1 files changed, 278 insertions, 0 deletions
diff --git a/crypto/bn256/curve.go b/crypto/bn256/curve.go
new file mode 100644
index 000000000..93f858def
--- /dev/null
+++ b/crypto/bn256/curve.go
@@ -0,0 +1,278 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package bn256
+
+import (
+	"math/big"
+)
+
+// curvePoint implements the elliptic curve y²=x³+3. Points are kept in
+// Jacobian form and t=z² when valid. G₁ is the set of points of this curve on
+// GF(p).
+type curvePoint struct {
+	x, y, z, t *big.Int
+}
+
+var curveB = new(big.Int).SetInt64(3)
+
+// curveGen is the generator of G₁.
+var curveGen = &curvePoint{
+	new(big.Int).SetInt64(1),
+	new(big.Int).SetInt64(-2),
+	new(big.Int).SetInt64(1),
+	new(big.Int).SetInt64(1),
+}
+
+func newCurvePoint(pool *bnPool) *curvePoint {
+	return &curvePoint{
+		pool.Get(),
+		pool.Get(),
+		pool.Get(),
+		pool.Get(),
+	}
+}
+
+func (c *curvePoint) String() string {
+	c.MakeAffine(new(bnPool))
+	return "(" + c.x.String() + ", " + c.y.String() + ")"
+}
+
+func (c *curvePoint) Put(pool *bnPool) {
+	pool.Put(c.x)
+	pool.Put(c.y)
+	pool.Put(c.z)
+	pool.Put(c.t)
+}
+
+func (c *curvePoint) Set(a *curvePoint) {
+	c.x.Set(a.x)
+	c.y.Set(a.y)
+	c.z.Set(a.z)
+	c.t.Set(a.t)
+}
+
+// IsOnCurve returns true iff c is on the curve where c must be in affine form.
+func (c *curvePoint) IsOnCurve() bool {
+	yy := new(big.Int).Mul(c.y, c.y)
+	xxx := new(big.Int).Mul(c.x, c.x)
+	xxx.Mul(xxx, c.x)
+	yy.Sub(yy, xxx)
+	yy.Sub(yy, curveB)
+	if yy.Sign() < 0 || yy.Cmp(P) >= 0 {
+		yy.Mod(yy, P)
+	}
+	return yy.Sign() == 0
+}
+
+func (c *curvePoint) SetInfinity() {
+	c.z.SetInt64(0)
+}
+
+func (c *curvePoint) IsInfinity() bool {
+	return c.z.Sign() == 0
+}
+
+func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) {
+	if a.IsInfinity() {
+		c.Set(b)
+		return
+	}
+	if b.IsInfinity() {
+		c.Set(a)
+		return
+	}
+
+	// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3
+
+	// Normalize the points by replacing a = [x1:y1:z1] and b = [x2:y2:z2]
+	// by [u1:s1:z1·z2] and [u2:s2:z1·z2]
+	// where u1 = x1·z2², s1 = y1·z2³ and u1 = x2·z1², s2 = y2·z1³
+	z1z1 := pool.Get().Mul(a.z, a.z)
+	z1z1.Mod(z1z1, P)
+	z2z2 := pool.Get().Mul(b.z, b.z)
+	z2z2.Mod(z2z2, P)
+	u1 := pool.Get().Mul(a.x, z2z2)
+	u1.Mod(u1, P)
+	u2 := pool.Get().Mul(b.x, z1z1)
+	u2.Mod(u2, P)
+
+	t := pool.Get().Mul(b.z, z2z2)
+	t.Mod(t, P)
+	s1 := pool.Get().Mul(a.y, t)
+	s1.Mod(s1, P)
+
+	t.Mul(a.z, z1z1)
+	t.Mod(t, P)
+	s2 := pool.Get().Mul(b.y, t)
+	s2.Mod(s2, P)
+
+	// Compute x = (2h)²(s²-u1-u2)
+	// where s = (s2-s1)/(u2-u1) is the slope of the line through
+	// (u1,s1) and (u2,s2). The extra factor 2h = 2(u2-u1) comes from the value of z below.
+	// This is also:
+	// 4(s2-s1)² - 4h²(u1+u2) = 4(s2-s1)² - 4h³ - 4h²(2u1)
+	//                        = r² - j - 2v
+	// with the notations below.
+	h := pool.Get().Sub(u2, u1)
+	xEqual := h.Sign() == 0
+
+	t.Add(h, h)
+	// i = 4h²
+	i := pool.Get().Mul(t, t)
+	i.Mod(i, P)
+	// j = 4h³
+	j := pool.Get().Mul(h, i)
+	j.Mod(j, P)
+
+	t.Sub(s2, s1)
+	yEqual := t.Sign() == 0
+	if xEqual && yEqual {
+		c.Double(a, pool)
+		return
+	}
+	r := pool.Get().Add(t, t)
+
+	v := pool.Get().Mul(u1, i)
+	v.Mod(v, P)
+
+	// t4 = 4(s2-s1)²
+	t4 := pool.Get().Mul(r, r)
+	t4.Mod(t4, P)
+	t.Add(v, v)
+	t6 := pool.Get().Sub(t4, j)
+	c.x.Sub(t6, t)
+
+	// Set y = -(2h)³(s1 + s*(x/4h²-u1))
+	// This is also
+	// y = - 2·s1·j - (s2-s1)(2x - 2i·u1) = r(v-x) - 2·s1·j
+	t.Sub(v, c.x) // t7
+	t4.Mul(s1, j) // t8
+	t4.Mod(t4, P)
+	t6.Add(t4, t4) // t9
+	t4.Mul(r, t)   // t10
+	t4.Mod(t4, P)
+	c.y.Sub(t4, t6)
+
+	// Set z = 2(u2-u1)·z1·z2 = 2h·z1·z2
+	t.Add(a.z, b.z) // t11
+	t4.Mul(t, t)    // t12
+	t4.Mod(t4, P)
+	t.Sub(t4, z1z1) // t13
+	t4.Sub(t, z2z2) // t14
+	c.z.Mul(t4, h)
+	c.z.Mod(c.z, P)
+
+	pool.Put(z1z1)
+	pool.Put(z2z2)
+	pool.Put(u1)
+	pool.Put(u2)
+	pool.Put(t)
+	pool.Put(s1)
+	pool.Put(s2)
+	pool.Put(h)
+	pool.Put(i)
+	pool.Put(j)
+	pool.Put(r)
+	pool.Put(v)
+	pool.Put(t4)
+	pool.Put(t6)
+}
+
+func (c *curvePoint) Double(a *curvePoint, pool *bnPool) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
+	A := pool.Get().Mul(a.x, a.x)
+	A.Mod(A, P)
+	B := pool.Get().Mul(a.y, a.y)
+	B.Mod(B, P)
+	C := pool.Get().Mul(B, B)
+	C.Mod(C, P)
+
+	t := pool.Get().Add(a.x, B)
+	t2 := pool.Get().Mul(t, t)
+	t2.Mod(t2, P)
+	t.Sub(t2, A)
+	t2.Sub(t, C)
+	d := pool.Get().Add(t2, t2)
+	t.Add(A, A)
+	e := pool.Get().Add(t, A)
+	f := pool.Get().Mul(e, e)
+	f.Mod(f, P)
+
+	t.Add(d, d)
+	c.x.Sub(f, t)
+
+	t.Add(C, C)
+	t2.Add(t, t)
+	t.Add(t2, t2)
+	c.y.Sub(d, c.x)
+	t2.Mul(e, c.y)
+	t2.Mod(t2, P)
+	c.y.Sub(t2, t)
+
+	t.Mul(a.y, a.z)
+	t.Mod(t, P)
+	c.z.Add(t, t)
+
+	pool.Put(A)
+	pool.Put(B)
+	pool.Put(C)
+	pool.Put(t)
+	pool.Put(t2)
+	pool.Put(d)
+	pool.Put(e)
+	pool.Put(f)
+}
+
+func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int, pool *bnPool) *curvePoint {
+	sum := newCurvePoint(pool)
+	sum.SetInfinity()
+	t := newCurvePoint(pool)
+
+	for i := scalar.BitLen(); i >= 0; i-- {
+		t.Double(sum, pool)
+		if scalar.Bit(i) != 0 {
+			sum.Add(t, a, pool)
+		} else {
+			sum.Set(t)
+		}
+	}
+
+	c.Set(sum)
+	sum.Put(pool)
+	t.Put(pool)
+	return c
+}
+
+func (c *curvePoint) MakeAffine(pool *bnPool) *curvePoint {
+	if words := c.z.Bits(); len(words) == 1 && words[0] == 1 {
+		return c
+	}
+
+	zInv := pool.Get().ModInverse(c.z, P)
+	t := pool.Get().Mul(c.y, zInv)
+	t.Mod(t, P)
+	zInv2 := pool.Get().Mul(zInv, zInv)
+	zInv2.Mod(zInv2, P)
+	c.y.Mul(t, zInv2)
+	c.y.Mod(c.y, P)
+	t.Mul(c.x, zInv2)
+	t.Mod(t, P)
+	c.x.Set(t)
+	c.z.SetInt64(1)
+	c.t.SetInt64(1)
+
+	pool.Put(zInv)
+	pool.Put(t)
+	pool.Put(zInv2)
+
+	return c
+}
+
+func (c *curvePoint) Negative(a *curvePoint) {
+	c.x.Set(a.x)
+	c.y.Neg(a.y)
+	c.z.Set(a.z)
+	c.t.SetInt64(0)
+}