340 lines
10 KiB
Go
340 lines
10 KiB
Go
package fp448
|
|
|
|
import (
|
|
"encoding/binary"
|
|
"math/bits"
|
|
)
|
|
|
|
func cmovGeneric(x, y *Elt, n uint) {
|
|
m := -uint64(n & 0x1)
|
|
x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
|
x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
|
x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
|
x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
|
x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
|
x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
|
x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
|
|
|
y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8])
|
|
y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8])
|
|
y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8])
|
|
y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8])
|
|
y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8])
|
|
y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8])
|
|
y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8])
|
|
|
|
x0 = (x0 &^ m) | (y0 & m)
|
|
x1 = (x1 &^ m) | (y1 & m)
|
|
x2 = (x2 &^ m) | (y2 & m)
|
|
x3 = (x3 &^ m) | (y3 & m)
|
|
x4 = (x4 &^ m) | (y4 & m)
|
|
x5 = (x5 &^ m) | (y5 & m)
|
|
x6 = (x6 &^ m) | (y6 & m)
|
|
|
|
binary.LittleEndian.PutUint64(x[0*8:1*8], x0)
|
|
binary.LittleEndian.PutUint64(x[1*8:2*8], x1)
|
|
binary.LittleEndian.PutUint64(x[2*8:3*8], x2)
|
|
binary.LittleEndian.PutUint64(x[3*8:4*8], x3)
|
|
binary.LittleEndian.PutUint64(x[4*8:5*8], x4)
|
|
binary.LittleEndian.PutUint64(x[5*8:6*8], x5)
|
|
binary.LittleEndian.PutUint64(x[6*8:7*8], x6)
|
|
}
|
|
|
|
func cswapGeneric(x, y *Elt, n uint) {
|
|
m := -uint64(n & 0x1)
|
|
x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
|
x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
|
x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
|
x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
|
x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
|
x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
|
x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
|
|
|
y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8])
|
|
y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8])
|
|
y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8])
|
|
y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8])
|
|
y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8])
|
|
y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8])
|
|
y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8])
|
|
|
|
t0 := m & (x0 ^ y0)
|
|
t1 := m & (x1 ^ y1)
|
|
t2 := m & (x2 ^ y2)
|
|
t3 := m & (x3 ^ y3)
|
|
t4 := m & (x4 ^ y4)
|
|
t5 := m & (x5 ^ y5)
|
|
t6 := m & (x6 ^ y6)
|
|
x0 ^= t0
|
|
x1 ^= t1
|
|
x2 ^= t2
|
|
x3 ^= t3
|
|
x4 ^= t4
|
|
x5 ^= t5
|
|
x6 ^= t6
|
|
y0 ^= t0
|
|
y1 ^= t1
|
|
y2 ^= t2
|
|
y3 ^= t3
|
|
y4 ^= t4
|
|
y5 ^= t5
|
|
y6 ^= t6
|
|
|
|
binary.LittleEndian.PutUint64(x[0*8:1*8], x0)
|
|
binary.LittleEndian.PutUint64(x[1*8:2*8], x1)
|
|
binary.LittleEndian.PutUint64(x[2*8:3*8], x2)
|
|
binary.LittleEndian.PutUint64(x[3*8:4*8], x3)
|
|
binary.LittleEndian.PutUint64(x[4*8:5*8], x4)
|
|
binary.LittleEndian.PutUint64(x[5*8:6*8], x5)
|
|
binary.LittleEndian.PutUint64(x[6*8:7*8], x6)
|
|
|
|
binary.LittleEndian.PutUint64(y[0*8:1*8], y0)
|
|
binary.LittleEndian.PutUint64(y[1*8:2*8], y1)
|
|
binary.LittleEndian.PutUint64(y[2*8:3*8], y2)
|
|
binary.LittleEndian.PutUint64(y[3*8:4*8], y3)
|
|
binary.LittleEndian.PutUint64(y[4*8:5*8], y4)
|
|
binary.LittleEndian.PutUint64(y[5*8:6*8], y5)
|
|
binary.LittleEndian.PutUint64(y[6*8:7*8], y6)
|
|
}
|
|
|
|
func addGeneric(z, x, y *Elt) {
|
|
x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
|
x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
|
x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
|
x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
|
x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
|
x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
|
x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
|
|
|
y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8])
|
|
y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8])
|
|
y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8])
|
|
y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8])
|
|
y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8])
|
|
y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8])
|
|
y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8])
|
|
|
|
z0, c0 := bits.Add64(x0, y0, 0)
|
|
z1, c1 := bits.Add64(x1, y1, c0)
|
|
z2, c2 := bits.Add64(x2, y2, c1)
|
|
z3, c3 := bits.Add64(x3, y3, c2)
|
|
z4, c4 := bits.Add64(x4, y4, c3)
|
|
z5, c5 := bits.Add64(x5, y5, c4)
|
|
z6, z7 := bits.Add64(x6, y6, c5)
|
|
|
|
z0, c0 = bits.Add64(z0, z7, 0)
|
|
z1, c1 = bits.Add64(z1, 0, c0)
|
|
z2, c2 = bits.Add64(z2, 0, c1)
|
|
z3, c3 = bits.Add64(z3, z7<<32, c2)
|
|
z4, c4 = bits.Add64(z4, 0, c3)
|
|
z5, c5 = bits.Add64(z5, 0, c4)
|
|
z6, z7 = bits.Add64(z6, 0, c5)
|
|
|
|
z0, c0 = bits.Add64(z0, z7, 0)
|
|
z1, c1 = bits.Add64(z1, 0, c0)
|
|
z2, c2 = bits.Add64(z2, 0, c1)
|
|
z3, c3 = bits.Add64(z3, z7<<32, c2)
|
|
z4, c4 = bits.Add64(z4, 0, c3)
|
|
z5, c5 = bits.Add64(z5, 0, c4)
|
|
z6, _ = bits.Add64(z6, 0, c5)
|
|
|
|
binary.LittleEndian.PutUint64(z[0*8:1*8], z0)
|
|
binary.LittleEndian.PutUint64(z[1*8:2*8], z1)
|
|
binary.LittleEndian.PutUint64(z[2*8:3*8], z2)
|
|
binary.LittleEndian.PutUint64(z[3*8:4*8], z3)
|
|
binary.LittleEndian.PutUint64(z[4*8:5*8], z4)
|
|
binary.LittleEndian.PutUint64(z[5*8:6*8], z5)
|
|
binary.LittleEndian.PutUint64(z[6*8:7*8], z6)
|
|
}
|
|
|
|
func subGeneric(z, x, y *Elt) {
|
|
x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
|
x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
|
x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
|
x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
|
x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
|
x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
|
x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
|
|
|
y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8])
|
|
y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8])
|
|
y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8])
|
|
y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8])
|
|
y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8])
|
|
y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8])
|
|
y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8])
|
|
|
|
z0, c0 := bits.Sub64(x0, y0, 0)
|
|
z1, c1 := bits.Sub64(x1, y1, c0)
|
|
z2, c2 := bits.Sub64(x2, y2, c1)
|
|
z3, c3 := bits.Sub64(x3, y3, c2)
|
|
z4, c4 := bits.Sub64(x4, y4, c3)
|
|
z5, c5 := bits.Sub64(x5, y5, c4)
|
|
z6, z7 := bits.Sub64(x6, y6, c5)
|
|
|
|
z0, c0 = bits.Sub64(z0, z7, 0)
|
|
z1, c1 = bits.Sub64(z1, 0, c0)
|
|
z2, c2 = bits.Sub64(z2, 0, c1)
|
|
z3, c3 = bits.Sub64(z3, z7<<32, c2)
|
|
z4, c4 = bits.Sub64(z4, 0, c3)
|
|
z5, c5 = bits.Sub64(z5, 0, c4)
|
|
z6, z7 = bits.Sub64(z6, 0, c5)
|
|
|
|
z0, c0 = bits.Sub64(z0, z7, 0)
|
|
z1, c1 = bits.Sub64(z1, 0, c0)
|
|
z2, c2 = bits.Sub64(z2, 0, c1)
|
|
z3, c3 = bits.Sub64(z3, z7<<32, c2)
|
|
z4, c4 = bits.Sub64(z4, 0, c3)
|
|
z5, c5 = bits.Sub64(z5, 0, c4)
|
|
z6, _ = bits.Sub64(z6, 0, c5)
|
|
|
|
binary.LittleEndian.PutUint64(z[0*8:1*8], z0)
|
|
binary.LittleEndian.PutUint64(z[1*8:2*8], z1)
|
|
binary.LittleEndian.PutUint64(z[2*8:3*8], z2)
|
|
binary.LittleEndian.PutUint64(z[3*8:4*8], z3)
|
|
binary.LittleEndian.PutUint64(z[4*8:5*8], z4)
|
|
binary.LittleEndian.PutUint64(z[5*8:6*8], z5)
|
|
binary.LittleEndian.PutUint64(z[6*8:7*8], z6)
|
|
}
|
|
|
|
func addsubGeneric(x, y *Elt) {
|
|
z := &Elt{}
|
|
addGeneric(z, x, y)
|
|
subGeneric(y, x, y)
|
|
*x = *z
|
|
}
|
|
|
|
func mulGeneric(z, x, y *Elt) {
|
|
x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
|
x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
|
x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
|
x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
|
x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
|
x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
|
x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
|
|
|
y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8])
|
|
y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8])
|
|
y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8])
|
|
y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8])
|
|
y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8])
|
|
y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8])
|
|
y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8])
|
|
|
|
yy := [7]uint64{y0, y1, y2, y3, y4, y5, y6}
|
|
zz := [7]uint64{}
|
|
|
|
yi := yy[0]
|
|
h0, l0 := bits.Mul64(x0, yi)
|
|
h1, l1 := bits.Mul64(x1, yi)
|
|
h2, l2 := bits.Mul64(x2, yi)
|
|
h3, l3 := bits.Mul64(x3, yi)
|
|
h4, l4 := bits.Mul64(x4, yi)
|
|
h5, l5 := bits.Mul64(x5, yi)
|
|
h6, l6 := bits.Mul64(x6, yi)
|
|
|
|
zz[0] = l0
|
|
a0, c0 := bits.Add64(h0, l1, 0)
|
|
a1, c1 := bits.Add64(h1, l2, c0)
|
|
a2, c2 := bits.Add64(h2, l3, c1)
|
|
a3, c3 := bits.Add64(h3, l4, c2)
|
|
a4, c4 := bits.Add64(h4, l5, c3)
|
|
a5, c5 := bits.Add64(h5, l6, c4)
|
|
a6, _ := bits.Add64(h6, 0, c5)
|
|
|
|
for i := 1; i < 7; i++ {
|
|
yi = yy[i]
|
|
h0, l0 = bits.Mul64(x0, yi)
|
|
h1, l1 = bits.Mul64(x1, yi)
|
|
h2, l2 = bits.Mul64(x2, yi)
|
|
h3, l3 = bits.Mul64(x3, yi)
|
|
h4, l4 = bits.Mul64(x4, yi)
|
|
h5, l5 = bits.Mul64(x5, yi)
|
|
h6, l6 = bits.Mul64(x6, yi)
|
|
|
|
zz[i], c0 = bits.Add64(a0, l0, 0)
|
|
a0, c1 = bits.Add64(a1, l1, c0)
|
|
a1, c2 = bits.Add64(a2, l2, c1)
|
|
a2, c3 = bits.Add64(a3, l3, c2)
|
|
a3, c4 = bits.Add64(a4, l4, c3)
|
|
a4, c5 = bits.Add64(a5, l5, c4)
|
|
a5, a6 = bits.Add64(a6, l6, c5)
|
|
|
|
a0, c0 = bits.Add64(a0, h0, 0)
|
|
a1, c1 = bits.Add64(a1, h1, c0)
|
|
a2, c2 = bits.Add64(a2, h2, c1)
|
|
a3, c3 = bits.Add64(a3, h3, c2)
|
|
a4, c4 = bits.Add64(a4, h4, c3)
|
|
a5, c5 = bits.Add64(a5, h5, c4)
|
|
a6, _ = bits.Add64(a6, h6, c5)
|
|
}
|
|
red64(z, &zz, &[7]uint64{a0, a1, a2, a3, a4, a5, a6})
|
|
}
|
|
|
|
func sqrGeneric(z, x *Elt) { mulGeneric(z, x, x) }
|
|
|
|
func red64(z *Elt, l, h *[7]uint64) {
|
|
/* (2C13, 2C12, 2C11, 2C10|C10, C9, C8, C7) + (C6,...,C0) */
|
|
h0 := h[0]
|
|
h1 := h[1]
|
|
h2 := h[2]
|
|
h3 := ((h[3] & (0xFFFFFFFF << 32)) << 1) | (h[3] & 0xFFFFFFFF)
|
|
h4 := (h[3] >> 63) | (h[4] << 1)
|
|
h5 := (h[4] >> 63) | (h[5] << 1)
|
|
h6 := (h[5] >> 63) | (h[6] << 1)
|
|
h7 := (h[6] >> 63)
|
|
|
|
l0, c0 := bits.Add64(h0, l[0], 0)
|
|
l1, c1 := bits.Add64(h1, l[1], c0)
|
|
l2, c2 := bits.Add64(h2, l[2], c1)
|
|
l3, c3 := bits.Add64(h3, l[3], c2)
|
|
l4, c4 := bits.Add64(h4, l[4], c3)
|
|
l5, c5 := bits.Add64(h5, l[5], c4)
|
|
l6, c6 := bits.Add64(h6, l[6], c5)
|
|
l7, _ := bits.Add64(h7, 0, c6)
|
|
|
|
/* (C10C9, C9C8,C8C7,C7C13,C13C12,C12C11,C11C10) + (C6,...,C0) */
|
|
h0 = (h[3] >> 32) | (h[4] << 32)
|
|
h1 = (h[4] >> 32) | (h[5] << 32)
|
|
h2 = (h[5] >> 32) | (h[6] << 32)
|
|
h3 = (h[6] >> 32) | (h[0] << 32)
|
|
h4 = (h[0] >> 32) | (h[1] << 32)
|
|
h5 = (h[1] >> 32) | (h[2] << 32)
|
|
h6 = (h[2] >> 32) | (h[3] << 32)
|
|
|
|
l0, c0 = bits.Add64(l0, h0, 0)
|
|
l1, c1 = bits.Add64(l1, h1, c0)
|
|
l2, c2 = bits.Add64(l2, h2, c1)
|
|
l3, c3 = bits.Add64(l3, h3, c2)
|
|
l4, c4 = bits.Add64(l4, h4, c3)
|
|
l5, c5 = bits.Add64(l5, h5, c4)
|
|
l6, c6 = bits.Add64(l6, h6, c5)
|
|
l7, _ = bits.Add64(l7, 0, c6)
|
|
|
|
/* (C7) + (C6,...,C0) */
|
|
l0, c0 = bits.Add64(l0, l7, 0)
|
|
l1, c1 = bits.Add64(l1, 0, c0)
|
|
l2, c2 = bits.Add64(l2, 0, c1)
|
|
l3, c3 = bits.Add64(l3, l7<<32, c2)
|
|
l4, c4 = bits.Add64(l4, 0, c3)
|
|
l5, c5 = bits.Add64(l5, 0, c4)
|
|
l6, l7 = bits.Add64(l6, 0, c5)
|
|
|
|
/* (C7) + (C6,...,C0) */
|
|
l0, c0 = bits.Add64(l0, l7, 0)
|
|
l1, c1 = bits.Add64(l1, 0, c0)
|
|
l2, c2 = bits.Add64(l2, 0, c1)
|
|
l3, c3 = bits.Add64(l3, l7<<32, c2)
|
|
l4, c4 = bits.Add64(l4, 0, c3)
|
|
l5, c5 = bits.Add64(l5, 0, c4)
|
|
l6, _ = bits.Add64(l6, 0, c5)
|
|
|
|
binary.LittleEndian.PutUint64(z[0*8:1*8], l0)
|
|
binary.LittleEndian.PutUint64(z[1*8:2*8], l1)
|
|
binary.LittleEndian.PutUint64(z[2*8:3*8], l2)
|
|
binary.LittleEndian.PutUint64(z[3*8:4*8], l3)
|
|
binary.LittleEndian.PutUint64(z[4*8:5*8], l4)
|
|
binary.LittleEndian.PutUint64(z[5*8:6*8], l5)
|
|
binary.LittleEndian.PutUint64(z[6*8:7*8], l6)
|
|
}
|