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Merge fa3cc24302 into 9feec51e2d

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Péter Szilágyi 2017-09-25 08:10:52 +00:00 committed by GitHub
commit 700347ea4e
3 changed files with 156 additions and 106 deletions
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98
core/vm/contracts_test.go
View file

@ -110,61 +110,75 @@ var bn256AddTests = []precompiledTest{
expected: "2bd3e6d0f3b142924f5ca7b49ce5b9d54c4703d7ae5648e61d02268b1a0a9fb721611ce0a6af85915e2f1d70300909ce2e49dfad4a4619c8390cae66cefdb204", expected: "2bd3e6d0f3b142924f5ca7b49ce5b9d54c4703d7ae5648e61d02268b1a0a9fb721611ce0a6af85915e2f1d70300909ce2e49dfad4a4619c8390cae66cefdb204",
name: "chfast2", name: "chfast2",
}, { }, {
input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio1", name: "cdetrio1",
noBenchmark: true,
}, { }, {
input: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio2", name: "cdetrio2",
noBenchmark: true,
}, { }, {
input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio3", name: "cdetrio3",
noBenchmark: true,
}, { }, {
input: "", input: "",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio4", name: "cdetrio4",
noBenchmark: true,
}, { }, {
input: "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio5", name: "cdetrio5",
noBenchmark: true,
}, { }, {
input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", input: "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
name: "cdetrio6", name: "cdetrio6",
noBenchmark: true,
}, { }, {
input: "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
name: "cdetrio7", name: "cdetrio7",
noBenchmark: true,
}, { }, {
input: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", input: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
name: "cdetrio8", name: "cdetrio8",
noBenchmark: true,
}, { }, {
input: "0000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "0000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
name: "cdetrio9", name: "cdetrio9",
noBenchmark: true,
}, { }, {
input: "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", expected: "00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
name: "cdetrio10", name: "cdetrio10",
noBenchmark: true,
}, { }, {
input: "0000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002", input: "0000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
expected: "030644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd315ed738c0e0a7c92e7845f96b2ae9c0a68a6a449e3538fc7ff3ebf7a5a18a2c4", expected: "030644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd315ed738c0e0a7c92e7845f96b2ae9c0a68a6a449e3538fc7ff3ebf7a5a18a2c4",
name: "cdetrio11", name: "cdetrio11",
noBenchmark: true,
}, { }, {
input: "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000020000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000020000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "030644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd315ed738c0e0a7c92e7845f96b2ae9c0a68a6a449e3538fc7ff3ebf7a5a18a2c4", expected: "030644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd315ed738c0e0a7c92e7845f96b2ae9c0a68a6a449e3538fc7ff3ebf7a5a18a2c4",
name: "cdetrio12", name: "cdetrio12",
noBenchmark: true,
}, { }, {
input: "17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa901e0559bacb160664764a357af8a9fe70baa9258e0b959273ffc5718c6d4cc7c039730ea8dff1254c0fee9c0ea777d29a9c710b7e616683f194f18c43b43b869073a5ffcc6fc7a28c30723d6e58ce577356982d65b833a5a5c15bf9024b43d98", input: "17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa901e0559bacb160664764a357af8a9fe70baa9258e0b959273ffc5718c6d4cc7c039730ea8dff1254c0fee9c0ea777d29a9c710b7e616683f194f18c43b43b869073a5ffcc6fc7a28c30723d6e58ce577356982d65b833a5a5c15bf9024b43d98",
expected: "15bf2bb17880144b5d1cd2b1f46eff9d617bffd1ca57c37fb5a49bd84e53cf66049c797f9ce0d17083deb32b5e36f2ea2a212ee036598dd7624c168993d1355f", expected: "15bf2bb17880144b5d1cd2b1f46eff9d617bffd1ca57c37fb5a49bd84e53cf66049c797f9ce0d17083deb32b5e36f2ea2a212ee036598dd7624c168993d1355f",
name: "cdetrio13", name: "cdetrio13",
noBenchmark: true,
}, { }, {
input: "17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa901e0559bacb160664764a357af8a9fe70baa9258e0b959273ffc5718c6d4cc7c17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa92e83f8d734803fc370eba25ed1f6b8768bd6d83887b87165fc2434fe11a830cb00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", input: "17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa901e0559bacb160664764a357af8a9fe70baa9258e0b959273ffc5718c6d4cc7c17c139df0efee0f766bc0204762b774362e4ded88953a39ce849a8a7fa163fa92e83f8d734803fc370eba25ed1f6b8768bd6d83887b87165fc2434fe11a830cb00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", expected: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
name: "cdetrio14", name: "cdetrio14",
noBenchmark: true,
}, },
} }

147
crypto/bn256/curve.go
View file

@ -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] // Normalize the points by replacing a = [x1:y1:z1] and b = [x2:y2:z2]
// by [u1:s1:z1·z2] and [u2:s2:z1·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 // where u1 = x1·z2², s1 = y1·z2³ and u1 = x2·z1², s2 = y2·z1³
z1z1 := pool.Get().Mul(a.z, a.z) tmp := pool.Get()
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) z1z1 := pool.Get()
t.Mod(t, P) tmp.Mul(a.z, a.z)
s1 := pool.Get().Mul(a.y, t) z1z1.Mod(tmp, P)
s1.Mod(s1, P)
t.Mul(a.z, z1z1) z2z2 := pool.Get()
t.Mod(t, P) tmp.Mul(b.z, b.z)
s2 := pool.Get().Mul(b.y, t) z2z2.Mod(tmp, P)
s2.Mod(s2, 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) // Compute x = (2h)²(s²-u1-u2)
// where s = (s2-s1)/(u2-u1) is the slope of the line through // 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) t.Add(h, h)
// i = 4h² // i = 4h²
i := pool.Get().Mul(t, t) i := pool.Get()
i.Mod(i, P) tmp.Mul(t, t)
i.Mod(tmp, P)
// j = 4h³ // j = 4h³
j := pool.Get().Mul(h, i) j := pool.Get()
j.Mod(j, P) tmp.Mul(h, i)
j.Mod(tmp, P)
t.Sub(s2, s1) t.Sub(s2, s1)
yEqual := t.Sign() == 0 yEqual := t.Sign() == 0
@ -134,12 +150,15 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) {
} }
r := pool.Get().Add(t, t) r := pool.Get().Add(t, t)
v := pool.Get().Mul(u1, i) v := pool.Get()
v.Mod(v, P) tmp.Mul(u1, i)
v.Mod(tmp, P)
// t4 = 4(s2-s1)² // t4 = 4(s2-s1)²
t4 := pool.Get().Mul(r, r) t4 := pool.Get()
t4.Mod(t4, P) tmp.Mul(r, r)
t4.Mod(tmp, P)
t.Add(v, v) t.Add(v, v)
t6 := pool.Get().Sub(t4, j) t6 := pool.Get().Sub(t4, j)
c.x.Sub(t6, t) 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)) // Set y = -(2h)³(s1 + s*(x/4h²-u1))
// This is also // This is also
// y = - 2·s1·j - (s2-s1)(2x - 2i·u1) = r(v-x) - 2·s1·j // y = - 2·s1·j - (s2-s1)(2x - 2i·u1) = r(v-x) - 2·s1·j
t.Sub(v, c.x) // t7 t.Sub(v, c.x) // t7
t4.Mul(s1, j) // t8 tmp.Mul(s1, j) // t8
t4.Mod(t4, P) t4.Mod(tmp, P)
t6.Add(t4, t4) // t9 t6.Add(t4, t4) // t9
t4.Mul(r, t) // t10 tmp.Mul(r, t) // t10
t4.Mod(t4, P) t4.Mod(tmp, P)
c.y.Sub(t4, t6) c.y.Sub(t4, t6)
// Set z = 2(u2-u1)·z1·z2 = 2h·z1·z2 // Set z = 2(u2-u1)·z1·z2 = 2h·z1·z2
t.Add(a.z, b.z) // t11 t.Add(a.z, b.z) // t11
t4.Mul(t, t) // t12 tmp.Mul(t, t) // t12
t4.Mod(t4, P) t4.Mod(tmp, P)
t.Sub(t4, z1z1) // t13 t.Sub(t4, z1z1) // t13
t4.Sub(t, z2z2) // t14 t4.Sub(t, z2z2) // t14
c.z.Mul(t4, h) tmp.Mul(t4, h)
c.z.Mod(c.z, P) c.z.Mod(tmp, P)
pool.Put(z1z1) pool.Put(z1z1)
pool.Put(z2z2) pool.Put(z2z2)
@ -178,27 +197,37 @@ func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) {
pool.Put(v) pool.Put(v)
pool.Put(t4) pool.Put(t4)
pool.Put(t6) pool.Put(t6)
pool.Put(tmp)
} }
func (c *curvePoint) Double(a *curvePoint, pool *bnPool) { func (c *curvePoint) Double(a *curvePoint, pool *bnPool) {
// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3 // See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
A := pool.Get().Mul(a.x, a.x) tmp := pool.Get()
A.Mod(A, P)
B := pool.Get().Mul(a.y, a.y) A := pool.Get()
B.Mod(B, P) tmp.Mul(a.x, a.x)
C_ := pool.Get().Mul(B, B) A.Mod(tmp, P)
C_.Mod(C_, 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) t := pool.Get().Add(a.x, B)
t2 := pool.Get().Mul(t, t) t2 := pool.Get()
t2.Mod(t2, P) tmp.Mul(t, t)
t2.Mod(tmp, P)
t.Sub(t2, A) t.Sub(t2, A)
t2.Sub(t, C_) t2.Sub(t, C_)
d := pool.Get().Add(t2, t2) d := pool.Get().Add(t2, t2)
t.Add(A, A) t.Add(A, A)
e := pool.Get().Add(t, A) e := pool.Get().Add(t, A)
f := pool.Get().Mul(e, e) f := pool.Get()
f.Mod(f, P) tmp.Mul(e, e)
f.Mod(tmp, P)
t.Add(d, d) t.Add(d, d)
c.x.Sub(f, t) c.x.Sub(f, t)
@ -207,12 +236,12 @@ func (c *curvePoint) Double(a *curvePoint, pool *bnPool) {
t2.Add(t, t) t2.Add(t, t)
t.Add(t2, t2) t.Add(t2, t2)
c.y.Sub(d, c.x) c.y.Sub(d, c.x)
t2.Mul(e, c.y) tmp.Mul(e, c.y)
t2.Mod(t2, P) t2.Mod(tmp, P)
c.y.Sub(t2, t) c.y.Sub(t2, t)
t.Mul(a.y, a.z) tmp.Mul(a.y, a.z)
t.Mod(t, P) t.Mod(tmp, P)
c.z.Add(t, t) c.z.Add(t, t)
pool.Put(A) pool.Put(A)
@ -223,6 +252,7 @@ func (c *curvePoint) Double(a *curvePoint, pool *bnPool) {
pool.Put(d) pool.Put(d)
pool.Put(e) pool.Put(e)
pool.Put(f) pool.Put(f)
pool.Put(tmp)
} }
func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int, pool *bnPool) *curvePoint { 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 { if words := c.z.Bits(); len(words) == 1 && words[0] == 1 {
return c return c
} }
tmp := pool.Get()
zInv := pool.Get().ModInverse(c.z, P) zInv := pool.Get().ModInverse(c.z, P)
t := pool.Get().Mul(c.y, zInv)
t.Mod(t, P) t := pool.Get()
zInv2 := pool.Get().Mul(zInv, zInv) tmp.Mul(c.y, zInv)
zInv2.Mod(zInv2, P) t.Mod(tmp, P)
c.y.Mul(t, zInv2)
c.y.Mod(c.y, 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.Mul(c.x, zInv2)
t.Mod(t, P) c.x.Mod(t, P)
c.x.Set(t)
c.z.SetInt64(1) c.z.SetInt64(1)
c.t.SetInt64(1) c.t.SetInt64(1)
pool.Put(zInv) pool.Put(zInv)
pool.Put(t) pool.Put(t)
pool.Put(zInv2) pool.Put(zInv2)
pool.Put(tmp)
return c return c
} }

17
crypto/bn256/gfp2.go
View file

@ -130,13 +130,13 @@ func (e *gfP2) Mul(a, b *gfP2, pool *bnPool) *gfP2 {
tx := pool.Get().Mul(a.x, b.y) tx := pool.Get().Mul(a.x, b.y)
t := pool.Get().Mul(b.x, a.y) t := pool.Get().Mul(b.x, a.y)
tx.Add(tx, t) 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) ty := pool.Get().Mul(a.y, b.y)
t.Mul(a.x, b.x)
ty.Sub(ty, t) ty.Sub(ty, t)
e.y.Mod(ty, P) e.y.Mod(ty, P)
e.x.Set(tx)
pool.Put(tx) pool.Put(tx)
pool.Put(ty) pool.Put(ty)
@ -177,13 +177,12 @@ func (e *gfP2) Square(a *gfP2, pool *bnPool) *gfP2 {
t1 := pool.Get().Sub(a.y, a.x) t1 := pool.Get().Sub(a.y, a.x)
t2 := pool.Get().Add(a.x, a.y) t2 := pool.Get().Add(a.x, a.y)
ty := pool.Get().Mul(t1, t2) ty := pool.Get().Mul(t1, t2)
ty.Mod(ty, P)
t1.Mul(a.x, a.y) t1.Mul(a.x, a.y)
t1.Lsh(t1, 1) t1.Lsh(t1, 1)
e.x.Mod(t1, P) e.x.Mod(t1, P)
e.y.Set(ty) e.y.Mod(ty, P)
pool.Put(t1) pool.Put(t1)
pool.Put(t2) pool.Put(t2)
@ -205,11 +204,11 @@ func (e *gfP2) Invert(a *gfP2, pool *bnPool) *gfP2 {
inv.ModInverse(t, P) inv.ModInverse(t, P)
e.x.Neg(a.x) e.x.Neg(a.x)
e.x.Mul(e.x, inv) t.Mul(e.x, inv)
e.x.Mod(e.x, P) e.x.Mod(t, P)
e.y.Mul(a.y, inv) t.Mul(a.y, inv)
e.y.Mod(e.y, P) e.y.Mod(t, P)
pool.Put(t) pool.Put(t)
pool.Put(t2) pool.Put(t2)