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p256Inverse using addchain generated code

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Sun Yimin 2022-05-16 12:51:43 +08:00 committed by GitHub
parent 60f734b82c
commit 8fda97f991
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1 changed files with 57 additions and 54 deletions
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111
sm2/p256_asm.go
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@ -357,61 +357,64 @@ func (p *p256Point) CopyConditional(src *p256Point, v int) {
// p256Inverse sets out to in^-1 mod p.
func p256Inverse(out, in []uint64) {
var stack [8 * 4]uint64
p2 := stack[4*0 : 4*0+4]
p4 := stack[4*1 : 4*1+4]
p8 := stack[4*2 : 4*2+4]
p16 := stack[4*3 : 4*3+4]
p32 := stack[4*4 : 4*4+4]
p64 := stack[4*5 : 4*5+4]
p32m2 := stack[4*6 : 4*6+4]
ptmp := stack[4*7 : 4*7+4]
// Inversion is calculated through exponentiation by p - 2, per Fermat's
// little theorem.
//
// The sequence of 14 multiplications and 255 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain
// v0.4.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _110 = 2*_11
// _111 = 1 + _110
// _111000 = _111 << 3
// _111111 = _111 + _111000
// _1111110 = 2*_111111
// _1111111 = 1 + _1111110
// x12 = _1111110 << 5 + _111111
// x24 = x12 << 12 + x12
// x31 = x24 << 7 + _1111111
// i39 = x31 << 2
// i68 = i39 << 29
// x62 = x31 + i68
// i71 = i68 << 2
// x64 = i39 + i71 + _11
// i265 = ((i71 << 32 + x64) << 64 + x64) << 94
// return (x62 + i265) << 2 + 1
var stack [3 * 4]uint64
t0 := stack[4*0 : 4*0+4]
t1 := stack[4*1 : 4*1+4]
t2 := stack[4*2 : 4*2+4]
p256Sqr(ptmp, in, 1) // 2^1
p256Mul(p2, ptmp, in) // 2^2 - 2^0
p256Sqr(out, p2, 2) // 2^4 - 2^2
p256Mul(ptmp, out, ptmp) // 2^4 - 2^1
p256Mul(p4, out, p2) // 2^4 - 2^0
p256Sqr(out, p4, 4) // 2^8 - 2^4
p256Mul(ptmp, out, ptmp) // 2^8 - 2^1
p256Mul(p8, out, p4) // 2^8 - 2^0
p256Sqr(out, p8, 8) // 2^16 - 2^8
p256Mul(ptmp, out, ptmp) // 2^16 - 2^1
p256Mul(p16, out, p8) // 2^16 - 2^0
p256Sqr(out, p16, 16) // 2^32 - 2^16
p256Mul(p32m2, out, ptmp) // 2^32 - 2^1
p256Mul(p32, out, p16) // 2^32 - 2^0
p256Sqr(out, p32, 32) //2^64 - 2^32
p256Mul(p64, out, p32) // 2^64 - 2^0
p256Sqr(out, p64, 64) //2^128 - 2^64
p256Mul(out, out, p64) // 2^128 - 2^0
p256Sqr(ptmp, out, 96) // 2^224 - 2^96
p256Sqr(out, p32m2, 224) //2^256 - 2^225
p256Mul(ptmp, ptmp, out) //2^256 - 2^224 - 2^96
p256Sqr(out, p32, 16) // 2^48 - 2^16
p256Mul(out, out, p16) // 2^48 - 2^0
p256Sqr(out, out, 8) // 2^56 - 2^8
p256Mul(out, out, p8) // 2^56 - 2^0
p256Sqr(out, out, 4) // 2^60 - 2^4
p256Mul(out, out, p4) // 2^60 - 2^0
p256Sqr(out, out, 2) // 2^62 - 2^2
p256Mul(out, out, p2) // 2^62 - 2^0
p256Sqr(out, out, 2) // 2^64 - 2^2
p256Mul(out, out, in) //2^64 - 2^2 + 2^0
p256Mul(out, out, ptmp) //2^256 - 2^224 - 2^96 + 2^64 - 3
p256Sqr(out, in, 1)
p256Mul(t0, in, out)
p256Sqr(out, t0, 1)
p256Mul(out, in, out)
p256Sqr(t1, out, 3)
p256Mul(t1, out, t1)
p256Sqr(t2, t1, 1)
p256Mul(out, in, t2)
p256Sqr(t2, t2, 5)
p256Mul(t1, t1, t2)
p256Sqr(t2, t1, 12)
p256Mul(t1, t1, t2)
p256Sqr(t1, t1, 7)
p256Mul(out, out, t1)
p256Sqr(t2, out, 2)
p256Sqr(t1, t2, 29)
p256Mul(out, out, t1)
p256Sqr(t1, t1, 2)
p256Mul(t2, t2, t1)
p256Mul(t0, t0, t2)
p256Sqr(t1, t1, 32)
p256Mul(t1, t0, t1)
p256Sqr(t1, t1, 64)
p256Mul(t0, t0, t1)
p256Sqr(t0, t0, 94)
p256Mul(out, out, t0)
p256Sqr(out, out, 2)
p256Mul(out, in, out)
}
func (p *p256Point) p256StorePoint(r *[16 * 4 * 3]uint64, index int) {