diff --git a/crypto/bn256/curve.go b/crypto/bn256/curve.go index 233b1f2521..f15b7dac91 100644 --- a/crypto/bn256/curve.go +++ b/crypto/bn256/curve.go @@ -89,24 +89,38 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { // 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) + tmp := pool.Get() - t := pool.Get().Mul(b.z, z2z2) - t.Mod(t, P) - s1 := pool.Get().Mul(a.y, t) - s1.Mod(s1, P) + z1z1 := pool.Get() + tmp.Mul(a.z, a.z) + z1z1.Mod(tmp, P) - t.Mul(a.z, z1z1) - t.Mod(t, P) - s2 := pool.Get().Mul(b.y, t) - s2.Mod(s2, P) + z2z2 := pool.Get() + tmp.Mul(b.z, b.z) + z2z2.Mod(tmp, P) + + u1 := pool.Get() + tmp.Mul(a.x, z2z2) + u1.Mod(tmp, P) + + u2 := pool.Get() + tmp.Mul(b.x, z1z1) + u2.Mod(tmp, P) + + t := pool.Get() + tmp.Mul(b.z, z2z2) + t.Mod(tmp, P) + + s1 := pool.Get() + tmp.Mul(a.y, t) + s1.Mod(tmp, P) + + tmp.Mul(a.z, z1z1) + t.Mod(tmp, P) + + s2 := pool.Get() + tmp.Mul(b.y, t) + s2.Mod(tmp, P) // Compute x = (2h)²(s²-u1-u2) // where s = (s2-s1)/(u2-u1) is the slope of the line through @@ -120,11 +134,13 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { t.Add(h, h) // i = 4h² - i := pool.Get().Mul(t, t) - i.Mod(i, P) + i := pool.Get() + tmp.Mul(t, t) + i.Mod(tmp, P) // j = 4h³ - j := pool.Get().Mul(h, i) - j.Mod(j, P) + j := pool.Get() + tmp.Mul(h, i) + j.Mod(tmp, P) t.Sub(s2, s1) yEqual := t.Sign() == 0 @@ -134,12 +150,15 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { } r := pool.Get().Add(t, t) - v := pool.Get().Mul(u1, i) - v.Mod(v, P) + v := pool.Get() + tmp.Mul(u1, i) + v.Mod(tmp, P) // t4 = 4(s2-s1)² - t4 := pool.Get().Mul(r, r) - t4.Mod(t4, P) + t4 := pool.Get() + tmp.Mul(r, r) + t4.Mod(tmp, P) + t.Add(v, v) t6 := pool.Get().Sub(t4, j) c.x.Sub(t6, t) @@ -147,22 +166,22 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { // 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) + t.Sub(v, c.x) // t7 + tmp.Mul(s1, j) // t8 + t4.Mod(tmp, P) t6.Add(t4, t4) // t9 - t4.Mul(r, t) // t10 - t4.Mod(t4, P) + tmp.Mul(r, t) // t10 + t4.Mod(tmp, 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) + tmp.Mul(t, t) // t12 + t4.Mod(tmp, P) t.Sub(t4, z1z1) // t13 t4.Sub(t, z2z2) // t14 - c.z.Mul(t4, h) - c.z.Mod(c.z, P) + tmp.Mul(t4, h) + c.z.Mod(tmp, P) pool.Put(z1z1) pool.Put(z2z2) @@ -178,27 +197,37 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { pool.Put(v) pool.Put(t4) pool.Put(t6) + pool.Put(tmp) } 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) + tmp := pool.Get() + + A := pool.Get() + tmp.Mul(a.x, a.x) + A.Mod(tmp, P) + + B := pool.Get() + tmp.Mul(a.y, a.y) + B.Mod(tmp, P) + + C_ := pool.Get() + tmp.Mul(B, B) + C_.Mod(tmp, P) t := pool.Get().Add(a.x, B) - t2 := pool.Get().Mul(t, t) - t2.Mod(t2, P) + t2 := pool.Get() + tmp.Mul(t, t) + t2.Mod(tmp, 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) + f := pool.Get() + tmp.Mul(e, e) + f.Mod(tmp, P) t.Add(d, d) c.x.Sub(f, t) @@ -207,12 +236,12 @@ func (c *curvePoint) Double(a *curvePoint, pool *bnPool) { t2.Add(t, t) t.Add(t2, t2) c.y.Sub(d, c.x) - t2.Mul(e, c.y) - t2.Mod(t2, P) + tmp.Mul(e, c.y) + t2.Mod(tmp, P) c.y.Sub(t2, t) - t.Mul(a.y, a.z) - t.Mod(t, P) + tmp.Mul(a.y, a.z) + t.Mod(tmp, P) c.z.Add(t, t) pool.Put(A) @@ -223,6 +252,7 @@ func (c *curvePoint) Double(a *curvePoint, pool *bnPool) { pool.Put(d) pool.Put(e) pool.Put(f) + pool.Put(tmp) } func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int, pool *bnPool) *curvePoint { @@ -249,23 +279,30 @@ func (c *curvePoint) MakeAffine(pool *bnPool) *curvePoint { if words := c.z.Bits(); len(words) == 1 && words[0] == 1 { return c } + tmp := pool.Get() 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 := pool.Get() + tmp.Mul(c.y, zInv) + t.Mod(tmp, P) + + zInv2 := pool.Get() + tmp.Mul(zInv, zInv) + zInv2.Mod(tmp, P) + + tmp.Mul(t, zInv2) + c.y.Mod(tmp, P) + t.Mul(c.x, zInv2) - t.Mod(t, P) - c.x.Set(t) + c.x.Mod(t, P) c.z.SetInt64(1) c.t.SetInt64(1) pool.Put(zInv) pool.Put(t) pool.Put(zInv2) + pool.Put(tmp) return c } diff --git a/crypto/bn256/gfp2.go b/crypto/bn256/gfp2.go index 3981f6cb4f..efcf1a6bbe 100644 --- a/crypto/bn256/gfp2.go +++ b/crypto/bn256/gfp2.go @@ -130,13 +130,13 @@ func (e *gfP2) Mul(a, b *gfP2, pool *bnPool) *gfP2 { tx := pool.Get().Mul(a.x, b.y) t := pool.Get().Mul(b.x, a.y) tx.Add(tx, t) - tx.Mod(tx, P) + + t.Mul(a.x, b.x) + e.x.Mod(tx, P) ty := pool.Get().Mul(a.y, b.y) - t.Mul(a.x, b.x) ty.Sub(ty, t) e.y.Mod(ty, P) - e.x.Set(tx) pool.Put(tx) pool.Put(ty) @@ -177,13 +177,12 @@ func (e *gfP2) Square(a *gfP2, pool *bnPool) *gfP2 { t1 := pool.Get().Sub(a.y, a.x) t2 := pool.Get().Add(a.x, a.y) ty := pool.Get().Mul(t1, t2) - ty.Mod(ty, P) t1.Mul(a.x, a.y) t1.Lsh(t1, 1) e.x.Mod(t1, P) - e.y.Set(ty) + e.y.Mod(ty, P) pool.Put(t1) pool.Put(t2) @@ -205,11 +204,11 @@ func (e *gfP2) Invert(a *gfP2, pool *bnPool) *gfP2 { inv.ModInverse(t, P) e.x.Neg(a.x) - e.x.Mul(e.x, inv) - e.x.Mod(e.x, P) + t.Mul(e.x, inv) + e.x.Mod(t, P) - e.y.Mul(a.y, inv) - e.y.Mod(e.y, P) + t.Mul(a.y, inv) + e.y.Mod(t, P) pool.Put(t) pool.Put(t2)