1 files changed, 204 insertions, 0 deletions
diff --git a/crypto/bn256/cloudflare/twist.go b/crypto/bn256/cloudflare/twist.go
new file mode 100644
index 000000000..0c2f80d4e
--- /dev/null
+++ b/crypto/bn256/cloudflare/twist.go
@@ -0,0 +1,204 @@
+package bn256
+
+import (
+	"math/big"
+)
+
+// twistPoint implements the elliptic curve y²=x³+3/ξ over GF(p²). Points are
+// kept in Jacobian form and t=z² when valid. The group G₂ is the set of
+// n-torsion points of this curve over GF(p²) (where n = Order)
+type twistPoint struct {
+	x, y, z, t gfP2
+}
+
+var twistB = &gfP2{
+	gfP{0x38e7ecccd1dcff67, 0x65f0b37d93ce0d3e, 0xd749d0dd22ac00aa, 0x0141b9ce4a688d4d},
+	gfP{0x3bf938e377b802a8, 0x020b1b273633535d, 0x26b7edf049755260, 0x2514c6324384a86d},
+}
+
+// twistGen is the generator of group G₂.
+var twistGen = &twistPoint{
+	gfP2{
+		gfP{0xafb4737da84c6140, 0x6043dd5a5802d8c4, 0x09e950fc52a02f86, 0x14fef0833aea7b6b},
+		gfP{0x8e83b5d102bc2026, 0xdceb1935497b0172, 0xfbb8264797811adf, 0x19573841af96503b},
+	},
+	gfP2{
+		gfP{0x64095b56c71856ee, 0xdc57f922327d3cbb, 0x55f935be33351076, 0x0da4a0e693fd6482},
+		gfP{0x619dfa9d886be9f6, 0xfe7fd297f59e9b78, 0xff9e1a62231b7dfe, 0x28fd7eebae9e4206},
+	},
+	gfP2{*newGFp(0), *newGFp(1)},
+	gfP2{*newGFp(0), *newGFp(1)},
+}
+
+func (c *twistPoint) String() string {
+	c.MakeAffine()
+	x, y := gfP2Decode(&c.x), gfP2Decode(&c.y)
+	return "(" + x.String() + ", " + y.String() + ")"
+}
+
+func (c *twistPoint) Set(a *twistPoint) {
+	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.
+func (c *twistPoint) IsOnCurve() bool {
+	c.MakeAffine()
+	if c.IsInfinity() {
+		return true
+	}
+
+	y2, x3 := &gfP2{}, &gfP2{}
+	y2.Square(&c.y)
+	x3.Square(&c.x).Mul(x3, &c.x).Add(x3, twistB)
+
+	if *y2 != *x3 {
+		return false
+	}
+	cneg := &twistPoint{}
+	cneg.Mul(c, Order)
+	return cneg.z.IsZero()
+}
+
+func (c *twistPoint) SetInfinity() {
+	c.x.SetZero()
+	c.y.SetOne()
+	c.z.SetZero()
+	c.t.SetZero()
+}
+
+func (c *twistPoint) IsInfinity() bool {
+	return c.z.IsZero()
+}
+
+func (c *twistPoint) Add(a, b *twistPoint) {
+	// For additional comments, see the same function in curve.go.
+
+	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
+	z12 := (&gfP2{}).Square(&a.z)
+	z22 := (&gfP2{}).Square(&b.z)
+	u1 := (&gfP2{}).Mul(&a.x, z22)
+	u2 := (&gfP2{}).Mul(&b.x, z12)
+
+	t := (&gfP2{}).Mul(&b.z, z22)
+	s1 := (&gfP2{}).Mul(&a.y, t)
+
+	t.Mul(&a.z, z12)
+	s2 := (&gfP2{}).Mul(&b.y, t)
+
+	h := (&gfP2{}).Sub(u2, u1)
+	xEqual := h.IsZero()
+
+	t.Add(h, h)
+	i := (&gfP2{}).Square(t)
+	j := (&gfP2{}).Mul(h, i)
+
+	t.Sub(s2, s1)
+	yEqual := t.IsZero()
+	if xEqual && yEqual {
+		c.Double(a)
+		return
+	}
+	r := (&gfP2{}).Add(t, t)
+
+	v := (&gfP2{}).Mul(u1, i)
+
+	t4 := (&gfP2{}).Square(r)
+	t.Add(v, v)
+	t6 := (&gfP2{}).Sub(t4, j)
+	c.x.Sub(t6, t)
+
+	t.Sub(v, &c.x) // t7
+	t4.Mul(s1, j)  // t8
+	t6.Add(t4, t4) // t9
+	t4.Mul(r, t)   // t10
+	c.y.Sub(t4, t6)
+
+	t.Add(&a.z, &b.z) // t11
+	t4.Square(t)      // t12
+	t.Sub(t4, z12)    // t13
+	t4.Sub(t, z22)    // t14
+	c.z.Mul(t4, h)
+}
+
+func (c *twistPoint) Double(a *twistPoint) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
+	A := (&gfP2{}).Square(&a.x)
+	B := (&gfP2{}).Square(&a.y)
+	C := (&gfP2{}).Square(B)
+
+	t := (&gfP2{}).Add(&a.x, B)
+	t2 := (&gfP2{}).Square(t)
+	t.Sub(t2, A)
+	t2.Sub(t, C)
+	d := (&gfP2{}).Add(t2, t2)
+	t.Add(A, A)
+	e := (&gfP2{}).Add(t, A)
+	f := (&gfP2{}).Square(e)
+
+	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)
+	c.y.Sub(t2, t)
+
+	t.Mul(&a.y, &a.z)
+	c.z.Add(t, t)
+}
+
+func (c *twistPoint) Mul(a *twistPoint, scalar *big.Int) {
+	sum, t := &twistPoint{}, &twistPoint{}
+
+	for i := scalar.BitLen(); i >= 0; i-- {
+		t.Double(sum)
+		if scalar.Bit(i) != 0 {
+			sum.Add(t, a)
+		} else {
+			sum.Set(t)
+		}
+	}
+
+	c.Set(sum)
+}
+
+func (c *twistPoint) MakeAffine() {
+	if c.z.IsOne() {
+		return
+	} else if c.z.IsZero() {
+		c.x.SetZero()
+		c.y.SetOne()
+		c.t.SetZero()
+		return
+	}
+
+	zInv := (&gfP2{}).Invert(&c.z)
+	t := (&gfP2{}).Mul(&c.y, zInv)
+	zInv2 := (&gfP2{}).Square(zInv)
+	c.y.Mul(t, zInv2)
+	t.Mul(&c.x, zInv2)
+	c.x.Set(t)
+	c.z.SetOne()
+	c.t.SetOne()
+}
+
+func (c *twistPoint) Neg(a *twistPoint) {
+	c.x.Set(&a.x)
+	c.y.Neg(&a.y)
+	c.z.Set(&a.z)
+	c.t.SetZero()
+}