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sm9/bn256: rename special square function name

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Sun Yimin 2023-07-18 17:29:10 +08:00 committed by GitHub
parent 929e1b892b
commit b9bbf94b47
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9 changed files with 86 additions and 58 deletions
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13
sm9/bn256/bn_pair.go
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@ -218,10 +218,9 @@ func finalExponentiation(in *gfP12) *gfP12 {
y0.MulNC(fp, fp2).Mul(y0, fp3) // y0 = (t1^p) * (t1^(p^2)) * (t1^(p^3))
// reuse fp, fp2, fp3 local variables
// [gfP12ExpU] is most time consuming operation
fu := fp.gfP12ExpU(t1)
fu2 := fp2.gfP12ExpU(fu)
fu3 := fp3.gfP12ExpU(fu2)
fu := fp.Cyclo6PowToU(t1)
fu2 := fp2.Cyclo6PowToU(fu)
fu3 := fp3.Cyclo6PowToU(fu2)
fu2p := (&gfP12{}).Frobenius(fu2)
fu3p := (&gfP12{}).Frobenius(fu3)
@ -237,14 +236,14 @@ func finalExponentiation(in *gfP12) *gfP12 {
y6.Conjugate(y6) // y6 = 1 / (t1^(u^3) * (t1^(u^3))^p)
// https://eprint.iacr.org/2008/490.pdf
t0 := (&gfP12{}).SpecialSquareNC(y6)
t0 := (&gfP12{}).Cyclo6SquareNC(y6)
t0.Mul(t0, y4).Mul(t0, y5)
t1.Mul(y3, y5).Mul(t1, t0)
t0.Mul(t0, y2)
t1.SpecialSquare(t1).Mul(t1, t0).SpecialSquare(t1)
t1.Cyclo6Square(t1).Mul(t1, t0).Cyclo6Square(t1)
t0.Mul(t1, y1)
t1.Mul(t1, y0)
t0.SpecialSquare(t0).Mul(t0, t1)
t0.Cyclo6Square(t0).Mul(t0, t1)
return t0
}

13
sm9/bn256/bn_pair_b6.go
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@ -155,10 +155,9 @@ func finalExponentiationB6(in *gfP12b6) *gfP12b6 {
y0.MulNC(fp, fp2).Mul(y0, fp3)
// reuse fp, fp2, fp3 local variables
// [gfP12ExpU] is most time consuming operation
fu := fp.gfP12ExpU(t1)
fu2 := fp2.gfP12ExpU(fu)
fu3 := fp3.gfP12ExpU(fu2)
fu := fp.Cyclo6PowToU(t1)
fu2 := fp2.Cyclo6PowToU(fu)
fu3 := fp3.Cyclo6PowToU(fu2)
y3 := (&gfP12b6{}).Frobenius(fu)
fu2p := (&gfP12b6{}).Frobenius(fu2)
@ -174,14 +173,14 @@ func finalExponentiationB6(in *gfP12b6) *gfP12b6 {
y6 := (&gfP12b6{}).MulNC(fu3, fu3p)
y6.Conjugate(y6)
t0 := (&gfP12b6{}).SpecialSquareNC(y6)
t0 := (&gfP12b6{}).Cyclo6SquareNC(y6)
t0.Mul(t0, y4).Mul(t0, y5)
t1.Mul(y3, y5).Mul(t1, t0)
t0.Mul(t0, y2)
t1.SpecialSquare(t1).Mul(t1, t0).SpecialSquare(t1)
t1.Cyclo6Square(t1).Mul(t1, t0).Cyclo6Square(t1)
t0.Mul(t1, y1)
t1.Mul(t1, y0)
t0.SpecialSquare(t0).Mul(t0, t1)
t0.Cyclo6Square(t0).Mul(t0, t1)
return t0
}

2
sm9/bn256/curve.go
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@ -182,7 +182,7 @@ func (c *curvePoint) Double(a *curvePoint) {
gfpSub(t2, t, C)
d, e, f := &gfP{}, &gfP{}, &gfP{}
gfpAdd(d, t2, t2)
gfpDouble(d, t2)
gfpDouble(t, A)
gfpAdd(e, t, A)
gfpSqr(f, e, 1)

20
sm9/bn256/gfp12.go
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@ -226,13 +226,19 @@ func (e *gfP12) SquareNC(a *gfP12) *gfP12 {
return e
}
// Special squaring for use on elements in T_6(fp2) (after the
// easy part of the final exponentiation. Used in the hard part
// of the final exponentiation. Function uses formulas in
// Cyclo6Square is used in final exponentiation after easy part(a ^ ((p^2 + 1)(p^6-1))).
// Note that after the easy part of the final exponentiation,
// the resulting element lies in cyclotomic subgroup.
// "New software speed records for cryptographic pairings"
// Section 3.3, Final exponentiation
// https://cryptojedi.org/papers/dclxvi-20100714.pdf
// The fomula reference:
// Granger/Scott (PKC2010).
func (e *gfP12) SpecialSquare(a *gfP12) *gfP12 {
// Section 3.2
// https://eprint.iacr.org/2009/565.pdf
func (e *gfP12) Cyclo6Square(a *gfP12) *gfP12 {
tmp := &gfP12{}
tmp.SpecialSquareNC(a)
tmp.Cyclo6SquareNC(a)
gfp12Copy(e, tmp)
return e
}
@ -241,7 +247,7 @@ func (e *gfP12) SpecialSquare(a *gfP12) *gfP12 {
// easy part of the final exponentiation. Used in the hard part
// of the final exponentiation. Function uses formulas in
// Granger/Scott (PKC2010).
func (e *gfP12) SpecialSquares(a *gfP12, n int) *gfP12 {
func (e *gfP12) Cyclo6Squares(a *gfP12, n int) *gfP12 {
// Square first round
in := &gfP12{}
tx, ty, tz := &gfP4{}, &gfP4{}, &gfP4{}
@ -306,7 +312,7 @@ func (e *gfP12) SpecialSquares(a *gfP12, n int) *gfP12 {
}
// Special Square without value copy, will use e directly, so e can't be same as a.
func (e *gfP12) SpecialSquareNC(a *gfP12) *gfP12 {
func (e *gfP12) Cyclo6SquareNC(a *gfP12) *gfP12 {
tx, ty, tz := &gfP4{}, &gfP4{}, &gfP4{}
v0 := &e.x

20
sm9/bn256/gfp12_b6.go
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@ -201,20 +201,26 @@ func (e *gfP12b6) SquareNC(a *gfP12b6) *gfP12b6 {
return e
}
// Special squaring for use on elements in T_6(fp2) (after the
// easy part of the final exponentiation. Used in the hard part
// of the final exponentiation. Function uses formulas in
// Cyclo6Square is used in final exponentiation after easy part(a ^ ((p^2 + 1)(p^6-1))).
// Note that after the easy part of the final exponentiation,
// the resulting element lies in cyclotomic subgroup.
// "New software speed records for cryptographic pairings"
// Section 3.3, Final exponentiation
// https://cryptojedi.org/papers/dclxvi-20100714.pdf
// The fomula reference:
// Granger/Scott (PKC2010).
func (e *gfP12b6) SpecialSquare(a *gfP12b6) *gfP12b6 {
// Section 3.2
// https://eprint.iacr.org/2009/565.pdf
func (e *gfP12b6) Cyclo6Square(a *gfP12b6) *gfP12b6 {
tmp := &gfP12b6{}
tmp.SpecialSquareNC(a)
tmp.Cyclo6SquareNC(a)
e.x.Set(&tmp.x)
e.y.Set(&tmp.y)
return e
}
// Special Square without value copy, will use e directly, so e can't be same as a.
func (e *gfP12b6) SpecialSquareNC(a *gfP12b6) *gfP12b6 {
func (e *gfP12b6) Cyclo6SquareNC(a *gfP12b6) *gfP12b6 {
f02 := &e.y.x
f01 := &e.y.y
f00 := &e.y.z
@ -265,7 +271,7 @@ func (e *gfP12b6) SpecialSquareNC(a *gfP12b6) *gfP12b6 {
return e
}
func (e *gfP12b6) SpecialSquares(a *gfP12b6, n int) *gfP12b6 {
func (e *gfP12b6) Cyclo6Squares(a *gfP12b6, n int) *gfP12b6 {
// Square first round
in := &gfP12b6{}
f02 := &in.y.x

2
sm9/bn256/gfp12_b6_test.go
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@ -330,7 +330,7 @@ func TestGfP12b6SpecialSquare(t *testing.T) {
got := &gfP12b6{}
expected := &gfP12b6{}
got.SpecialSquare(t1)
got.Cyclo6Square(t1)
expected.Square(t1)
if *got != *expected {
t.Errorf("not same got=%v, expected=%v", got, expected)

18
sm9/bn256/gfp12_exp_u.go
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@ -1,7 +1,7 @@
package bn256
// Use special square
func (e *gfP12) gfP12ExpU(x *gfP12) *gfP12 {
func (e *gfP12) Cyclo6PowToU(x *gfP12) *gfP12 {
// The sequence of 10 multiplications and 61 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
@ -21,23 +21,23 @@ func (e *gfP12) gfP12ExpU(x *gfP12) *gfP12 {
var t2 = new(gfP12)
var t3 = new(gfP12)
t2.SpecialSquareNC(x)
t1.SpecialSquareNC(t2)
t2.Cyclo6SquareNC(x)
t1.Cyclo6SquareNC(t2)
z.MulNC(x, t1)
t0.MulNC(t1, z)
t2.Mul(t2, t0)
t3.MulNC(x, t2)
t3.SpecialSquares(t3, 40)
t3.Cyclo6Squares(t3, 40)
t3.Mul(t2, t3)
t3.SpecialSquares(t3, 7)
t3.Cyclo6Squares(t3, 7)
t2.Mul(t2, t3)
t1.Mul(t1, t2)
t1.SpecialSquares(t1, 4)
t1.Cyclo6Squares(t1, 4)
t0.Mul(t0, t1)
t0.SpecialSquare(t0)
t0.Cyclo6Square(t0)
t0.Mul(x, t0)
t0.SpecialSquares(t0, 6)
t0.Cyclo6Squares(t0, 6)
z.Mul(z, t0)
z.SpecialSquare(z)
z.Cyclo6Square(z)
return e
}

34
sm9/bn256/gfp12_test.go
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@ -35,7 +35,7 @@ func Test_gfP12Square(t *testing.T) {
}
}
func TestSpecialSquare(t *testing.T) {
func TestCyclo6Square(t *testing.T) {
in := &gfP12{
testdataP4,
testdataP4,
@ -51,9 +51,18 @@ func TestSpecialSquare(t *testing.T) {
t2 := inv.FrobeniusP2(t1) // reuse inv
t1.Mul(t1, t2) // t1 = in ^ ((p^6 - 1) * (p^2 + 1)), the first two parts of the exponentiation
one := (&gfP12{}).SetOne()
t3 := (&gfP12{}).FrobeniusP2(t1)
t4 := (&gfP12{}).FrobeniusP2(t3)
t5 := (&gfP12{}).Invert(t3)
t5.Mul(t4, t5).Mul(t1, t5)
if *t5 != *one {
t.Errorf("t1 should be in Cyclotomic Subgroup")
}
got := &gfP12{}
expected := &gfP12{}
got.SpecialSquare(t1)
got.Cyclo6Square(t1)
expected.Square(t1)
if *got != *expected {
t.Errorf("not same got=%v, expected=%v", got, expected)
@ -74,7 +83,7 @@ func BenchmarkGfP12Square(b *testing.B) {
}
}
func BenchmarkGfP12SpecialSquare(b *testing.B) {
func BenchmarkGfP12Cyclo6Square(b *testing.B) {
in := &gfP12{
testdataP4,
testdataP4,
@ -93,7 +102,7 @@ func BenchmarkGfP12SpecialSquare(b *testing.B) {
b.ReportAllocs()
b.ResetTimer()
for i := 0; i < b.N; i++ {
x2.SpecialSquare(t1)
x2.Cyclo6Square(t1)
}
}
@ -116,7 +125,7 @@ func BenchmarkGfP12SpecialSqures(b *testing.B) {
b.ReportAllocs()
b.ResetTimer()
for i := 0; i < b.N; i++ {
got.SpecialSquares(in, 61)
got.Cyclo6Squares(in, 61)
}
}
@ -433,13 +442,22 @@ func BenchmarkGfP12ExpU(b *testing.B) {
testdataP4,
testdataP4,
}
// This is the p^6-Frobenius
t1 := (&gfP12{}).FrobeniusP6(x)
inv := (&gfP12{}).Invert(x)
t1.Mul(t1, inv)
t2 := inv.FrobeniusP2(t1) // reuse inv
t1.Mul(t1, t2) // t1 = in ^ ((p^6 - 1) * (p^2 + 1)), the first two parts of the exponentiation
got := &gfP12{}
b.ReportAllocs()
b.ResetTimer()
for i := 0; i < b.N; i++ {
got.gfP12ExpU(x)
got.gfP12ExpU(x)
got.gfP12ExpU(x)
got.Cyclo6PowToU(t1)
got.Cyclo6PowToU(t1)
got.Cyclo6PowToU(t1)
}
}

18
sm9/bn256/gfp12b6_exp_u.go
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@ -1,7 +1,7 @@
package bn256
// Use special square
func (e *gfP12b6) gfP12ExpU(x *gfP12b6) *gfP12b6 {
func (e *gfP12b6) Cyclo6PowToU(x *gfP12b6) *gfP12b6 {
// The sequence of 10 multiplications and 61 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
@ -21,23 +21,23 @@ func (e *gfP12b6) gfP12ExpU(x *gfP12b6) *gfP12b6 {
var t2 = new(gfP12b6)
var t3 = new(gfP12b6)
t2.SpecialSquareNC(x)
t1.SpecialSquareNC(t2)
t2.Cyclo6SquareNC(x)
t1.Cyclo6SquareNC(t2)
z.MulNC(x, t1)
t0.MulNC(t1, z)
t2.Mul(t2, t0)
t3.MulNC(x, t2)
t3.SpecialSquares(t3, 40)
t3.Cyclo6Squares(t3, 40)
t3.Mul(t2, t3)
t3.SpecialSquares(t3, 7)
t3.Cyclo6Squares(t3, 7)
t2.Mul(t2, t3)
t1.Mul(t1, t2)
t1.SpecialSquares(t1, 4)
t1.Cyclo6Squares(t1, 4)
t0.Mul(t0, t1)
t0.SpecialSquare(t0)
t0.Cyclo6Square(t0)
t0.Mul(x, t0)
t0.SpecialSquares(t0, 6)
t0.Cyclo6Squares(t0, 6)
z.Mul(z, t0)
z.SpecialSquare(z)
z.Cyclo6Square(z)
return e
}