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scalar.go
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scalar.go
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package curve256k1
import "math/bits"
type scalar struct {
l0, l1, l2, l3 uint64
// l4 is workspace, and up to 3bit.
l4 uint64
}
// Lsh8 sets s = v << 8, and return s.
func (s *scalar) Lsh8(v *scalar) *scalar {
l0 := v.l0 << 8
l1 := v.l1<<8 | v.l0>>56
l2 := v.l2<<8 | v.l1>>56
l3 := v.l3<<8 | v.l2>>56
l4 := v.l4<<8 | v.l3>>56
// carry is l4 * 0x1_45512319_50b75fc4_402da173_2fc9bebf
var h, l, c, c0 uint64
l2, c = bits.Add64(l2, l4, 0)
l3, c = bits.Add64(l3, 0, c)
c0 += c
h, l = bits.Mul64(l4, 0x45512319_50b75fc4)
l1, c = bits.Add64(l1, l, 0)
l2, c = bits.Add64(l2, h, c)
l3, c = bits.Add64(l3, 0, c)
c0 += c
h, l = bits.Mul64(l4, 0x402da173_2fc9bebf)
l0, c = bits.Add64(l0, l, 0)
l1, c = bits.Add64(l1, h, c)
l2, c = bits.Add64(l2, 0, c)
l3, c = bits.Add64(l3, 0, c)
c0 += c
s.l0 = l0
s.l1 = l1
s.l2 = l2
s.l3 = l3
s.l4 = c0
return s
}
func (s *scalar) reduce() *scalar {
l0 := s.l0
l1 := s.l1
l2 := s.l2
l3 := s.l3
l4 := s.l4
// carry is l4 * 0x1_45512319_50b75fc4_402da173_2fc9bebf
var h, l, c uint64
l2, c = bits.Add64(l2, l4, 0)
l3, _ = bits.Add64(l3, 0, c)
h, l = bits.Mul64(l4, 0x45512319_50b75fc4)
l1, c = bits.Add64(l1, l, 0)
l2, c = bits.Add64(l2, h, c)
l3, _ = bits.Add64(l3, 0, c)
h, l = bits.Mul64(l4, 0x402da173_2fc9bebf)
l0, c = bits.Add64(l0, l, 0)
l1, c = bits.Add64(l1, h, c)
l2, c = bits.Add64(l2, 0, c)
l3, _ = bits.Add64(l3, 0, c)
// If v >= l, then v + 0x1_45512319_50b75fc4_402da173_2fc9bebf >= 2^256,
// which would overflow 2^256 - 1, generating a carry.
// That is, c will be 0 if v < l, and 1 otherwise.
_, c = bits.Add64(l0, 0x402da173_2fc9bebf, 0)
_, c = bits.Add64(l1, 0x45512319_50b75fc4, c)
_, c = bits.Add64(l2, 1, c)
_, c = bits.Add64(l3, 0, c)
c0 := c
// NOTE: c0 is 0 or 1, so c0*0x45512319_50b75fc4 doesn't overflow
l0, c = bits.Add64(l0, c0*0x402da173_2fc9bebf, 0)
l1, c = bits.Add64(l1, c0*0x45512319_50b75fc4, c)
l2, c = bits.Add64(l2, c0, c)
l3, _ = bits.Add64(l3, 0, c)
s.l0 = l0
s.l1 = l1
s.l2 = l2
s.l3 = l3
s.l4 = 0
return s
}
func (s *scalar) Add8(v *scalar, u uint8) *scalar {
l0, c := bits.Add64(v.l0, uint64(u), 0)
l1, c := bits.Add64(v.l1, 0, c)
l2, c := bits.Add64(v.l2, 0, c)
l3, c := bits.Add64(v.l3, 0, c)
l4, _ := bits.Add64(v.l4, 0, c)
s.l0 = l0
s.l1 = l1
s.l2 = l2
s.l3 = l3
s.l4 = l4
return s
}
func (s *scalar) bytes(buf *[32]byte) {
s0 := *s
s0.reduce()
buf[31] = byte(s0.l0 >> 0)
buf[30] = byte(s0.l0 >> 8)
buf[29] = byte(s0.l0 >> 16)
buf[28] = byte(s0.l0 >> 24)
buf[27] = byte(s0.l0 >> 32)
buf[26] = byte(s0.l0 >> 40)
buf[25] = byte(s0.l0 >> 48)
buf[24] = byte(s0.l0 >> 56)
buf[23] = byte(s0.l1 >> 0)
buf[22] = byte(s0.l1 >> 8)
buf[21] = byte(s0.l1 >> 16)
buf[20] = byte(s0.l1 >> 24)
buf[19] = byte(s0.l1 >> 32)
buf[18] = byte(s0.l1 >> 40)
buf[17] = byte(s0.l1 >> 48)
buf[16] = byte(s0.l1 >> 56)
buf[15] = byte(s0.l2 >> 0)
buf[14] = byte(s0.l2 >> 8)
buf[13] = byte(s0.l2 >> 16)
buf[12] = byte(s0.l2 >> 24)
buf[11] = byte(s0.l2 >> 32)
buf[10] = byte(s0.l2 >> 40)
buf[9] = byte(s0.l2 >> 48)
buf[8] = byte(s0.l2 >> 56)
buf[7] = byte(s0.l3 >> 0)
buf[6] = byte(s0.l3 >> 8)
buf[5] = byte(s0.l3 >> 16)
buf[4] = byte(s0.l3 >> 24)
buf[3] = byte(s0.l3 >> 32)
buf[2] = byte(s0.l3 >> 40)
buf[1] = byte(s0.l3 >> 48)
buf[0] = byte(s0.l3 >> 56)
}
// parse k as big-endian integer,
// and returns k mod 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141.
func normalizeScalar(k []byte) [32]byte {
var s scalar
for _, b := range k {
s.Lsh8(&s)
s.Add8(&s, b)
}
var buf [32]byte
s.bytes(&buf)
return buf
}