof.r == nil || proof.challenge == nil || proof.m == nil {
return internal.ErrNilArguments
}
if ciphertext.u == nil || ciphertext.v == nil || ciphertext.e == nil {
return internal.ErrNilArguments
}
if len(proof.m) > len(ek.y1) {
return fmt.Errorf("number of messages %d is more than supported by this key %d", len(proof.m), len(ek.y1))
}
// Reconstruct u
// 2c
c2 := new(big.Int).Lsh(proof.challenge, 1)
// 2r
r2 := new(big.Int).Lsh(proof.r, 1)
// u^{2c} mod n^2
uc := ek.group.Exp(ciphertext.u, c2)
// Reconstruct e
// g^{2r} mod n^2
gr := ek.group.Gexp(r2)
// u^{2c} * g^{2r} mod n^2
u := ek.group.Mul(uc, gr)
e := make([]*big.Int, len(proof.m))
for i, mm := range proof.m {
// e^{2c}
ec := ek.group.Exp(ciphertext.e[i], c2)
// y1^{2r}
yr := ek.group.Exp(ek.y1[i], r2)
// h^{2m}
hm := ek.group.Hexp(new(big.Int).Lsh(mm, 1))
// e = ec * yr * hm mod n^2
e[i] = ek.group.Mul(ek.group.Mul(ec, yr), hm)
}
// Reconstruct v
// v^{2c}
hs, err := ek.group.Hash(ciphertext.u, ciphertext.e, nonce)
if err != nil {
return err
}
vc := ek.group.Exp(ciphertext.v, c2)
y3hs := ek.group.Exp(ek.y3, hs)
y2y3hs := ek.group.Mul(ek.y2, y3hs)
y2y3hsr := ek.group.Exp(y2y3hs, r2)
v := ek.group.Mul(vc, y2y3hsr)
ciphertextTestValues := &CipherText{u, v, e}
challenge, err := ek.fiatShamir(nonce, ciphertext, ciphertextTestValues)
if err != nil {
return err
}
if challenge.Cmp(proof.challenge) == 0 {
return nil
} else {
return fmt.Errorf("invalid ciphertext")
}
}