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 +1,128 @@
+package bn256
+
+import (
+	"math/big"
+)
+
+// useLattice switch if we use lattice and GLV to accelerate computing.
+// In product version, it could be a const.
+// const useLattice = true
+var useLattice = true
+
+var half = new(big.Int).Rsh(N, 1)
+
+var curveLattice = &lattice{
+	vectors: [][]*big.Int{
+		{bigFromBase10("287113247090025866066532163502283840641"), bigFromBase10("13835058055293825813")},
+		{bigFromBase10("13835058055293825813"), bigFromBase10("-287113247090025866052697105446990014828")},
+	},
+	inverse: []*big.Int{
+		bigFromBase10("287113247090025866052697105446990014828"),
+		bigFromBase10("13835058055293825813"),
+	},
+	det: bigFromBase16("B640000002A3A6F1D603AB4FF58EC74449F2934B18EA8BEEE56EE19CD69ECF25"),
+}
+
+var targetLattice = &lattice{
+	vectors: [][]*big.Int{
+		{bigFromBase10("6917529027646912907"), bigFromBase10("6917529027646912906"), bigFromBase10("6917529027646912906"), bigFromBase10("-13835058055293825812")},
+		{bigFromBase10("13835058055293825813"), bigFromBase10("-6917529027646912906"), bigFromBase10("-6917529027646912907"), bigFromBase10("-6917529027646912906")},
+		{bigFromBase10("13835058055293825812"), bigFromBase10("13835058055293825813"), bigFromBase10("13835058055293825813"), bigFromBase10("13835058055293825813")},
+		{bigFromBase10("6917529027646912905"), bigFromBase10("27670116110587651626"), bigFromBase10("-13835058055293825811"), bigFromBase10("6917529027646912905")},
+	},
+
+	inverse: []*big.Int{
+		bigFromBase10("95704415696675288700373269546839468391"),
+		bigFromBase10("3972228441934428951444310461776851119314861197558173512586"),
+		bigFromBase10("1986114220967214475722155230888425559660889363292910212746"),
+		bigFromBase10("-95704415696675288686538211491545642578"),
+	},
+
+	det: new(big.Int).Set(N),
+}
+
+type lattice struct {
+	vectors [][]*big.Int
+	inverse []*big.Int
+	det     *big.Int
+}
+
+// decompose takes a scalar mod Order as input and finds a short, positive decomposition of it wrt to the lattice basis.
+// output: out[0] + lambda*out[1] = 0 mod n
+// [lambda](x,y) = (eta*x, y), eta^3 = 1
+// TODO out[0] and out[1] should > 0 or ?
+func (l *lattice) decompose(k *big.Int) []*big.Int {
+	n := len(l.inverse)
+
+	// Calculate closest vector in lattice to <k,0,0,...> with Babai's rounding.
+	c := make([]*big.Int, n)
+	for i := 0; i < n; i++ {
+		c[i] = new(big.Int).Mul(k, l.inverse[i])
+		round(c[i], l.det)
+	}
+
+	// Transform vectors according to c and subtract <k,0,0,...>.
+	out := make([]*big.Int, n)
+	temp := new(big.Int)
+
+	for i := 0; i < n; i++ {
+		out[i] = new(big.Int)
+
+		for j := 0; j < n; j++ {
+			temp.Mul(c[j], l.vectors[j][i])
+			out[i].Add(out[i], temp)
+		}
+
+		out[i].Neg(out[i])
+
+		//TODO why add
+		out[i].Add(out[i], l.vectors[0][i]).Add(out[i], l.vectors[0][i])
+	}
+	out[0].Add(out[0], k)
+
+	return out
+}
+
+func (l *lattice) Precompute(add func(i, j uint)) {
+	n := uint(len(l.vectors))
+	total := uint(1) << uint(n)
+
+	for i := uint(0); i < n; i++ {
+		for j := uint(0); j < total; j++ {
+			if (j>>i)&1 == 1 {
+				add(i, j)
+			}
+		}
+	}
+}
+
+func (l *lattice) Multi(scalar *big.Int) []uint8 {
+	decomp := l.decompose(scalar)
+
+	maxLen := 0
+	for _, x := range decomp {
+		if x.BitLen() > maxLen {
+			maxLen = x.BitLen()
+		}
+	}
+
+	out := make([]uint8, maxLen)
+	for j, x := range decomp {
+		for i := 0; i < maxLen; i++ {
+			//out[i] += uint8(x.Bit(i)) << uint(j)
+			out[i] += uint8(x.Abs(x).Bit(i)) << uint(j)
+		}
+	}
+
+	return out
+}
+
+// round sets num to num/denom rounded to the nearest integer.
+func round(num, denom *big.Int) {
+	r := new(big.Int)
+	num.DivMod(num, denom, r)
+
+	if r.Cmp(half) == 1 {
+		num.Add(num, big.NewInt(1))
+	}
+}