init: v1.0.0

2026-05-27 23:03:00 +08:00
commit 8d97f750eb
466 changed files with 80067 additions and 0 deletions
@@ -0,0 +1,249 @@
+package bn256
+
+// For details of the algorithms used, see "Multiplication and Squaring on
+// Pairing-Friendly Fields, Devegili et al.
+// http://eprint.iacr.org/2006/471.pdf.
+
+import (
+	"math/big"
+)
+
+// gfP12 implements the field of size P¹² as a quadratic extension of gfP6
+// where ω²=τ.
+type gfP12 struct {
+	x, y gfP6 // value is xω + y
+}
+
+// gfP12Gen = e(g1, g2)
+var gfP12Gen = &gfP12{
+	x: gfP6{
+		x: gfP2{
+			x: gfP{0xeb2aeaa2823d010c, 0xe192c39d7c3e6440, 0x68411e843fea2a9b, 0x5f23b1ce3ac438e7},
+			y: gfP{0x65c1ad6d376db4f, 0xe2447d6d5edfdda6, 0xd4eba5c8c017781, 0x61ebca2110d736bf},
+		},
+		y: gfP2{
+			x: gfP{0xc219536a54552cae, 0xc4e4ad66027f8f55, 0xff31b23d5bc78184, 0x3b0fc03d5711c93d},
+			y: gfP{0x290e1c8bdb9441aa, 0x74e1694c800c130, 0xfa196a2583564700, 0x254eb32dea84e64d},
+		},
+		z: gfP2{
+			x: gfP{0x24fb5abe38626c9c, 0xd32d71f71d7bd3de, 0x671d686fd9c9271d, 0xa3eec3cd6a795be8},
+			y: gfP{0x7b9c733c1f964b52, 0x9b988c0c238fb05e, 0xe546ccb8d6e1f9b8, 0xb101d668bfbf8ac8},
+		},
+	},
+	y: gfP6{
+		x: gfP2{
+			x: gfP{0x487ab1a6229d91f3, 0x7e2a3e36c6c822c7, 0x282c24f00c10930f, 0x2efe33f18332bb77},
+			y: gfP{0x346965f4dc5b5813, 0xed43ed38c0ce33e6, 0x9ba7630e295a5ce7, 0xa6db7142e0ca24ae},
+		},
+		y: gfP2{
+			x: gfP{0xfea0bce10965b32b, 0x441e074b4573390c, 0xe9d6067a4cf3c571, 0x9ee43c7e3740bcd8},
+			y: gfP{0xe06727b47ee6118, 0xb01ab631f2f10a18, 0xb0ebd9852fc780ef, 0xaa07010f9d42787c},
+		},
+		z: gfP2{
+			x: gfP{0xbe7381e2bce90a00, 0x2a72158dbf514e31, 0x44e199bee3498d4d, 0x6a5fed210720de58},
+			y: gfP{0xb55d63ee8d7a8468, 0x9ef5d413e3176666, 0x796c802ec3f1370b, 0xa0f422c35d7b6262},
+		},
+	},
+}
+
+func gfP12Decode(in *gfP12) *gfP12 { // nolint
+	return &gfP12{
+		*gfP6Decode(&in.x),
+		*gfP6Decode(&in.y),
+	}
+}
+
+func (e *gfP12) Equal(other *gfP12) bool {
+	return e.x.Equal(&other.x) && e.y.Equal(&other.y)
+}
+
+func (e *gfP12) String() string {
+	return "(" + e.x.String() + "," + e.y.String() + ")"
+}
+
+func (e *gfP12) Set(a *gfP12) *gfP12 {
+	e.x.Set(&a.x)
+	e.y.Set(&a.y)
+	return e
+}
+
+func (e *gfP12) SetZero() *gfP12 {
+	e.x.SetZero()
+	e.y.SetZero()
+	return e
+}
+
+func (e *gfP12) SetOne() *gfP12 {
+	e.x.SetZero()
+	e.y.SetOne()
+	return e
+}
+
+func (e *gfP12) IsZero() bool {
+	return e.x.IsZero() && e.y.IsZero()
+}
+
+func (e *gfP12) IsOne() bool {
+	return e.x.IsZero() && e.y.IsOne()
+}
+
+func (e *gfP12) Conjugate(a *gfP12) *gfP12 {
+	e.x.Neg(&a.x)
+	e.y.Set(&a.y)
+	return e
+}
+
+func (e *gfP12) Neg(a *gfP12) *gfP12 {
+	e.x.Neg(&a.x)
+	e.y.Neg(&a.y)
+	return e
+}
+
+// Frobenius computes (xω+y)^P = x^P ω·ξ^((P-1)/6) + y^P
+func (e *gfP12) Frobenius(a *gfP12) *gfP12 {
+	e.x.Frobenius(&a.x)
+	e.y.Frobenius(&a.y)
+
+	e.x.MulGFP(&e.x, xiToPMinus1Over6)
+	return e
+}
+
+// FrobeniusP2 computes (xω+y)^P² = x^P² ω·ξ^((P²-1)/6) + y^P²
+func (e *gfP12) FrobeniusP2(a *gfP12) *gfP12 {
+	e.x.FrobeniusP2(&a.x)
+	e.x.MulGFP(&e.x, xiToPSquaredMinus1Over6)
+	e.y.FrobeniusP2(&a.y)
+	return e
+}
+
+func (e *gfP12) FrobeniusP4(a *gfP12) *gfP12 {
+	e.x.FrobeniusP4(&a.x)
+	e.x.MulGFP(&e.x, xiToPSquaredMinus1Over3)
+	e.y.FrobeniusP4(&a.y)
+	return e
+}
+
+func (e *gfP12) Add(a, b *gfP12) *gfP12 {
+	e.x.Add(&a.x, &b.x)
+	e.y.Add(&a.y, &b.y)
+	return e
+}
+
+func (e *gfP12) Sub(a, b *gfP12) *gfP12 {
+	e.x.Sub(&a.x, &b.x)
+	e.y.Sub(&a.y, &b.y)
+	return e
+}
+
+func (e *gfP12) Mul(a, b *gfP12) *gfP12 {
+	tx := (&gfP6{}).Mul(&a.x, &b.y)
+	t := (&gfP6{}).Mul(&b.x, &a.y)
+	tx.Add(tx, t)
+
+	ty := (&gfP6{}).Mul(&a.y, &b.y)
+	t.Mul(&a.x, &b.x).MulTau(t)
+
+	e.x.Set(tx)
+	e.y.Add(ty, t)
+	return e
+}
+
+func (e *gfP12) MulScalar(a *gfP12, b *gfP6) *gfP12 {
+	e.x.Mul(&e.x, b)
+	e.y.Mul(&e.y, b)
+	return e
+}
+
+// Exp compute c = a^power, and return c. Exp is the common square-mul, for all
+// Elements in gfp12
+func (e *gfP12) Exp(a *gfP12, power *big.Int) *gfP12 {
+	sum := (&gfP12{}).SetOne()
+	t := &gfP12{}
+
+	for i := power.BitLen() - 1; i >= 0; i-- {
+		t.Square(sum)
+		if power.Bit(i) != 0 {
+			sum.Mul(t, a)
+		} else {
+			sum.Set(t)
+		}
+	}
+
+	return e.Set(sum)
+
+}
+
+// for element in GT
+func (e *gfP12) latticeExp(a *gfP12, power *big.Int) *gfP12 {
+	base := [1 << 2]*gfP12{{}, {}, {}, {}}
+	base[0].Set(a)
+	base[1].Frobenius(base[0])
+	base[2].FrobeniusP2(base[0])
+	base[3].Frobenius(base[2])
+
+	decomp := targetLattice.decompose(power)
+	//fmt.Println(decomp)
+	for i := 0; i < len(decomp); i++ {
+		if decomp[i].Sign() < 0 {
+			base[i].Conjugate(base[i])
+		}
+	}
+
+	precomp := [1 << 4]*gfP12{}
+	targetLattice.Precompute(func(i, j uint) {
+		if precomp[j] == nil {
+			precomp[j] = &gfP12{}
+			precomp[j].SetOne()
+		}
+		precomp[j].Mul(precomp[j], base[i])
+	})
+	multiPower := targetLattice.Multi(power)
+
+	sum := &gfP12{}
+	sum.SetOne()
+	t := &gfP12{}
+
+	for i := len(multiPower) - 1; i >= 0; i-- {
+		t.Square(sum)
+		if multiPower[i] == 0 {
+			sum.Set(t)
+		} else {
+			sum.Mul(t, precomp[multiPower[i]])
+		}
+	}
+
+	e.Set(sum)
+	return e
+}
+
+func (e *gfP12) Square(a *gfP12) *gfP12 {
+	// Complex squaring algorithm
+	v0 := (&gfP6{}).Mul(&a.x, &a.y)
+
+	t := (&gfP6{}).MulTau(&a.x)
+	t.Add(&a.y, t)
+	ty := (&gfP6{}).Add(&a.x, &a.y)
+	ty.Mul(ty, t).Sub(ty, v0)
+	t.MulTau(v0)
+	ty.Sub(ty, t)
+
+	e.x.Add(v0, v0)
+	e.y.Set(ty)
+	return e
+}
+
+func (e *gfP12) Invert(a *gfP12) *gfP12 {
+	// See "Implementing cryptographic pairings", M. Scott, section 3.2.
+	// ftp://136.206.11.249/pub/crypto/pairings.pdf
+	t1, t2 := &gfP6{}, &gfP6{}
+
+	t1.Square(&a.x)
+	t2.Square(&a.y)
+	t1.MulTau(t1).Sub(t2, t1)
+	t2.Invert(t1)
+
+	e.x.Neg(&a.x)
+	e.y.Set(&a.y)
+	e.MulScalar(e, t2)
+	return e
+}