mirror of
https://github.com/emmansun/gmsm.git
synced 2025-04-24 03:06:18 +08:00
273 lines
7.7 KiB
Go
273 lines
7.7 KiB
Go
package bn256
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import (
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"crypto/subtle"
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"math/big"
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)
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// curvePoint implements the elliptic curve y²=x³+5. Points are kept in Jacobian
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// form and t=z² when valid. G₁ is the set of points of this curve on GF(p).
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type curvePoint struct {
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x, y, z, t gfP
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}
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var curveB = newGFp(5)
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var threeCurveB = newGFp(3 * 5)
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// curveGen is the generator of G₁.
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var curveGen = &curvePoint{
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x: *fromBigInt(bigFromHex("93DE051D62BF718FF5ED0704487D01D6E1E4086909DC3280E8C4E4817C66DDDD")),
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y: *fromBigInt(bigFromHex("21FE8DDA4F21E607631065125C395BBC1C1C00CBFA6024350C464CD70A3EA616")),
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z: *one,
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t: *one,
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}
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func (c *curvePoint) String() string {
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c.MakeAffine()
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x, y := &gfP{}, &gfP{}
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montDecode(x, &c.x)
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montDecode(y, &c.y)
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return "(" + x.String() + ", " + y.String() + ")"
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}
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func (c *curvePoint) Set(a *curvePoint) {
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c.x.Set(&a.x)
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c.y.Set(&a.y)
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c.z.Set(&a.z)
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c.t.Set(&a.t)
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}
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func (c *curvePoint) polynomial(x *gfP) *gfP {
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x3 := &gfP{}
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gfpSqr(x3, x, 1)
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gfpMul(x3, x3, x)
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gfpAdd(x3, x3, curveB)
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return x3
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}
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// IsOnCurve returns true if c is on the curve.
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func (c *curvePoint) IsOnCurve() bool {
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c.MakeAffine()
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if c.IsInfinity() { // TBC: This is not same as golang elliptic
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return true
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}
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y2 := &gfP{}
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gfpSqr(y2, &c.y, 1)
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x3 := c.polynomial(&c.x)
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return y2.Equal(x3) == 1
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}
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func NewCurvePoint() *curvePoint {
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c := &curvePoint{}
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c.SetInfinity()
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return c
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}
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func NewCurveGenerator() *curvePoint {
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c := &curvePoint{}
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c.Set(curveGen)
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return c
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}
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func (c *curvePoint) SetInfinity() {
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c.x.Set(zero)
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c.y.Set(one)
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c.z.Set(zero)
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c.t.Set(zero)
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}
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func (c *curvePoint) IsInfinity() bool {
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return c.z.Equal(zero) == 1
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}
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func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int) {
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sum, t := &curvePoint{}, &curvePoint{}
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sum.SetInfinity()
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for i := scalar.BitLen(); i >= 0; i-- {
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t.Double(sum)
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if scalar.Bit(i) != 0 {
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sum.Add(t, a)
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} else {
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sum.Set(t)
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}
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}
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c.Set(sum)
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}
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// MakeAffine reverses the Jacobian transform.
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// the Jacobian coordinates are (x1, y1, z1)
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// where x = x1/z1² and y = y1/z1³.
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func (c *curvePoint) AffineFromJacobian() {
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if c.z.Equal(one) == 1 {
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return
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} else if c.z.Equal(zero) == 1 {
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c.x.Set(zero)
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c.y.Set(one)
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c.t.Set(zero)
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return
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}
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zInv := &gfP{}
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zInv.Invert(&c.z)
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t, zInv2 := &gfP{}, &gfP{}
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gfpMul(t, &c.y, zInv) // t = y/z
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gfpSqr(zInv2, zInv, 1)
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gfpMul(&c.x, &c.x, zInv2) // x = x / z^2
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gfpMul(&c.y, t, zInv2) // y = y / z^3
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c.z.Set(one)
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c.t.Set(one)
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}
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func (c *curvePoint) Neg(a *curvePoint) {
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c.x.Set(&a.x)
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gfpNeg(&c.y, &a.y)
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c.z.Set(&a.z)
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c.t.Set(zero)
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}
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// A curvePointTable holds the first 15 multiples of a point at offset -1, so [1]P
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// is at table[0], [15]P is at table[14], and [0]P is implicitly the identity
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// point.
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type curvePointTable [15]*curvePoint
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// Select selects the n-th multiple of the table base point into p. It works in
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// constant time by iterating over every entry of the table. n must be in [0, 15].
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func (table *curvePointTable) Select(p *curvePoint, n uint8) {
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if n >= 16 {
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panic("sm9: internal error: curvePointTable called with out-of-bounds value")
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}
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p.SetInfinity()
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for i, f := range table {
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cond := subtle.ConstantTimeByteEq(uint8(i+1), n)
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curvePointMovCond(p, f, p, cond)
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}
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}
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// Equal compare e and other
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func (e *curvePoint) Equal(other *curvePoint) bool {
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return e.x.Equal(&other.x) == 1 &&
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e.y.Equal(&other.y) == 1 &&
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e.z.Equal(&other.z) == 1 &&
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e.t.Equal(&other.t) == 1
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}
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// Below methods are POC yet, the line add/double functions are still based on
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// Jacobian coordination.
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func (c *curvePoint) Add(p1, p2 *curvePoint) {
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// Complete addition formula for a = 0 from "Complete addition formulas for
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// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §3.2.
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// Algorithm 7: Complete, projective point addition for prime order j-invariant 0 short Weierstrass curves.
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t0, t1, t2, t3, t4 := new(gfP), new(gfP), new(gfP), new(gfP), new(gfP)
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x3, y3, z3 := new(gfP), new(gfP), new(gfP)
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gfpMul(t0, &p1.x, &p2.x) // t0 := X1X2
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gfpMul(t1, &p1.y, &p2.y) // t1 := Y1Y2
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gfpMul(t2, &p1.z, &p2.z) // t2 := Z1Z2
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gfpAdd(t3, &p1.x, &p1.y) // t3 := X1 + Y1
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gfpAdd(t4, &p2.x, &p2.y) // t4 := X2 + Y2
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gfpMul(t3, t3, t4) // t3 := t3 * t4 = (X1 + Y1) * (X2 + Y2)
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gfpAdd(t4, t0, t1) // t4 := t0 + t1
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gfpSub(t3, t3, t4) // t3 := t3 - t4 = X1Y2 + X2Y1
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gfpAdd(t4, &p1.y, &p1.z) // t4 := Y1 + Z1
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gfpAdd(x3, &p2.y, &p2.z) // X3 := Y2 + Z2
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gfpMul(t4, t4, x3) // t4 := t4 * X3 = (Y1 + Z1)(Y2 + Z2)
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gfpAdd(x3, t1, t2) // X3 := t1 + t2
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gfpSub(t4, t4, x3) // t4 := t4 - X3 = Y1Z2 + Y2Z1
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gfpAdd(x3, &p1.x, &p1.z) // X3 := X1 + Z1
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gfpAdd(y3, &p2.x, &p2.z) // Y3 := X2 + Z2
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gfpMul(x3, x3, y3) // X3 := X3 * Y3
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gfpAdd(y3, t0, t2) // Y3 := t0 + t2
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gfpSub(y3, x3, y3) // Y3 := X3 - Y3 = X1Z2 + X2Z1
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gfpTriple(t0, t0) // t0 := t0 + t0 + t0 = 3X1X2
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gfpMul(t2, threeCurveB, t2) // t2 := 3b * t2 = 3bZ1Z2
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gfpAdd(z3, t1, t2) // Z3 := t1 + t2 = Y1Y2 + 3bZ1Z2
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gfpSub(t1, t1, t2) // t1 := t1 - t2 = Y1Y2 - 3bZ1Z2
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gfpMul(y3, threeCurveB, y3) // Y3 = 3b * Y3 = 3b(X1Z2 + X2Z1)
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gfpMul(x3, t4, y3) // X3 := t4 * Y3 = 3b(X1Z2 + X2Z1)(Y1Z2 + Y2Z1)
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gfpMul(t2, t3, t1) // t2 := t3 * t1 = (X1Y2 + X2Y1)(Y1Y2 - 3bZ1Z2)
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gfpSub(x3, t2, x3) // X3 := t2 - X3 = (X1Y2 + X2Y1)(Y1Y2 - 3bZ1Z2) - 3b(Y1Z2 + Y2Z1)(X1Z2 + X2Z1)
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gfpMul(y3, y3, t0) // Y3 := Y3 * t0 = 9bX1X2(X1Z2 + X2Z1)
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gfpMul(t1, t1, z3) // t1 := t1 * Z3 = (Y1Y2 + 3bZ1Z2)(Y1Y2 - 3bZ1Z2)
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gfpAdd(y3, t1, y3) // Y3 := t1 + Y3 = (Y1Y2 + 3bZ1Z2)(Y1Y2 - 3bZ1Z2) + 9bX1X2(X1Z2 + X2Z1)
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gfpMul(t0, t0, t3) // t0 := t0 * t3 = 3X1X2(X1Y2 + X2Y1)
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gfpMul(z3, z3, t4) // Z3 := Z3 * t4 = (Y1Z2 + Y2Z1)(Y1Y2 + 3bZ1Z2)
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gfpAdd(z3, z3, t0) // Z3 := Z3 + t0 = (Y1Z2 + Y2Z1)(Y1Y2 + 3bZ1Z2) + 3X1X2(X1Y2 + X2Y1)
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c.x.Set(x3)
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c.y.Set(y3)
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c.z.Set(z3)
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}
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func (c *curvePoint) AddComplete(p1, p2 *curvePoint) {
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c.Add(p1, p2)
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}
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func (c *curvePoint) Double(p *curvePoint) {
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// Complete addition formula for a = 0 from "Complete addition formulas for
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// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §3.2.
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// Algorithm 9: Exception-free point doubling for prime order j-invariant 0 short Weierstrass curves.
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t0, t1, t2 := new(gfP), new(gfP), new(gfP)
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x3, y3, z3 := new(gfP), new(gfP), new(gfP)
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gfpSqr(t0, &p.y, 1) // t0 := Y^2
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gfpDouble(z3, t0) // Z3 := t0 + t0
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gfpDouble(z3, z3) // Z3 := Z3 + Z3
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gfpDouble(z3, z3) // Z3 := Z3 + Z3
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gfpMul(t1, &p.y, &p.z) // t1 := YZ
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gfpSqr(t2, &p.z, 1) // t0 := Z^2
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gfpMul(t2, threeCurveB, t2) // t2 := 3b * t2 = 3bZ^2
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gfpMul(x3, t2, z3) // X3 := t2 * Z3
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gfpAdd(y3, t0, t2) // Y3 := t0 + t2
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gfpMul(z3, t1, z3) // Z3 := t1 * Z3
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gfpTriple(t2, t2) // t2 := t2 + t2 + t2
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gfpSub(t0, t0, t2) // t0 := t0 - t2
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gfpMul(y3, t0, y3) // t0 := t0 * Y3
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gfpAdd(y3, x3, y3) // Y3 := X3 + Y3
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gfpMul(t1, &p.x, &p.y) // t1 := XY
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gfpMul(x3, t0, t1) // X3 := t0 * t1
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gfpDouble(x3, x3) // X3 := X3 + X3
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c.x.Set(x3)
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c.y.Set(y3)
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c.z.Set(z3)
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}
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func (c *curvePoint) DoubleComplete(p *curvePoint) {
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c.Double(p)
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}
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// MakeAffine reverses the Projective transform.
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// A = 1/Z1
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// X3 = A*X1
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// Y3 = A*Y1
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// Z3 = 1
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func (c *curvePoint) MakeAffine() {
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// TODO: do we need to change it to constant-time implementation?
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if c.z.Equal(one) == 1 {
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return
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} else if c.z.Equal(zero) == 1 {
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c.x.Set(zero)
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c.y.Set(one)
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c.t.Set(zero)
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return
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}
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zInv := &gfP{}
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zInv.Invert(&c.z)
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gfpMul(&c.x, &c.x, zInv)
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gfpMul(&c.y, &c.y, zInv)
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c.z.Set(one)
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c.t.Set(one)
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}
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func (c *curvePoint) AffineFromProjective() {
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c.MakeAffine()
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}
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