ceremonyclient/ec/bls48581/FP.go

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/*
* 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
}
} */