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yaole
2026-05-27 23:03:00 +08:00
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package ssss
import (
"crypto/rand"
"io"
"math/big"
"xdx.jelly/xgcl/gerrors"
)
/* coefficients of some irreducible polynomials over GF(2) */
// var irred_coeff = [...]byte{
// 4, 3, 1, 5, 3, 1, 4, 3, 1, 7, 3, 2, 5, 4, 3, 5, 3, 2, 7, 4, 2, 4, 3, 1, 10, 9, 3, 9, 4, 2, 7, 6, 2, 10, 9,
// 6, 4, 3, 1, 5, 4, 3, 4, 3, 1, 7, 2, 1, 5, 3, 2, 7, 4, 2, 6, 3, 2, 5, 3, 2, 15, 3, 2, 11, 3, 2, 9, 8, 7, 7,
// 2, 1, 5, 3, 2, 9, 3, 1, 7, 3, 1, 9, 8, 3, 9, 4, 2, 8, 5, 3, 15, 14, 10, 10, 5, 2, 9, 6, 2, 9, 3, 2, 9, 5,
// 2, 11, 10, 1, 7, 3, 2, 11, 2, 1, 9, 7, 4, 4, 3, 1, 8, 3, 1, 7, 4, 1, 7, 2, 1, 13, 11, 6, 5, 3, 2, 7, 3, 2,
// 8, 7, 5, 12, 3, 2, 13, 10, 6, 5, 3, 2, 5, 3, 2, 9, 5, 2, 9, 7, 2, 13, 4, 3, 4, 3, 1, 11, 6, 4, 18, 9, 6,
// 19, 18, 13, 11, 3, 2, 15, 9, 6, 4, 3, 1, 16, 5, 2, 15, 14, 6, 8, 5, 2, 15, 11, 2, 11, 6, 2, 7, 5, 3, 8,
// 3, 1, 19, 16, 9, 11, 9, 6, 15, 7, 6, 13, 4, 3, 14, 13, 3, 13, 6, 3, 9, 5, 2, 19, 13, 6, 19, 10, 3, 11,
// 6, 5, 9, 2, 1, 14, 3, 2, 13, 3, 1, 7, 5, 4, 11, 9, 8, 11, 6, 5, 23, 16, 9, 19, 14, 6, 23, 10, 2, 8, 3,
// 2, 5, 4, 3, 9, 6, 4, 4, 3, 2, 13, 8, 6, 13, 11, 1, 13, 10, 3, 11, 6, 5, 19, 17, 4, 15, 14, 7, 13, 9, 6,
// 9, 7, 3, 9, 7, 1, 14, 3, 2, 11, 8, 2, 11, 6, 4, 13, 5, 2, 11, 5, 1, 11, 4, 1, 19, 10, 3, 21, 10, 6, 13,
// 3, 1, 15, 7, 5, 19, 18, 10, 7, 5, 3, 12, 7, 2, 7, 5, 1, 14, 9, 6, 10, 3, 2, 15, 13, 12, 12, 11, 9, 16,
// 9, 7, 12, 9, 3, 9, 5, 2, 17, 10, 6, 24, 9, 3, 17, 15, 13, 5, 4, 3, 19, 17, 8, 15, 6, 3, 19, 6, 1}
// irreducible polynomials of GF(2)
var irred_coeff = [...][3]byte{
{4, 3, 1}, // x^8 + x^4 + x^3 + x + 1
{5, 3, 1}, // x^16 + x^5 + x^3 + x + 1
{4, 3, 1}, // x^24 + x^4 + x^3 + x + 1
{7, 3, 2}, // x^32 + x^7 + x^3 + x^2 + 1
{5, 4, 3}, // x^40 + x^5 + x^4 + x^3 + 1
{5, 3, 2}, // x^48 + x^5 + x^3 + x^2 + 1
{7, 4, 2}, // x^56 + x^7 + x^4 + x^2 + 1
{4, 3, 1}, // x^64 + x^4 + x^3 + x + 1
{10, 9, 3}, // x^72 + x^10 + x^9 + x^3 + 1
{9, 4, 2}, // x^80 + x^9 + x^4 + x^2 + 1
{7, 6, 2}, // x^88 + x^7 + x^6 + x^2 + 1
{10, 9, 6}, // x^96 + x^10 + x^9 + x^6 + 1
{4, 3, 1}, // x^104 + x^4 + x^3 + x + 1
{5, 4, 3}, // x^112 + x^5 + x^4 + x^3 + 1
{4, 3, 1}, // x^120 + x^4 + x^3 + x + 1
{7, 2, 1}, // x^128 + x^7 + x^2 + x + 1
{5, 3, 2}, // x^136 + x^5 + x^3 + x^2 + 1
{7, 4, 2}, // x^144 + x^7 + x^4 + x^2 + 1
{6, 3, 2}, // x^152 + x^6 + x^3 + x^2 + 1
{5, 3, 2}, // x^160 + x^5 + x^3 + x^2 + 1
{15, 3, 2}, // x^168 + x^15 + x^3 + x^2 + 1
{11, 3, 2}, // x^176 + x^11 + x^3 + x^2 + 1
{9, 8, 7}, // x^184 + x^9 + x^8 + x^7 + 1
{7, 2, 1}, // x^192 + x^7 + x^2 + x + 1
{5, 3, 2}, // x^200 + x^5 + x^3 + x^2 + 1
{9, 3, 1}, // x^208 + x^9 + x^3 + x + 1
{7, 3, 1}, // x^216 + x^7 + x^3 + x + 1
{9, 8, 3}, // x^224 + x^9 + x^8 + x^3 + 1
{9, 4, 2}, // x^232 + x^9 + x^4 + x^2 + 1
{8, 5, 3}, // x^240 + x^8 + x^5 + x^3 + 1
{15, 14, 10}, // x^248 + x^15 + x^14 + x^10 + 1
{10, 5, 2}, // x^256 + x^10 + x^5 + x^2 + 1
{9, 6, 2}, // x^264 + x^9 + x^6 + x^2 + 1
{9, 3, 2}, // x^272 + x^9 + x^3 + x^2 + 1
{9, 5, 2}, // x^280 + x^9 + x^5 + x^2 + 1
{11, 10, 1}, // x^288 + x^11 + x^10 + x + 1
{7, 3, 2}, // x^296 + x^7 + x^3 + x^2 + 1
{11, 2, 1}, // x^304 + x^11 + x^2 + x + 1
{9, 7, 4}, // x^312 + x^9 + x^7 + x^4 + 1
{4, 3, 1}, // x^320 + x^4 + x^3 + x + 1
{8, 3, 1}, // x^328 + x^8 + x^3 + x + 1
{7, 4, 1}, // x^336 + x^7 + x^4 + x + 1
{7, 2, 1}, // x^344 + x^7 + x^2 + x + 1
{13, 11, 6}, // x^352 + x^13 + x^11 + x^6 + 1
{5, 3, 2}, // x^360 + x^5 + x^3 + x^2 + 1
{7, 3, 2}, // x^368 + x^7 + x^3 + x^2 + 1
{8, 7, 5}, // x^376 + x^8 + x^7 + x^5 + 1
{12, 3, 2}, // x^384 + x^12 + x^3 + x^2 + 1
{13, 10, 6}, // x^392 + x^13 + x^10 + x^6 + 1
{5, 3, 2}, // x^400 + x^5 + x^3 + x^2 + 1
{5, 3, 2}, // x^408 + x^5 + x^3 + x^2 + 1
{9, 5, 2}, // x^416 + x^9 + x^5 + x^2 + 1
{9, 7, 2}, // x^424 + x^9 + x^7 + x^2 + 1
{13, 4, 3}, // x^432 + x^13 + x^4 + x^3 + 1
{4, 3, 1}, // x^440 + x^4 + x^3 + x + 1
{11, 6, 4}, // x^448 + x^11 + x^6 + x^4 + 1
{18, 9, 6}, // x^456 + x^18 + x^9 + x^6 + 1
{19, 18, 13}, // x^464 + x^19 + x^18 + x^13 + 1
{11, 3, 2}, // x^472 + x^11 + x^3 + x^2 + 1
{15, 9, 6}, // x^480 + x^15 + x^9 + x^6 + 1
{4, 3, 1}, // x^488 + x^4 + x^3 + x + 1
{16, 5, 2}, // x^496 + x^16 + x^5 + x^2 + 1
{15, 14, 6}, // x^504 + x^15 + x^14 + x^6 + 1
{8, 5, 2}, // x^512 + x^8 + x^5 + x^2 + 1
{15, 11, 2}, // x^520 + x^15 + x^11 + x^2 + 1
{11, 6, 2}, // x^528 + x^11 + x^6 + x^2 + 1
{7, 5, 3}, // x^536 + x^7 + x^5 + x^3 + 1
{8, 3, 1}, // x^544 + x^8 + x^3 + x + 1
{19, 16, 9}, // x^552 + x^19 + x^16 + x^9 + 1
{11, 9, 6}, // x^560 + x^11 + x^9 + x^6 + 1
{15, 7, 6}, // x^568 + x^15 + x^7 + x^6 + 1
{13, 4, 3}, // x^576 + x^13 + x^4 + x^3 + 1
{14, 13, 3}, // x^584 + x^14 + x^13 + x^3 + 1
{13, 6, 3}, // x^592 + x^13 + x^6 + x^3 + 1
{9, 5, 2}, // x^600 + x^9 + x^5 + x^2 + 1
{19, 13, 6}, // x^608 + x^19 + x^13 + x^6 + 1
{19, 10, 3}, // x^616 + x^19 + x^10 + x^3 + 1
{11, 6, 5}, // x^624 + x^11 + x^6 + x^5 + 1
{9, 2, 1}, // x^632 + x^9 + x^2 + x + 1
{14, 3, 2}, // x^640 + x^14 + x^3 + x^2 + 1
{13, 3, 1}, // x^648 + x^13 + x^3 + x + 1
{7, 5, 4}, // x^656 + x^7 + x^5 + x^4 + 1
{11, 9, 8}, // x^664 + x^11 + x^9 + x^8 + 1
{11, 6, 5}, // x^672 + x^11 + x^6 + x^5 + 1
{23, 16, 9}, // x^680 + x^23 + x^16 + x^9 + 1
{19, 14, 6}, // x^688 + x^19 + x^14 + x^6 + 1
{23, 10, 2}, // x^696 + x^23 + x^10 + x^2 + 1
{8, 3, 2}, // x^704 + x^8 + x^3 + x^2 + 1
{5, 4, 3}, // x^712 + x^5 + x^4 + x^3 + 1
{9, 6, 4}, // x^720 + x^9 + x^6 + x^4 + 1
{4, 3, 2}, // x^728 + x^4 + x^3 + x^2 + 1
{13, 8, 6}, // x^736 + x^13 + x^8 + x^6 + 1
{13, 11, 1}, // x^744 + x^13 + x^11 + x + 1
{13, 10, 3}, // x^752 + x^13 + x^10 + x^3 + 1
{11, 6, 5}, // x^760 + x^11 + x^6 + x^5 + 1
{19, 17, 4}, // x^768 + x^19 + x^17 + x^4 + 1
{15, 14, 7}, // x^776 + x^15 + x^14 + x^7 + 1
{13, 9, 6}, // x^784 + x^13 + x^9 + x^6 + 1
{9, 7, 3}, // x^792 + x^9 + x^7 + x^3 + 1
{9, 7, 1}, // x^800 + x^9 + x^7 + x + 1
{14, 3, 2}, // x^808 + x^14 + x^3 + x^2 + 1
{11, 8, 2}, // x^816 + x^11 + x^8 + x^2 + 1
{11, 6, 4}, // x^824 + x^11 + x^6 + x^4 + 1
{13, 5, 2}, // x^832 + x^13 + x^5 + x^2 + 1
{11, 5, 1}, // x^840 + x^11 + x^5 + x + 1
{11, 4, 1}, // x^848 + x^11 + x^4 + x + 1
{19, 10, 3}, // x^856 + x^19 + x^10 + x^3 + 1
{21, 10, 6}, // x^864 + x^21 + x^10 + x^6 + 1
{13, 3, 1}, // x^872 + x^13 + x^3 + x + 1
{15, 7, 5}, // x^880 + x^15 + x^7 + x^5 + 1
{19, 18, 10}, // x^888 + x^19 + x^18 + x^10 + 1
{7, 5, 3}, // x^896 + x^7 + x^5 + x^3 + 1
{12, 7, 2}, // x^904 + x^12 + x^7 + x^2 + 1
{7, 5, 1}, // x^912 + x^7 + x^5 + x + 1
{14, 9, 6}, // x^920 + x^14 + x^9 + x^6 + 1
{10, 3, 2}, // x^928 + x^10 + x^3 + x^2 + 1
{15, 13, 12}, // x^936 + x^15 + x^13 + x^12 + 1
{12, 11, 9}, // x^944 + x^12 + x^11 + x^9 + 1
{16, 9, 7}, // x^952 + x^16 + x^9 + x^7 + 1
{12, 9, 3}, // x^960 + x^12 + x^9 + x^3 + 1
{9, 5, 2}, // x^968 + x^9 + x^5 + x^2 + 1
{17, 10, 6}, // x^976 + x^17 + x^10 + x^6 + 1
{24, 9, 3}, // x^984 + x^24 + x^9 + x^3 + 1
{17, 15, 13}, // x^992 + x^17 + x^15 + x^13 + 1
{5, 4, 3}, // x^1000 + x^5 + x^4 + x^3 + 1
{19, 17, 8}, // x^1008 + x^19 + x^17 + x^8 + 1
{15, 6, 3}, // x^1016 + x^15 + x^6 + x^3 + 1
{19, 6, 1}, // x^1024 + x^19 + x^6 + x + 1
}
// f2m, the extention filed over GF(2) of degree m
type gf2x struct {
poly *big.Int
degree int
intPool []*big.Int
}
func init() {
}
// newGF2x return the irred. polynomial of degree deg, where deg must divided by 8.
func newGF2x(deg int) *gf2x {
poly := big.NewInt(1)
poly.SetBit(poly, deg, 1)
// poly.SetBit(poly, int(irred_coeff[3*(deg/8-1)+0]), 1)
// poly.SetBit(poly, int(irred_coeff[3*(deg/8-1)+1]), 1)
// poly.SetBit(poly, int(irred_coeff[3*(deg/8-1)+2]), 1)
poly.SetBit(poly, int(irred_coeff[deg/8-1][0]), 1)
poly.SetBit(poly, int(irred_coeff[deg/8-1][1]), 1)
poly.SetBit(poly, int(irred_coeff[deg/8-1][2]), 1)
return &gf2x{
poly: poly,
degree: deg,
}
}
func (g *gf2x) getInt() (r *big.Int) {
if len(g.intPool) > 0 {
r = g.intPool[len(g.intPool)-1]
r.SetInt64(0)
g.intPool = g.intPool[:len(g.intPool)-1]
return
}
return new(big.Int)
}
func (g *gf2x) putInt(r *big.Int) {
g.intPool = append(g.intPool, r)
}
func (g *gf2x) rand(r io.Reader) (*big.Int, error) {
for {
x, err := rand.Int(r, g.poly)
x.SetBit(x, g.degree, 0)
if err == nil && x.Sign() != 0 {
return x, nil
}
if err != nil {
return nil, gerrors.WithStack(err)
}
}
}
func (g *gf2x) add(z, x, y *big.Int) {
z.Xor(x, y)
}
// z can't be y, z could be x
func (g *gf2x) mul(z, x, y *big.Int) {
var yy *big.Int
if z == y {
yy = g.getInt().Set(y)
defer g.putInt(yy)
} else {
yy = y
}
b := g.getInt()
defer g.putInt(b)
// note that z may be x, so make b a copy of x
b.Set(x)
if yy.Bit(0) == 1 {
// y = 1 + y1*X + y2*X^2 + ...
z.Set(b)
} else {
z.SetInt64(0)
}
for i := 1; i < g.degree; i++ {
b.Lsh(b, 1)
if b.Bit(g.degree) == 1 {
b.Xor(b, g.poly)
}
if yy.Bit(i) == 1 {
z.Xor(z, b)
}
}
}
var one = new(big.Int).SetInt64(1)
// extend eudlic algorithm
func (f *gf2x) invert(z, x *big.Int) error {
u := f.getInt()
v := f.getInt()
g := f.getInt()
h := f.getInt()
t := f.getInt()
defer func() {
f.putInt(u)
f.putInt(v)
f.putInt(g)
f.putInt(h)
f.putInt(t)
}()
if x.Sign() == 0 {
return gerrors.WithAnnotating(ErrDivideZero, "input x is zero")
}
u.Set(x)
v.Set(f.poly)
g.SetInt64(0)
h.SetInt64(1)
// x*h = u mod poly
// x*g = v mod poly
for u.Cmp(one) != 0 {
i := u.BitLen() - v.BitLen()
if i < 0 {
u, v, h, g = v, u, g, h
i = -i
}
t.Lsh(v, uint(i))
u.Xor(u, t)
t.Lsh(g, uint(i))
h.Xor(h, t)
}
z.Set(h)
return nil
}