scalar: replace the Christmas tree with a fiat-crypto generated scalar field
This commit is contained in:
George Tankersley
Filippo Valsorda
parent
51f382caa1
commit
306e451b8b
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@ -74,7 +74,9 @@ func TestMultByCofactor(t *testing.T) {
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checkOnCurve(t, p8)
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// 8 * p == (8 * s) * B
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s.Multiply(s, &Scalar{[32]byte{8}})
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reprEight := [32]byte{8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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scEight, _ := (&Scalar{}).SetCanonicalBytes(reprEight[:])
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s.Multiply(s, scEight)
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pp := (&Point{}).ScalarBaseMult(s)
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if p8.Equal(pp) != 1 {
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return false
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@ -104,13 +106,23 @@ func TestScalarInvert(t *testing.T) {
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xInv.Invert((*Scalar)(&x))
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var check Scalar
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check.Multiply((*Scalar)(&x), &xInv)
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return check == scOne && isReduced(&xInv)
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return check.Equal(&scOne) == 1 && isReduced(xInv.Bytes())
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}
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if err := quick.Check(invertWorks, quickCheckConfig32); err != nil {
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t.Error(err)
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}
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randomScalar := *dalekScalar
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randomInverse := NewScalar().Invert(&randomScalar)
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var check Scalar
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check.Multiply(&randomScalar, randomInverse)
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if check.Equal(&scOne) == 0 || !isReduced(randomInverse.Bytes()) {
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t.Error("inversion did not work")
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}
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zero := NewScalar()
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if xx := NewScalar().Invert(zero); xx.Equal(zero) != 1 {
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t.Errorf("inverting zero did not return zero")
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@ -162,7 +174,7 @@ func BenchmarkMultiScalarMultSize8(t *testing.B) {
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x := dalekScalar
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for i := 0; i < t.N; i++ {
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p.MultiScalarMult([]*Scalar{&x, &x, &x, &x, &x, &x, &x, &x},
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p.MultiScalarMult([]*Scalar{x, x, x, x, x, x, x, x},
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[]*Point{B, B, B, B, B, B, B, B})
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}
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}
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1777
fiat_scalar.go
Normal file
1777
fiat_scalar.go
Normal file
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@ -0,0 +1,1777 @@
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/* Autogenerated: ./src/ExtractionOCaml/word_by_word_montgomery --lang Go sc255 64 '2^252 + 27742317777372353535851937790883648493' */
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/* curve description: sc255 */
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/* machine_wordsize = 64 (from "64") */
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/* requested operations: (all) */
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/* m = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed (from "2^252 + 27742317777372353535851937790883648493") */
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/* */
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/* NOTE: In addition to the bounds specified above each function, all */
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/* functions synthesized for this Montgomery arithmetic require the */
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/* input to be strictly less than the prime modulus (m), and also */
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/* require the input to be in the unique saturated representation. */
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/* All functions also ensure that these two properties are true of */
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/* return values. */
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/* */
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/* Computed values: */
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/* eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) */
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/* bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) */
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package edwards25519
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import "math/bits"
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type fiat_sc255_uint1 uint8
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type fiat_sc255_int1 int8
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/* The function fiat_sc255_addcarryx_u64 is a thin wrapper around bits.Add64 that uses fiat_sc255_uint1 rather than uint64 */
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func fiat_sc255_addcarryx_u64(x uint64, y uint64, carry fiat_sc255_uint1) (uint64, fiat_sc255_uint1) {
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var sum uint64
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var carryOut uint64
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sum, carryOut = bits.Add64(x, y, uint64(carry))
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return sum, fiat_sc255_uint1(carryOut)
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}
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/* The function fiat_sc255_subborrowx_u64 is a thin wrapper around bits.Sub64 that uses fiat_sc255_uint1 rather than uint64 */
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func fiat_sc255_subborrowx_u64(x uint64, y uint64, carry fiat_sc255_uint1) (uint64, fiat_sc255_uint1) {
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var sum uint64
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var carryOut uint64
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sum, carryOut = bits.Sub64(x, y, uint64(carry))
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return sum, fiat_sc255_uint1(carryOut)
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}
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/*
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* The function fiat_sc255_cmovznz_u64 is a single-word conditional move.
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* Postconditions:
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* out1 = (if arg1 = 0 then arg2 else arg3)
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*
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* Input Bounds:
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* arg1: [0x0 ~> 0x1]
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* arg2: [0x0 ~> 0xffffffffffffffff]
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* arg3: [0x0 ~> 0xffffffffffffffff]
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* Output Bounds:
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* out1: [0x0 ~> 0xffffffffffffffff]
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*/
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/*inline*/
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func fiat_sc255_cmovznz_u64(out1 *uint64, arg1 fiat_sc255_uint1, arg2 uint64, arg3 uint64) {
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// var x1 fiat_sc255_uint1 = (! /* TODO: FIX ME */ (! /* TODO: FIX ME */ arg1))
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// var x2 uint64 = (uint64((fiat_sc255_int1(0x0) - fiat_sc255_int1(x1))) & 0xffffffffffffffff)
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// var x3 uint64 = ((x2 & arg3) | ((^x2) & arg2))
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// call with --cmovznz-by-mul for Go
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var x1 uint64 = (uint64(arg1) * 0xffffffffffffffff)
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var x2 uint64 = ((x1 & arg3) | ((^x1) & arg2))
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*out1 = x2
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}
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/*
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* The function fiat_sc255_mul multiplies two field elements in the Montgomery domain.
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* Preconditions:
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* 0 ≤ eval arg1 < m
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* 0 ≤ eval arg2 < m
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* Postconditions:
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* eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
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* 0 ≤ eval out1 < m
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*
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* Input Bounds:
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* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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/*inline*/
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func fiat_sc255_mul(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) {
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var x1 uint64 = (arg1[1])
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var x2 uint64 = (arg1[2])
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var x3 uint64 = (arg1[3])
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var x4 uint64 = (arg1[0])
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var x5 uint64
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var x6 uint64
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x6, x5 = bits.Mul64(x4, (arg2[3]))
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var x7 uint64
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var x8 uint64
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x8, x7 = bits.Mul64(x4, (arg2[2]))
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var x9 uint64
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var x10 uint64
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x10, x9 = bits.Mul64(x4, (arg2[1]))
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var x11 uint64
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var x12 uint64
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x12, x11 = bits.Mul64(x4, (arg2[0]))
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var x13 uint64
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var x14 fiat_sc255_uint1
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x13, x14 = fiat_sc255_addcarryx_u64(x12, x9, 0x0)
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var x15 uint64
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var x16 fiat_sc255_uint1
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x15, x16 = fiat_sc255_addcarryx_u64(x10, x7, x14)
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var x17 uint64
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var x18 fiat_sc255_uint1
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x17, x18 = fiat_sc255_addcarryx_u64(x8, x5, x16)
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var x19 uint64 = (uint64(x18) + x6)
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var x20 uint64
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_, x20 = bits.Mul64(x11, 0xd2b51da312547e1b)
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var x22 uint64
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var x23 uint64
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x23, x22 = bits.Mul64(x20, 0x1000000000000000)
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var x24 uint64
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var x25 uint64
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x25, x24 = bits.Mul64(x20, 0x14def9dea2f79cd6)
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var x26 uint64
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var x27 uint64
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x27, x26 = bits.Mul64(x20, 0x5812631a5cf5d3ed)
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var x28 uint64
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var x29 fiat_sc255_uint1
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x28, x29 = fiat_sc255_addcarryx_u64(x27, x24, 0x0)
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var x30 uint64 = (uint64(x29) + x25)
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var x32 fiat_sc255_uint1
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_, x32 = fiat_sc255_addcarryx_u64(x11, x26, 0x0)
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var x33 uint64
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var x34 fiat_sc255_uint1
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x33, x34 = fiat_sc255_addcarryx_u64(x13, x28, x32)
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var x35 uint64
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var x36 fiat_sc255_uint1
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x35, x36 = fiat_sc255_addcarryx_u64(x15, x30, x34)
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var x37 uint64
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var x38 fiat_sc255_uint1
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x37, x38 = fiat_sc255_addcarryx_u64(x17, x22, x36)
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var x39 uint64
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var x40 fiat_sc255_uint1
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x39, x40 = fiat_sc255_addcarryx_u64(x19, x23, x38)
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var x41 uint64
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var x42 uint64
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x42, x41 = bits.Mul64(x1, (arg2[3]))
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var x43 uint64
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var x44 uint64
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x44, x43 = bits.Mul64(x1, (arg2[2]))
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var x45 uint64
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var x46 uint64
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x46, x45 = bits.Mul64(x1, (arg2[1]))
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var x47 uint64
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var x48 uint64
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x48, x47 = bits.Mul64(x1, (arg2[0]))
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var x49 uint64
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var x50 fiat_sc255_uint1
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x49, x50 = fiat_sc255_addcarryx_u64(x48, x45, 0x0)
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var x51 uint64
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var x52 fiat_sc255_uint1
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x51, x52 = fiat_sc255_addcarryx_u64(x46, x43, x50)
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var x53 uint64
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var x54 fiat_sc255_uint1
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x53, x54 = fiat_sc255_addcarryx_u64(x44, x41, x52)
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var x55 uint64 = (uint64(x54) + x42)
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var x56 uint64
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var x57 fiat_sc255_uint1
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x56, x57 = fiat_sc255_addcarryx_u64(x33, x47, 0x0)
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var x58 uint64
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var x59 fiat_sc255_uint1
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x58, x59 = fiat_sc255_addcarryx_u64(x35, x49, x57)
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var x60 uint64
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var x61 fiat_sc255_uint1
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x60, x61 = fiat_sc255_addcarryx_u64(x37, x51, x59)
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var x62 uint64
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var x63 fiat_sc255_uint1
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x62, x63 = fiat_sc255_addcarryx_u64(x39, x53, x61)
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var x64 uint64
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var x65 fiat_sc255_uint1
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x64, x65 = fiat_sc255_addcarryx_u64(uint64(x40), x55, x63)
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var x66 uint64
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_, x66 = bits.Mul64(x56, 0xd2b51da312547e1b)
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var x68 uint64
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var x69 uint64
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x69, x68 = bits.Mul64(x66, 0x1000000000000000)
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var x70 uint64
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var x71 uint64
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x71, x70 = bits.Mul64(x66, 0x14def9dea2f79cd6)
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var x72 uint64
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var x73 uint64
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x73, x72 = bits.Mul64(x66, 0x5812631a5cf5d3ed)
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var x74 uint64
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var x75 fiat_sc255_uint1
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x74, x75 = fiat_sc255_addcarryx_u64(x73, x70, 0x0)
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var x76 uint64 = (uint64(x75) + x71)
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var x78 fiat_sc255_uint1
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_, x78 = fiat_sc255_addcarryx_u64(x56, x72, 0x0)
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var x79 uint64
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var x80 fiat_sc255_uint1
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x79, x80 = fiat_sc255_addcarryx_u64(x58, x74, x78)
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var x81 uint64
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var x82 fiat_sc255_uint1
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x81, x82 = fiat_sc255_addcarryx_u64(x60, x76, x80)
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var x83 uint64
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var x84 fiat_sc255_uint1
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x83, x84 = fiat_sc255_addcarryx_u64(x62, x68, x82)
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var x85 uint64
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var x86 fiat_sc255_uint1
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x85, x86 = fiat_sc255_addcarryx_u64(x64, x69, x84)
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var x87 uint64 = (uint64(x86) + uint64(x65))
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var x88 uint64
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var x89 uint64
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x89, x88 = bits.Mul64(x2, (arg2[3]))
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var x90 uint64
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var x91 uint64
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x91, x90 = bits.Mul64(x2, (arg2[2]))
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var x92 uint64
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var x93 uint64
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x93, x92 = bits.Mul64(x2, (arg2[1]))
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var x94 uint64
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var x95 uint64
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x95, x94 = bits.Mul64(x2, (arg2[0]))
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var x96 uint64
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var x97 fiat_sc255_uint1
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x96, x97 = fiat_sc255_addcarryx_u64(x95, x92, 0x0)
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var x98 uint64
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var x99 fiat_sc255_uint1
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x98, x99 = fiat_sc255_addcarryx_u64(x93, x90, x97)
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var x100 uint64
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var x101 fiat_sc255_uint1
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x100, x101 = fiat_sc255_addcarryx_u64(x91, x88, x99)
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var x102 uint64 = (uint64(x101) + x89)
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var x103 uint64
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var x104 fiat_sc255_uint1
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x103, x104 = fiat_sc255_addcarryx_u64(x79, x94, 0x0)
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var x105 uint64
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var x106 fiat_sc255_uint1
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x105, x106 = fiat_sc255_addcarryx_u64(x81, x96, x104)
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var x107 uint64
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var x108 fiat_sc255_uint1
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x107, x108 = fiat_sc255_addcarryx_u64(x83, x98, x106)
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var x109 uint64
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var x110 fiat_sc255_uint1
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x109, x110 = fiat_sc255_addcarryx_u64(x85, x100, x108)
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var x111 uint64
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var x112 fiat_sc255_uint1
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x111, x112 = fiat_sc255_addcarryx_u64(x87, x102, x110)
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var x113 uint64
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_, x113 = bits.Mul64(x103, 0xd2b51da312547e1b)
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var x115 uint64
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var x116 uint64
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x116, x115 = bits.Mul64(x113, 0x1000000000000000)
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var x117 uint64
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var x118 uint64
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x118, x117 = bits.Mul64(x113, 0x14def9dea2f79cd6)
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var x119 uint64
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var x120 uint64
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x120, x119 = bits.Mul64(x113, 0x5812631a5cf5d3ed)
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var x121 uint64
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var x122 fiat_sc255_uint1
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x121, x122 = fiat_sc255_addcarryx_u64(x120, x117, 0x0)
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var x123 uint64 = (uint64(x122) + x118)
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var x125 fiat_sc255_uint1
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_, x125 = fiat_sc255_addcarryx_u64(x103, x119, 0x0)
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var x126 uint64
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var x127 fiat_sc255_uint1
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x126, x127 = fiat_sc255_addcarryx_u64(x105, x121, x125)
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var x128 uint64
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var x129 fiat_sc255_uint1
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x128, x129 = fiat_sc255_addcarryx_u64(x107, x123, x127)
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var x130 uint64
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var x131 fiat_sc255_uint1
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x130, x131 = fiat_sc255_addcarryx_u64(x109, x115, x129)
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var x132 uint64
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var x133 fiat_sc255_uint1
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x132, x133 = fiat_sc255_addcarryx_u64(x111, x116, x131)
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var x134 uint64 = (uint64(x133) + uint64(x112))
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var x135 uint64
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var x136 uint64
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x136, x135 = bits.Mul64(x3, (arg2[3]))
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var x137 uint64
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var x138 uint64
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x138, x137 = bits.Mul64(x3, (arg2[2]))
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var x139 uint64
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var x140 uint64
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x140, x139 = bits.Mul64(x3, (arg2[1]))
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var x141 uint64
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var x142 uint64
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x142, x141 = bits.Mul64(x3, (arg2[0]))
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var x143 uint64
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var x144 fiat_sc255_uint1
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x143, x144 = fiat_sc255_addcarryx_u64(x142, x139, 0x0)
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var x145 uint64
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var x146 fiat_sc255_uint1
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x145, x146 = fiat_sc255_addcarryx_u64(x140, x137, x144)
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var x147 uint64
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var x148 fiat_sc255_uint1
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x147, x148 = fiat_sc255_addcarryx_u64(x138, x135, x146)
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var x149 uint64 = (uint64(x148) + x136)
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var x150 uint64
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var x151 fiat_sc255_uint1
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x150, x151 = fiat_sc255_addcarryx_u64(x126, x141, 0x0)
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var x152 uint64
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var x153 fiat_sc255_uint1
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x152, x153 = fiat_sc255_addcarryx_u64(x128, x143, x151)
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var x154 uint64
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||||
var x155 fiat_sc255_uint1
|
||||
x154, x155 = fiat_sc255_addcarryx_u64(x130, x145, x153)
|
||||
var x156 uint64
|
||||
var x157 fiat_sc255_uint1
|
||||
x156, x157 = fiat_sc255_addcarryx_u64(x132, x147, x155)
|
||||
var x158 uint64
|
||||
var x159 fiat_sc255_uint1
|
||||
x158, x159 = fiat_sc255_addcarryx_u64(x134, x149, x157)
|
||||
var x160 uint64
|
||||
_, x160 = bits.Mul64(x150, 0xd2b51da312547e1b)
|
||||
var x162 uint64
|
||||
var x163 uint64
|
||||
x163, x162 = bits.Mul64(x160, 0x1000000000000000)
|
||||
var x164 uint64
|
||||
var x165 uint64
|
||||
x165, x164 = bits.Mul64(x160, 0x14def9dea2f79cd6)
|
||||
var x166 uint64
|
||||
var x167 uint64
|
||||
x167, x166 = bits.Mul64(x160, 0x5812631a5cf5d3ed)
|
||||
var x168 uint64
|
||||
var x169 fiat_sc255_uint1
|
||||
x168, x169 = fiat_sc255_addcarryx_u64(x167, x164, 0x0)
|
||||
var x170 uint64 = (uint64(x169) + x165)
|
||||
var x172 fiat_sc255_uint1
|
||||
_, x172 = fiat_sc255_addcarryx_u64(x150, x166, 0x0)
|
||||
var x173 uint64
|
||||
var x174 fiat_sc255_uint1
|
||||
x173, x174 = fiat_sc255_addcarryx_u64(x152, x168, x172)
|
||||
var x175 uint64
|
||||
var x176 fiat_sc255_uint1
|
||||
x175, x176 = fiat_sc255_addcarryx_u64(x154, x170, x174)
|
||||
var x177 uint64
|
||||
var x178 fiat_sc255_uint1
|
||||
x177, x178 = fiat_sc255_addcarryx_u64(x156, x162, x176)
|
||||
var x179 uint64
|
||||
var x180 fiat_sc255_uint1
|
||||
x179, x180 = fiat_sc255_addcarryx_u64(x158, x163, x178)
|
||||
var x181 uint64 = (uint64(x180) + uint64(x159))
|
||||
var x182 uint64
|
||||
var x183 fiat_sc255_uint1
|
||||
x182, x183 = fiat_sc255_subborrowx_u64(x173, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x184 uint64
|
||||
var x185 fiat_sc255_uint1
|
||||
x184, x185 = fiat_sc255_subborrowx_u64(x175, 0x14def9dea2f79cd6, x183)
|
||||
var x186 uint64
|
||||
var x187 fiat_sc255_uint1
|
||||
x186, x187 = fiat_sc255_subborrowx_u64(x177, uint64(0x0), x185)
|
||||
var x188 uint64
|
||||
var x189 fiat_sc255_uint1
|
||||
x188, x189 = fiat_sc255_subborrowx_u64(x179, 0x1000000000000000, x187)
|
||||
var x191 fiat_sc255_uint1
|
||||
_, x191 = fiat_sc255_subborrowx_u64(x181, uint64(0x0), x189)
|
||||
var x192 uint64
|
||||
fiat_sc255_cmovznz_u64(&x192, x191, x182, x173)
|
||||
var x193 uint64
|
||||
fiat_sc255_cmovznz_u64(&x193, x191, x184, x175)
|
||||
var x194 uint64
|
||||
fiat_sc255_cmovznz_u64(&x194, x191, x186, x177)
|
||||
var x195 uint64
|
||||
fiat_sc255_cmovznz_u64(&x195, x191, x188, x179)
|
||||
out1[0] = x192
|
||||
out1[1] = x193
|
||||
out1[2] = x194
|
||||
out1[3] = x195
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_square squares a field element in the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_square(out1 *[4]uint64, arg1 *[4]uint64) {
|
||||
var x1 uint64 = (arg1[1])
|
||||
var x2 uint64 = (arg1[2])
|
||||
var x3 uint64 = (arg1[3])
|
||||
var x4 uint64 = (arg1[0])
|
||||
var x5 uint64
|
||||
var x6 uint64
|
||||
x6, x5 = bits.Mul64(x4, (arg1[3]))
|
||||
var x7 uint64
|
||||
var x8 uint64
|
||||
x8, x7 = bits.Mul64(x4, (arg1[2]))
|
||||
var x9 uint64
|
||||
var x10 uint64
|
||||
x10, x9 = bits.Mul64(x4, (arg1[1]))
|
||||
var x11 uint64
|
||||
var x12 uint64
|
||||
x12, x11 = bits.Mul64(x4, (arg1[0]))
|
||||
var x13 uint64
|
||||
var x14 fiat_sc255_uint1
|
||||
x13, x14 = fiat_sc255_addcarryx_u64(x12, x9, 0x0)
|
||||
var x15 uint64
|
||||
var x16 fiat_sc255_uint1
|
||||
x15, x16 = fiat_sc255_addcarryx_u64(x10, x7, x14)
|
||||
var x17 uint64
|
||||
var x18 fiat_sc255_uint1
|
||||
x17, x18 = fiat_sc255_addcarryx_u64(x8, x5, x16)
|
||||
var x19 uint64 = (uint64(x18) + x6)
|
||||
var x20 uint64
|
||||
_, x20 = bits.Mul64(x11, 0xd2b51da312547e1b)
|
||||
var x22 uint64
|
||||
var x23 uint64
|
||||
x23, x22 = bits.Mul64(x20, 0x1000000000000000)
|
||||
var x24 uint64
|
||||
var x25 uint64
|
||||
x25, x24 = bits.Mul64(x20, 0x14def9dea2f79cd6)
|
||||
var x26 uint64
|
||||
var x27 uint64
|
||||
x27, x26 = bits.Mul64(x20, 0x5812631a5cf5d3ed)
|
||||
var x28 uint64
|
||||
var x29 fiat_sc255_uint1
|
||||
x28, x29 = fiat_sc255_addcarryx_u64(x27, x24, 0x0)
|
||||
var x30 uint64 = (uint64(x29) + x25)
|
||||
var x32 fiat_sc255_uint1
|
||||
_, x32 = fiat_sc255_addcarryx_u64(x11, x26, 0x0)
|
||||
var x33 uint64
|
||||
var x34 fiat_sc255_uint1
|
||||
x33, x34 = fiat_sc255_addcarryx_u64(x13, x28, x32)
|
||||
var x35 uint64
|
||||
var x36 fiat_sc255_uint1
|
||||
x35, x36 = fiat_sc255_addcarryx_u64(x15, x30, x34)
|
||||
var x37 uint64
|
||||
var x38 fiat_sc255_uint1
|
||||
x37, x38 = fiat_sc255_addcarryx_u64(x17, x22, x36)
|
||||
var x39 uint64
|
||||
var x40 fiat_sc255_uint1
|
||||
x39, x40 = fiat_sc255_addcarryx_u64(x19, x23, x38)
|
||||
var x41 uint64
|
||||
var x42 uint64
|
||||
x42, x41 = bits.Mul64(x1, (arg1[3]))
|
||||
var x43 uint64
|
||||
var x44 uint64
|
||||
x44, x43 = bits.Mul64(x1, (arg1[2]))
|
||||
var x45 uint64
|
||||
var x46 uint64
|
||||
x46, x45 = bits.Mul64(x1, (arg1[1]))
|
||||
var x47 uint64
|
||||
var x48 uint64
|
||||
x48, x47 = bits.Mul64(x1, (arg1[0]))
|
||||
var x49 uint64
|
||||
var x50 fiat_sc255_uint1
|
||||
x49, x50 = fiat_sc255_addcarryx_u64(x48, x45, 0x0)
|
||||
var x51 uint64
|
||||
var x52 fiat_sc255_uint1
|
||||
x51, x52 = fiat_sc255_addcarryx_u64(x46, x43, x50)
|
||||
var x53 uint64
|
||||
var x54 fiat_sc255_uint1
|
||||
x53, x54 = fiat_sc255_addcarryx_u64(x44, x41, x52)
|
||||
var x55 uint64 = (uint64(x54) + x42)
|
||||
var x56 uint64
|
||||
var x57 fiat_sc255_uint1
|
||||
x56, x57 = fiat_sc255_addcarryx_u64(x33, x47, 0x0)
|
||||
var x58 uint64
|
||||
var x59 fiat_sc255_uint1
|
||||
x58, x59 = fiat_sc255_addcarryx_u64(x35, x49, x57)
|
||||
var x60 uint64
|
||||
var x61 fiat_sc255_uint1
|
||||
x60, x61 = fiat_sc255_addcarryx_u64(x37, x51, x59)
|
||||
var x62 uint64
|
||||
var x63 fiat_sc255_uint1
|
||||
x62, x63 = fiat_sc255_addcarryx_u64(x39, x53, x61)
|
||||
var x64 uint64
|
||||
var x65 fiat_sc255_uint1
|
||||
x64, x65 = fiat_sc255_addcarryx_u64(uint64(x40), x55, x63)
|
||||
var x66 uint64
|
||||
_, x66 = bits.Mul64(x56, 0xd2b51da312547e1b)
|
||||
var x68 uint64
|
||||
var x69 uint64
|
||||
x69, x68 = bits.Mul64(x66, 0x1000000000000000)
|
||||
var x70 uint64
|
||||
var x71 uint64
|
||||
x71, x70 = bits.Mul64(x66, 0x14def9dea2f79cd6)
|
||||
var x72 uint64
|
||||
var x73 uint64
|
||||
x73, x72 = bits.Mul64(x66, 0x5812631a5cf5d3ed)
|
||||
var x74 uint64
|
||||
var x75 fiat_sc255_uint1
|
||||
x74, x75 = fiat_sc255_addcarryx_u64(x73, x70, 0x0)
|
||||
var x76 uint64 = (uint64(x75) + x71)
|
||||
var x78 fiat_sc255_uint1
|
||||
_, x78 = fiat_sc255_addcarryx_u64(x56, x72, 0x0)
|
||||
var x79 uint64
|
||||
var x80 fiat_sc255_uint1
|
||||
x79, x80 = fiat_sc255_addcarryx_u64(x58, x74, x78)
|
||||
var x81 uint64
|
||||
var x82 fiat_sc255_uint1
|
||||
x81, x82 = fiat_sc255_addcarryx_u64(x60, x76, x80)
|
||||
var x83 uint64
|
||||
var x84 fiat_sc255_uint1
|
||||
x83, x84 = fiat_sc255_addcarryx_u64(x62, x68, x82)
|
||||
var x85 uint64
|
||||
var x86 fiat_sc255_uint1
|
||||
x85, x86 = fiat_sc255_addcarryx_u64(x64, x69, x84)
|
||||
var x87 uint64 = (uint64(x86) + uint64(x65))
|
||||
var x88 uint64
|
||||
var x89 uint64
|
||||
x89, x88 = bits.Mul64(x2, (arg1[3]))
|
||||
var x90 uint64
|
||||
var x91 uint64
|
||||
x91, x90 = bits.Mul64(x2, (arg1[2]))
|
||||
var x92 uint64
|
||||
var x93 uint64
|
||||
x93, x92 = bits.Mul64(x2, (arg1[1]))
|
||||
var x94 uint64
|
||||
var x95 uint64
|
||||
x95, x94 = bits.Mul64(x2, (arg1[0]))
|
||||
var x96 uint64
|
||||
var x97 fiat_sc255_uint1
|
||||
x96, x97 = fiat_sc255_addcarryx_u64(x95, x92, 0x0)
|
||||
var x98 uint64
|
||||
var x99 fiat_sc255_uint1
|
||||
x98, x99 = fiat_sc255_addcarryx_u64(x93, x90, x97)
|
||||
var x100 uint64
|
||||
var x101 fiat_sc255_uint1
|
||||
x100, x101 = fiat_sc255_addcarryx_u64(x91, x88, x99)
|
||||
var x102 uint64 = (uint64(x101) + x89)
|
||||
var x103 uint64
|
||||
var x104 fiat_sc255_uint1
|
||||
x103, x104 = fiat_sc255_addcarryx_u64(x79, x94, 0x0)
|
||||
var x105 uint64
|
||||
var x106 fiat_sc255_uint1
|
||||
x105, x106 = fiat_sc255_addcarryx_u64(x81, x96, x104)
|
||||
var x107 uint64
|
||||
var x108 fiat_sc255_uint1
|
||||
x107, x108 = fiat_sc255_addcarryx_u64(x83, x98, x106)
|
||||
var x109 uint64
|
||||
var x110 fiat_sc255_uint1
|
||||
x109, x110 = fiat_sc255_addcarryx_u64(x85, x100, x108)
|
||||
var x111 uint64
|
||||
var x112 fiat_sc255_uint1
|
||||
x111, x112 = fiat_sc255_addcarryx_u64(x87, x102, x110)
|
||||
var x113 uint64
|
||||
_, x113 = bits.Mul64(x103, 0xd2b51da312547e1b)
|
||||
var x115 uint64
|
||||
var x116 uint64
|
||||
x116, x115 = bits.Mul64(x113, 0x1000000000000000)
|
||||
var x117 uint64
|
||||
var x118 uint64
|
||||
x118, x117 = bits.Mul64(x113, 0x14def9dea2f79cd6)
|
||||
var x119 uint64
|
||||
var x120 uint64
|
||||
x120, x119 = bits.Mul64(x113, 0x5812631a5cf5d3ed)
|
||||
var x121 uint64
|
||||
var x122 fiat_sc255_uint1
|
||||
x121, x122 = fiat_sc255_addcarryx_u64(x120, x117, 0x0)
|
||||
var x123 uint64 = (uint64(x122) + x118)
|
||||
var x125 fiat_sc255_uint1
|
||||
_, x125 = fiat_sc255_addcarryx_u64(x103, x119, 0x0)
|
||||
var x126 uint64
|
||||
var x127 fiat_sc255_uint1
|
||||
x126, x127 = fiat_sc255_addcarryx_u64(x105, x121, x125)
|
||||
var x128 uint64
|
||||
var x129 fiat_sc255_uint1
|
||||
x128, x129 = fiat_sc255_addcarryx_u64(x107, x123, x127)
|
||||
var x130 uint64
|
||||
var x131 fiat_sc255_uint1
|
||||
x130, x131 = fiat_sc255_addcarryx_u64(x109, x115, x129)
|
||||
var x132 uint64
|
||||
var x133 fiat_sc255_uint1
|
||||
x132, x133 = fiat_sc255_addcarryx_u64(x111, x116, x131)
|
||||
var x134 uint64 = (uint64(x133) + uint64(x112))
|
||||
var x135 uint64
|
||||
var x136 uint64
|
||||
x136, x135 = bits.Mul64(x3, (arg1[3]))
|
||||
var x137 uint64
|
||||
var x138 uint64
|
||||
x138, x137 = bits.Mul64(x3, (arg1[2]))
|
||||
var x139 uint64
|
||||
var x140 uint64
|
||||
x140, x139 = bits.Mul64(x3, (arg1[1]))
|
||||
var x141 uint64
|
||||
var x142 uint64
|
||||
x142, x141 = bits.Mul64(x3, (arg1[0]))
|
||||
var x143 uint64
|
||||
var x144 fiat_sc255_uint1
|
||||
x143, x144 = fiat_sc255_addcarryx_u64(x142, x139, 0x0)
|
||||
var x145 uint64
|
||||
var x146 fiat_sc255_uint1
|
||||
x145, x146 = fiat_sc255_addcarryx_u64(x140, x137, x144)
|
||||
var x147 uint64
|
||||
var x148 fiat_sc255_uint1
|
||||
x147, x148 = fiat_sc255_addcarryx_u64(x138, x135, x146)
|
||||
var x149 uint64 = (uint64(x148) + x136)
|
||||
var x150 uint64
|
||||
var x151 fiat_sc255_uint1
|
||||
x150, x151 = fiat_sc255_addcarryx_u64(x126, x141, 0x0)
|
||||
var x152 uint64
|
||||
var x153 fiat_sc255_uint1
|
||||
x152, x153 = fiat_sc255_addcarryx_u64(x128, x143, x151)
|
||||
var x154 uint64
|
||||
var x155 fiat_sc255_uint1
|
||||
x154, x155 = fiat_sc255_addcarryx_u64(x130, x145, x153)
|
||||
var x156 uint64
|
||||
var x157 fiat_sc255_uint1
|
||||
x156, x157 = fiat_sc255_addcarryx_u64(x132, x147, x155)
|
||||
var x158 uint64
|
||||
var x159 fiat_sc255_uint1
|
||||
x158, x159 = fiat_sc255_addcarryx_u64(x134, x149, x157)
|
||||
var x160 uint64
|
||||
_, x160 = bits.Mul64(x150, 0xd2b51da312547e1b)
|
||||
var x162 uint64
|
||||
var x163 uint64
|
||||
x163, x162 = bits.Mul64(x160, 0x1000000000000000)
|
||||
var x164 uint64
|
||||
var x165 uint64
|
||||
x165, x164 = bits.Mul64(x160, 0x14def9dea2f79cd6)
|
||||
var x166 uint64
|
||||
var x167 uint64
|
||||
x167, x166 = bits.Mul64(x160, 0x5812631a5cf5d3ed)
|
||||
var x168 uint64
|
||||
var x169 fiat_sc255_uint1
|
||||
x168, x169 = fiat_sc255_addcarryx_u64(x167, x164, 0x0)
|
||||
var x170 uint64 = (uint64(x169) + x165)
|
||||
var x172 fiat_sc255_uint1
|
||||
_, x172 = fiat_sc255_addcarryx_u64(x150, x166, 0x0)
|
||||
var x173 uint64
|
||||
var x174 fiat_sc255_uint1
|
||||
x173, x174 = fiat_sc255_addcarryx_u64(x152, x168, x172)
|
||||
var x175 uint64
|
||||
var x176 fiat_sc255_uint1
|
||||
x175, x176 = fiat_sc255_addcarryx_u64(x154, x170, x174)
|
||||
var x177 uint64
|
||||
var x178 fiat_sc255_uint1
|
||||
x177, x178 = fiat_sc255_addcarryx_u64(x156, x162, x176)
|
||||
var x179 uint64
|
||||
var x180 fiat_sc255_uint1
|
||||
x179, x180 = fiat_sc255_addcarryx_u64(x158, x163, x178)
|
||||
var x181 uint64 = (uint64(x180) + uint64(x159))
|
||||
var x182 uint64
|
||||
var x183 fiat_sc255_uint1
|
||||
x182, x183 = fiat_sc255_subborrowx_u64(x173, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x184 uint64
|
||||
var x185 fiat_sc255_uint1
|
||||
x184, x185 = fiat_sc255_subborrowx_u64(x175, 0x14def9dea2f79cd6, x183)
|
||||
var x186 uint64
|
||||
var x187 fiat_sc255_uint1
|
||||
x186, x187 = fiat_sc255_subborrowx_u64(x177, uint64(0x0), x185)
|
||||
var x188 uint64
|
||||
var x189 fiat_sc255_uint1
|
||||
x188, x189 = fiat_sc255_subborrowx_u64(x179, 0x1000000000000000, x187)
|
||||
var x191 fiat_sc255_uint1
|
||||
_, x191 = fiat_sc255_subborrowx_u64(x181, uint64(0x0), x189)
|
||||
var x192 uint64
|
||||
fiat_sc255_cmovznz_u64(&x192, x191, x182, x173)
|
||||
var x193 uint64
|
||||
fiat_sc255_cmovznz_u64(&x193, x191, x184, x175)
|
||||
var x194 uint64
|
||||
fiat_sc255_cmovznz_u64(&x194, x191, x186, x177)
|
||||
var x195 uint64
|
||||
fiat_sc255_cmovznz_u64(&x195, x191, x188, x179)
|
||||
out1[0] = x192
|
||||
out1[1] = x193
|
||||
out1[2] = x194
|
||||
out1[3] = x195
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_add adds two field elements in the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* 0 ≤ eval arg2 < m
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_add(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) {
|
||||
var x1 uint64
|
||||
var x2 fiat_sc255_uint1
|
||||
x1, x2 = fiat_sc255_addcarryx_u64((arg1[0]), (arg2[0]), 0x0)
|
||||
var x3 uint64
|
||||
var x4 fiat_sc255_uint1
|
||||
x3, x4 = fiat_sc255_addcarryx_u64((arg1[1]), (arg2[1]), x2)
|
||||
var x5 uint64
|
||||
var x6 fiat_sc255_uint1
|
||||
x5, x6 = fiat_sc255_addcarryx_u64((arg1[2]), (arg2[2]), x4)
|
||||
var x7 uint64
|
||||
var x8 fiat_sc255_uint1
|
||||
x7, x8 = fiat_sc255_addcarryx_u64((arg1[3]), (arg2[3]), x6)
|
||||
var x9 uint64
|
||||
var x10 fiat_sc255_uint1
|
||||
x9, x10 = fiat_sc255_subborrowx_u64(x1, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x11 uint64
|
||||
var x12 fiat_sc255_uint1
|
||||
x11, x12 = fiat_sc255_subborrowx_u64(x3, 0x14def9dea2f79cd6, x10)
|
||||
var x13 uint64
|
||||
var x14 fiat_sc255_uint1
|
||||
x13, x14 = fiat_sc255_subborrowx_u64(x5, uint64(0x0), x12)
|
||||
var x15 uint64
|
||||
var x16 fiat_sc255_uint1
|
||||
x15, x16 = fiat_sc255_subborrowx_u64(x7, 0x1000000000000000, x14)
|
||||
var x18 fiat_sc255_uint1
|
||||
_, x18 = fiat_sc255_subborrowx_u64(uint64(x8), uint64(0x0), x16)
|
||||
var x19 uint64
|
||||
fiat_sc255_cmovznz_u64(&x19, x18, x9, x1)
|
||||
var x20 uint64
|
||||
fiat_sc255_cmovznz_u64(&x20, x18, x11, x3)
|
||||
var x21 uint64
|
||||
fiat_sc255_cmovznz_u64(&x21, x18, x13, x5)
|
||||
var x22 uint64
|
||||
fiat_sc255_cmovznz_u64(&x22, x18, x15, x7)
|
||||
out1[0] = x19
|
||||
out1[1] = x20
|
||||
out1[2] = x21
|
||||
out1[3] = x22
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_sub subtracts two field elements in the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* 0 ≤ eval arg2 < m
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_sub(out1 *[4]uint64, arg1 *[4]uint64, arg2 *[4]uint64) {
|
||||
var x1 uint64
|
||||
var x2 fiat_sc255_uint1
|
||||
x1, x2 = fiat_sc255_subborrowx_u64((arg1[0]), (arg2[0]), 0x0)
|
||||
var x3 uint64
|
||||
var x4 fiat_sc255_uint1
|
||||
x3, x4 = fiat_sc255_subborrowx_u64((arg1[1]), (arg2[1]), x2)
|
||||
var x5 uint64
|
||||
var x6 fiat_sc255_uint1
|
||||
x5, x6 = fiat_sc255_subborrowx_u64((arg1[2]), (arg2[2]), x4)
|
||||
var x7 uint64
|
||||
var x8 fiat_sc255_uint1
|
||||
x7, x8 = fiat_sc255_subborrowx_u64((arg1[3]), (arg2[3]), x6)
|
||||
var x9 uint64
|
||||
fiat_sc255_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
|
||||
var x10 uint64
|
||||
var x11 fiat_sc255_uint1
|
||||
x10, x11 = fiat_sc255_addcarryx_u64(x1, (x9 & 0x5812631a5cf5d3ed), 0x0)
|
||||
var x12 uint64
|
||||
var x13 fiat_sc255_uint1
|
||||
x12, x13 = fiat_sc255_addcarryx_u64(x3, (x9 & 0x14def9dea2f79cd6), x11)
|
||||
var x14 uint64
|
||||
var x15 fiat_sc255_uint1
|
||||
x14, x15 = fiat_sc255_addcarryx_u64(x5, uint64(0x0), x13)
|
||||
var x16 uint64
|
||||
x16, _ = fiat_sc255_addcarryx_u64(x7, (x9 & 0x1000000000000000), x15)
|
||||
out1[0] = x10
|
||||
out1[1] = x12
|
||||
out1[2] = x14
|
||||
out1[3] = x16
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_opp negates a field element in the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_opp(out1 *[4]uint64, arg1 *[4]uint64) {
|
||||
var x1 uint64
|
||||
var x2 fiat_sc255_uint1
|
||||
x1, x2 = fiat_sc255_subborrowx_u64(uint64(0x0), (arg1[0]), 0x0)
|
||||
var x3 uint64
|
||||
var x4 fiat_sc255_uint1
|
||||
x3, x4 = fiat_sc255_subborrowx_u64(uint64(0x0), (arg1[1]), x2)
|
||||
var x5 uint64
|
||||
var x6 fiat_sc255_uint1
|
||||
x5, x6 = fiat_sc255_subborrowx_u64(uint64(0x0), (arg1[2]), x4)
|
||||
var x7 uint64
|
||||
var x8 fiat_sc255_uint1
|
||||
x7, x8 = fiat_sc255_subborrowx_u64(uint64(0x0), (arg1[3]), x6)
|
||||
var x9 uint64
|
||||
fiat_sc255_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
|
||||
var x10 uint64
|
||||
var x11 fiat_sc255_uint1
|
||||
x10, x11 = fiat_sc255_addcarryx_u64(x1, (x9 & 0x5812631a5cf5d3ed), 0x0)
|
||||
var x12 uint64
|
||||
var x13 fiat_sc255_uint1
|
||||
x12, x13 = fiat_sc255_addcarryx_u64(x3, (x9 & 0x14def9dea2f79cd6), x11)
|
||||
var x14 uint64
|
||||
var x15 fiat_sc255_uint1
|
||||
x14, x15 = fiat_sc255_addcarryx_u64(x5, uint64(0x0), x13)
|
||||
var x16 uint64
|
||||
x16, _ = fiat_sc255_addcarryx_u64(x7, (x9 & 0x1000000000000000), x15)
|
||||
out1[0] = x10
|
||||
out1[1] = x12
|
||||
out1[2] = x14
|
||||
out1[3] = x16
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_from_montgomery translates a field element out of the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_from_montgomery(out1 *[4]uint64, arg1 *[4]uint64) {
|
||||
var x1 uint64 = (arg1[0])
|
||||
var x2 uint64
|
||||
_, x2 = bits.Mul64(x1, 0xd2b51da312547e1b)
|
||||
var x4 uint64
|
||||
var x5 uint64
|
||||
x5, x4 = bits.Mul64(x2, 0x1000000000000000)
|
||||
var x6 uint64
|
||||
var x7 uint64
|
||||
x7, x6 = bits.Mul64(x2, 0x14def9dea2f79cd6)
|
||||
var x8 uint64
|
||||
var x9 uint64
|
||||
x9, x8 = bits.Mul64(x2, 0x5812631a5cf5d3ed)
|
||||
var x10 uint64
|
||||
var x11 fiat_sc255_uint1
|
||||
x10, x11 = fiat_sc255_addcarryx_u64(x9, x6, 0x0)
|
||||
var x13 fiat_sc255_uint1
|
||||
_, x13 = fiat_sc255_addcarryx_u64(x1, x8, 0x0)
|
||||
var x14 uint64
|
||||
var x15 fiat_sc255_uint1
|
||||
x14, x15 = fiat_sc255_addcarryx_u64(uint64(0x0), x10, x13)
|
||||
var x16 uint64
|
||||
var x17 fiat_sc255_uint1
|
||||
x16, x17 = fiat_sc255_addcarryx_u64(x14, (arg1[1]), 0x0)
|
||||
var x18 uint64
|
||||
_, x18 = bits.Mul64(x16, 0xd2b51da312547e1b)
|
||||
var x20 uint64
|
||||
var x21 uint64
|
||||
x21, x20 = bits.Mul64(x18, 0x1000000000000000)
|
||||
var x22 uint64
|
||||
var x23 uint64
|
||||
x23, x22 = bits.Mul64(x18, 0x14def9dea2f79cd6)
|
||||
var x24 uint64
|
||||
var x25 uint64
|
||||
x25, x24 = bits.Mul64(x18, 0x5812631a5cf5d3ed)
|
||||
var x26 uint64
|
||||
var x27 fiat_sc255_uint1
|
||||
x26, x27 = fiat_sc255_addcarryx_u64(x25, x22, 0x0)
|
||||
var x29 fiat_sc255_uint1
|
||||
_, x29 = fiat_sc255_addcarryx_u64(x16, x24, 0x0)
|
||||
var x30 uint64
|
||||
var x31 fiat_sc255_uint1
|
||||
x30, x31 = fiat_sc255_addcarryx_u64((uint64(x17) + (uint64(x15) + (uint64(x11) + x7))), x26, x29)
|
||||
var x32 uint64
|
||||
var x33 fiat_sc255_uint1
|
||||
x32, x33 = fiat_sc255_addcarryx_u64(x4, (uint64(x27) + x23), x31)
|
||||
var x34 uint64
|
||||
var x35 fiat_sc255_uint1
|
||||
x34, x35 = fiat_sc255_addcarryx_u64(x5, x20, x33)
|
||||
var x36 uint64
|
||||
var x37 fiat_sc255_uint1
|
||||
x36, x37 = fiat_sc255_addcarryx_u64(x30, (arg1[2]), 0x0)
|
||||
var x38 uint64
|
||||
var x39 fiat_sc255_uint1
|
||||
x38, x39 = fiat_sc255_addcarryx_u64(x32, uint64(0x0), x37)
|
||||
var x40 uint64
|
||||
var x41 fiat_sc255_uint1
|
||||
x40, x41 = fiat_sc255_addcarryx_u64(x34, uint64(0x0), x39)
|
||||
var x42 uint64
|
||||
_, x42 = bits.Mul64(x36, 0xd2b51da312547e1b)
|
||||
var x44 uint64
|
||||
var x45 uint64
|
||||
x45, x44 = bits.Mul64(x42, 0x1000000000000000)
|
||||
var x46 uint64
|
||||
var x47 uint64
|
||||
x47, x46 = bits.Mul64(x42, 0x14def9dea2f79cd6)
|
||||
var x48 uint64
|
||||
var x49 uint64
|
||||
x49, x48 = bits.Mul64(x42, 0x5812631a5cf5d3ed)
|
||||
var x50 uint64
|
||||
var x51 fiat_sc255_uint1
|
||||
x50, x51 = fiat_sc255_addcarryx_u64(x49, x46, 0x0)
|
||||
var x53 fiat_sc255_uint1
|
||||
_, x53 = fiat_sc255_addcarryx_u64(x36, x48, 0x0)
|
||||
var x54 uint64
|
||||
var x55 fiat_sc255_uint1
|
||||
x54, x55 = fiat_sc255_addcarryx_u64(x38, x50, x53)
|
||||
var x56 uint64
|
||||
var x57 fiat_sc255_uint1
|
||||
x56, x57 = fiat_sc255_addcarryx_u64(x40, (uint64(x51) + x47), x55)
|
||||
var x58 uint64
|
||||
var x59 fiat_sc255_uint1
|
||||
x58, x59 = fiat_sc255_addcarryx_u64((uint64(x41) + (uint64(x35) + x21)), x44, x57)
|
||||
var x60 uint64
|
||||
var x61 fiat_sc255_uint1
|
||||
x60, x61 = fiat_sc255_addcarryx_u64(x54, (arg1[3]), 0x0)
|
||||
var x62 uint64
|
||||
var x63 fiat_sc255_uint1
|
||||
x62, x63 = fiat_sc255_addcarryx_u64(x56, uint64(0x0), x61)
|
||||
var x64 uint64
|
||||
var x65 fiat_sc255_uint1
|
||||
x64, x65 = fiat_sc255_addcarryx_u64(x58, uint64(0x0), x63)
|
||||
var x66 uint64
|
||||
_, x66 = bits.Mul64(x60, 0xd2b51da312547e1b)
|
||||
var x68 uint64
|
||||
var x69 uint64
|
||||
x69, x68 = bits.Mul64(x66, 0x1000000000000000)
|
||||
var x70 uint64
|
||||
var x71 uint64
|
||||
x71, x70 = bits.Mul64(x66, 0x14def9dea2f79cd6)
|
||||
var x72 uint64
|
||||
var x73 uint64
|
||||
x73, x72 = bits.Mul64(x66, 0x5812631a5cf5d3ed)
|
||||
var x74 uint64
|
||||
var x75 fiat_sc255_uint1
|
||||
x74, x75 = fiat_sc255_addcarryx_u64(x73, x70, 0x0)
|
||||
var x77 fiat_sc255_uint1
|
||||
_, x77 = fiat_sc255_addcarryx_u64(x60, x72, 0x0)
|
||||
var x78 uint64
|
||||
var x79 fiat_sc255_uint1
|
||||
x78, x79 = fiat_sc255_addcarryx_u64(x62, x74, x77)
|
||||
var x80 uint64
|
||||
var x81 fiat_sc255_uint1
|
||||
x80, x81 = fiat_sc255_addcarryx_u64(x64, (uint64(x75) + x71), x79)
|
||||
var x82 uint64
|
||||
var x83 fiat_sc255_uint1
|
||||
x82, x83 = fiat_sc255_addcarryx_u64((uint64(x65) + (uint64(x59) + x45)), x68, x81)
|
||||
var x84 uint64 = (uint64(x83) + x69)
|
||||
var x85 uint64
|
||||
var x86 fiat_sc255_uint1
|
||||
x85, x86 = fiat_sc255_subborrowx_u64(x78, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x87 uint64
|
||||
var x88 fiat_sc255_uint1
|
||||
x87, x88 = fiat_sc255_subborrowx_u64(x80, 0x14def9dea2f79cd6, x86)
|
||||
var x89 uint64
|
||||
var x90 fiat_sc255_uint1
|
||||
x89, x90 = fiat_sc255_subborrowx_u64(x82, uint64(0x0), x88)
|
||||
var x91 uint64
|
||||
var x92 fiat_sc255_uint1
|
||||
x91, x92 = fiat_sc255_subborrowx_u64(x84, 0x1000000000000000, x90)
|
||||
var x94 fiat_sc255_uint1
|
||||
_, x94 = fiat_sc255_subborrowx_u64(uint64(0x0), uint64(0x0), x92)
|
||||
var x95 uint64
|
||||
fiat_sc255_cmovznz_u64(&x95, x94, x85, x78)
|
||||
var x96 uint64
|
||||
fiat_sc255_cmovznz_u64(&x96, x94, x87, x80)
|
||||
var x97 uint64
|
||||
fiat_sc255_cmovznz_u64(&x97, x94, x89, x82)
|
||||
var x98 uint64
|
||||
fiat_sc255_cmovznz_u64(&x98, x94, x91, x84)
|
||||
out1[0] = x95
|
||||
out1[1] = x96
|
||||
out1[2] = x97
|
||||
out1[3] = x98
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_to_montgomery translates a field element into the Montgomery domain.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = eval arg1 mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_to_montgomery(out1 *[4]uint64, arg1 *[4]uint64) {
|
||||
var x1 uint64 = (arg1[1])
|
||||
var x2 uint64 = (arg1[2])
|
||||
var x3 uint64 = (arg1[3])
|
||||
var x4 uint64 = (arg1[0])
|
||||
var x5 uint64
|
||||
var x6 uint64
|
||||
x6, x5 = bits.Mul64(x4, 0x399411b7c309a3d)
|
||||
var x7 uint64
|
||||
var x8 uint64
|
||||
x8, x7 = bits.Mul64(x4, 0xceec73d217f5be65)
|
||||
var x9 uint64
|
||||
var x10 uint64
|
||||
x10, x9 = bits.Mul64(x4, 0xd00e1ba768859347)
|
||||
var x11 uint64
|
||||
var x12 uint64
|
||||
x12, x11 = bits.Mul64(x4, 0xa40611e3449c0f01)
|
||||
var x13 uint64
|
||||
var x14 fiat_sc255_uint1
|
||||
x13, x14 = fiat_sc255_addcarryx_u64(x12, x9, 0x0)
|
||||
var x15 uint64
|
||||
var x16 fiat_sc255_uint1
|
||||
x15, x16 = fiat_sc255_addcarryx_u64(x10, x7, x14)
|
||||
var x17 uint64
|
||||
var x18 fiat_sc255_uint1
|
||||
x17, x18 = fiat_sc255_addcarryx_u64(x8, x5, x16)
|
||||
var x19 uint64
|
||||
_, x19 = bits.Mul64(x11, 0xd2b51da312547e1b)
|
||||
var x21 uint64
|
||||
var x22 uint64
|
||||
x22, x21 = bits.Mul64(x19, 0x1000000000000000)
|
||||
var x23 uint64
|
||||
var x24 uint64
|
||||
x24, x23 = bits.Mul64(x19, 0x14def9dea2f79cd6)
|
||||
var x25 uint64
|
||||
var x26 uint64
|
||||
x26, x25 = bits.Mul64(x19, 0x5812631a5cf5d3ed)
|
||||
var x27 uint64
|
||||
var x28 fiat_sc255_uint1
|
||||
x27, x28 = fiat_sc255_addcarryx_u64(x26, x23, 0x0)
|
||||
var x30 fiat_sc255_uint1
|
||||
_, x30 = fiat_sc255_addcarryx_u64(x11, x25, 0x0)
|
||||
var x31 uint64
|
||||
var x32 fiat_sc255_uint1
|
||||
x31, x32 = fiat_sc255_addcarryx_u64(x13, x27, x30)
|
||||
var x33 uint64
|
||||
var x34 fiat_sc255_uint1
|
||||
x33, x34 = fiat_sc255_addcarryx_u64(x15, (uint64(x28) + x24), x32)
|
||||
var x35 uint64
|
||||
var x36 fiat_sc255_uint1
|
||||
x35, x36 = fiat_sc255_addcarryx_u64(x17, x21, x34)
|
||||
var x37 uint64
|
||||
var x38 uint64
|
||||
x38, x37 = bits.Mul64(x1, 0x399411b7c309a3d)
|
||||
var x39 uint64
|
||||
var x40 uint64
|
||||
x40, x39 = bits.Mul64(x1, 0xceec73d217f5be65)
|
||||
var x41 uint64
|
||||
var x42 uint64
|
||||
x42, x41 = bits.Mul64(x1, 0xd00e1ba768859347)
|
||||
var x43 uint64
|
||||
var x44 uint64
|
||||
x44, x43 = bits.Mul64(x1, 0xa40611e3449c0f01)
|
||||
var x45 uint64
|
||||
var x46 fiat_sc255_uint1
|
||||
x45, x46 = fiat_sc255_addcarryx_u64(x44, x41, 0x0)
|
||||
var x47 uint64
|
||||
var x48 fiat_sc255_uint1
|
||||
x47, x48 = fiat_sc255_addcarryx_u64(x42, x39, x46)
|
||||
var x49 uint64
|
||||
var x50 fiat_sc255_uint1
|
||||
x49, x50 = fiat_sc255_addcarryx_u64(x40, x37, x48)
|
||||
var x51 uint64
|
||||
var x52 fiat_sc255_uint1
|
||||
x51, x52 = fiat_sc255_addcarryx_u64(x31, x43, 0x0)
|
||||
var x53 uint64
|
||||
var x54 fiat_sc255_uint1
|
||||
x53, x54 = fiat_sc255_addcarryx_u64(x33, x45, x52)
|
||||
var x55 uint64
|
||||
var x56 fiat_sc255_uint1
|
||||
x55, x56 = fiat_sc255_addcarryx_u64(x35, x47, x54)
|
||||
var x57 uint64
|
||||
var x58 fiat_sc255_uint1
|
||||
x57, x58 = fiat_sc255_addcarryx_u64(((uint64(x36) + (uint64(x18) + x6)) + x22), x49, x56)
|
||||
var x59 uint64
|
||||
_, x59 = bits.Mul64(x51, 0xd2b51da312547e1b)
|
||||
var x61 uint64
|
||||
var x62 uint64
|
||||
x62, x61 = bits.Mul64(x59, 0x1000000000000000)
|
||||
var x63 uint64
|
||||
var x64 uint64
|
||||
x64, x63 = bits.Mul64(x59, 0x14def9dea2f79cd6)
|
||||
var x65 uint64
|
||||
var x66 uint64
|
||||
x66, x65 = bits.Mul64(x59, 0x5812631a5cf5d3ed)
|
||||
var x67 uint64
|
||||
var x68 fiat_sc255_uint1
|
||||
x67, x68 = fiat_sc255_addcarryx_u64(x66, x63, 0x0)
|
||||
var x70 fiat_sc255_uint1
|
||||
_, x70 = fiat_sc255_addcarryx_u64(x51, x65, 0x0)
|
||||
var x71 uint64
|
||||
var x72 fiat_sc255_uint1
|
||||
x71, x72 = fiat_sc255_addcarryx_u64(x53, x67, x70)
|
||||
var x73 uint64
|
||||
var x74 fiat_sc255_uint1
|
||||
x73, x74 = fiat_sc255_addcarryx_u64(x55, (uint64(x68) + x64), x72)
|
||||
var x75 uint64
|
||||
var x76 fiat_sc255_uint1
|
||||
x75, x76 = fiat_sc255_addcarryx_u64(x57, x61, x74)
|
||||
var x77 uint64
|
||||
var x78 uint64
|
||||
x78, x77 = bits.Mul64(x2, 0x399411b7c309a3d)
|
||||
var x79 uint64
|
||||
var x80 uint64
|
||||
x80, x79 = bits.Mul64(x2, 0xceec73d217f5be65)
|
||||
var x81 uint64
|
||||
var x82 uint64
|
||||
x82, x81 = bits.Mul64(x2, 0xd00e1ba768859347)
|
||||
var x83 uint64
|
||||
var x84 uint64
|
||||
x84, x83 = bits.Mul64(x2, 0xa40611e3449c0f01)
|
||||
var x85 uint64
|
||||
var x86 fiat_sc255_uint1
|
||||
x85, x86 = fiat_sc255_addcarryx_u64(x84, x81, 0x0)
|
||||
var x87 uint64
|
||||
var x88 fiat_sc255_uint1
|
||||
x87, x88 = fiat_sc255_addcarryx_u64(x82, x79, x86)
|
||||
var x89 uint64
|
||||
var x90 fiat_sc255_uint1
|
||||
x89, x90 = fiat_sc255_addcarryx_u64(x80, x77, x88)
|
||||
var x91 uint64
|
||||
var x92 fiat_sc255_uint1
|
||||
x91, x92 = fiat_sc255_addcarryx_u64(x71, x83, 0x0)
|
||||
var x93 uint64
|
||||
var x94 fiat_sc255_uint1
|
||||
x93, x94 = fiat_sc255_addcarryx_u64(x73, x85, x92)
|
||||
var x95 uint64
|
||||
var x96 fiat_sc255_uint1
|
||||
x95, x96 = fiat_sc255_addcarryx_u64(x75, x87, x94)
|
||||
var x97 uint64
|
||||
var x98 fiat_sc255_uint1
|
||||
x97, x98 = fiat_sc255_addcarryx_u64(((uint64(x76) + (uint64(x58) + (uint64(x50) + x38))) + x62), x89, x96)
|
||||
var x99 uint64
|
||||
_, x99 = bits.Mul64(x91, 0xd2b51da312547e1b)
|
||||
var x101 uint64
|
||||
var x102 uint64
|
||||
x102, x101 = bits.Mul64(x99, 0x1000000000000000)
|
||||
var x103 uint64
|
||||
var x104 uint64
|
||||
x104, x103 = bits.Mul64(x99, 0x14def9dea2f79cd6)
|
||||
var x105 uint64
|
||||
var x106 uint64
|
||||
x106, x105 = bits.Mul64(x99, 0x5812631a5cf5d3ed)
|
||||
var x107 uint64
|
||||
var x108 fiat_sc255_uint1
|
||||
x107, x108 = fiat_sc255_addcarryx_u64(x106, x103, 0x0)
|
||||
var x110 fiat_sc255_uint1
|
||||
_, x110 = fiat_sc255_addcarryx_u64(x91, x105, 0x0)
|
||||
var x111 uint64
|
||||
var x112 fiat_sc255_uint1
|
||||
x111, x112 = fiat_sc255_addcarryx_u64(x93, x107, x110)
|
||||
var x113 uint64
|
||||
var x114 fiat_sc255_uint1
|
||||
x113, x114 = fiat_sc255_addcarryx_u64(x95, (uint64(x108) + x104), x112)
|
||||
var x115 uint64
|
||||
var x116 fiat_sc255_uint1
|
||||
x115, x116 = fiat_sc255_addcarryx_u64(x97, x101, x114)
|
||||
var x117 uint64
|
||||
var x118 uint64
|
||||
x118, x117 = bits.Mul64(x3, 0x399411b7c309a3d)
|
||||
var x119 uint64
|
||||
var x120 uint64
|
||||
x120, x119 = bits.Mul64(x3, 0xceec73d217f5be65)
|
||||
var x121 uint64
|
||||
var x122 uint64
|
||||
x122, x121 = bits.Mul64(x3, 0xd00e1ba768859347)
|
||||
var x123 uint64
|
||||
var x124 uint64
|
||||
x124, x123 = bits.Mul64(x3, 0xa40611e3449c0f01)
|
||||
var x125 uint64
|
||||
var x126 fiat_sc255_uint1
|
||||
x125, x126 = fiat_sc255_addcarryx_u64(x124, x121, 0x0)
|
||||
var x127 uint64
|
||||
var x128 fiat_sc255_uint1
|
||||
x127, x128 = fiat_sc255_addcarryx_u64(x122, x119, x126)
|
||||
var x129 uint64
|
||||
var x130 fiat_sc255_uint1
|
||||
x129, x130 = fiat_sc255_addcarryx_u64(x120, x117, x128)
|
||||
var x131 uint64
|
||||
var x132 fiat_sc255_uint1
|
||||
x131, x132 = fiat_sc255_addcarryx_u64(x111, x123, 0x0)
|
||||
var x133 uint64
|
||||
var x134 fiat_sc255_uint1
|
||||
x133, x134 = fiat_sc255_addcarryx_u64(x113, x125, x132)
|
||||
var x135 uint64
|
||||
var x136 fiat_sc255_uint1
|
||||
x135, x136 = fiat_sc255_addcarryx_u64(x115, x127, x134)
|
||||
var x137 uint64
|
||||
var x138 fiat_sc255_uint1
|
||||
x137, x138 = fiat_sc255_addcarryx_u64(((uint64(x116) + (uint64(x98) + (uint64(x90) + x78))) + x102), x129, x136)
|
||||
var x139 uint64
|
||||
_, x139 = bits.Mul64(x131, 0xd2b51da312547e1b)
|
||||
var x141 uint64
|
||||
var x142 uint64
|
||||
x142, x141 = bits.Mul64(x139, 0x1000000000000000)
|
||||
var x143 uint64
|
||||
var x144 uint64
|
||||
x144, x143 = bits.Mul64(x139, 0x14def9dea2f79cd6)
|
||||
var x145 uint64
|
||||
var x146 uint64
|
||||
x146, x145 = bits.Mul64(x139, 0x5812631a5cf5d3ed)
|
||||
var x147 uint64
|
||||
var x148 fiat_sc255_uint1
|
||||
x147, x148 = fiat_sc255_addcarryx_u64(x146, x143, 0x0)
|
||||
var x150 fiat_sc255_uint1
|
||||
_, x150 = fiat_sc255_addcarryx_u64(x131, x145, 0x0)
|
||||
var x151 uint64
|
||||
var x152 fiat_sc255_uint1
|
||||
x151, x152 = fiat_sc255_addcarryx_u64(x133, x147, x150)
|
||||
var x153 uint64
|
||||
var x154 fiat_sc255_uint1
|
||||
x153, x154 = fiat_sc255_addcarryx_u64(x135, (uint64(x148) + x144), x152)
|
||||
var x155 uint64
|
||||
var x156 fiat_sc255_uint1
|
||||
x155, x156 = fiat_sc255_addcarryx_u64(x137, x141, x154)
|
||||
var x157 uint64 = ((uint64(x156) + (uint64(x138) + (uint64(x130) + x118))) + x142)
|
||||
var x158 uint64
|
||||
var x159 fiat_sc255_uint1
|
||||
x158, x159 = fiat_sc255_subborrowx_u64(x151, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x160 uint64
|
||||
var x161 fiat_sc255_uint1
|
||||
x160, x161 = fiat_sc255_subborrowx_u64(x153, 0x14def9dea2f79cd6, x159)
|
||||
var x162 uint64
|
||||
var x163 fiat_sc255_uint1
|
||||
x162, x163 = fiat_sc255_subborrowx_u64(x155, uint64(0x0), x161)
|
||||
var x164 uint64
|
||||
var x165 fiat_sc255_uint1
|
||||
x164, x165 = fiat_sc255_subborrowx_u64(x157, 0x1000000000000000, x163)
|
||||
var x167 fiat_sc255_uint1
|
||||
_, x167 = fiat_sc255_subborrowx_u64(uint64(0x0), uint64(0x0), x165)
|
||||
var x168 uint64
|
||||
fiat_sc255_cmovznz_u64(&x168, x167, x158, x151)
|
||||
var x169 uint64
|
||||
fiat_sc255_cmovznz_u64(&x169, x167, x160, x153)
|
||||
var x170 uint64
|
||||
fiat_sc255_cmovznz_u64(&x170, x167, x162, x155)
|
||||
var x171 uint64
|
||||
fiat_sc255_cmovznz_u64(&x171, x167, x164, x157)
|
||||
out1[0] = x168
|
||||
out1[1] = x169
|
||||
out1[2] = x170
|
||||
out1[3] = x171
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [0x0 ~> 0xffffffffffffffff]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_nonzero(out1 *uint64, arg1 *[4]uint64) {
|
||||
var x1 uint64 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))))
|
||||
*out1 = x1
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_selectznz is a multi-limb conditional select.
|
||||
* Postconditions:
|
||||
* eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [0x0 ~> 0x1]
|
||||
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_selectznz(out1 *[4]uint64, arg1 fiat_sc255_uint1, arg2 *[4]uint64, arg3 *[4]uint64) {
|
||||
var x1 uint64
|
||||
fiat_sc255_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]))
|
||||
var x2 uint64
|
||||
fiat_sc255_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]))
|
||||
var x3 uint64
|
||||
fiat_sc255_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]))
|
||||
var x4 uint64
|
||||
fiat_sc255_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]))
|
||||
out1[0] = x1
|
||||
out1[1] = x2
|
||||
out1[2] = x3
|
||||
out1[3] = x4
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg1 < m
|
||||
* Postconditions:
|
||||
* out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1fffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1f]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_to_bytes(out1 *[32]byte, arg1 *[4]uint64) {
|
||||
var x1 uint64 = (arg1[3])
|
||||
var x2 uint64 = (arg1[2])
|
||||
var x3 uint64 = (arg1[1])
|
||||
var x4 uint64 = (arg1[0])
|
||||
var x5 uint8 = (uint8(x4) & 0xff)
|
||||
var x6 uint64 = (x4 >> 8)
|
||||
var x7 uint8 = (uint8(x6) & 0xff)
|
||||
var x8 uint64 = (x6 >> 8)
|
||||
var x9 uint8 = (uint8(x8) & 0xff)
|
||||
var x10 uint64 = (x8 >> 8)
|
||||
var x11 uint8 = (uint8(x10) & 0xff)
|
||||
var x12 uint64 = (x10 >> 8)
|
||||
var x13 uint8 = (uint8(x12) & 0xff)
|
||||
var x14 uint64 = (x12 >> 8)
|
||||
var x15 uint8 = (uint8(x14) & 0xff)
|
||||
var x16 uint64 = (x14 >> 8)
|
||||
var x17 uint8 = (uint8(x16) & 0xff)
|
||||
var x18 uint8 = uint8((x16 >> 8))
|
||||
var x19 uint8 = (uint8(x3) & 0xff)
|
||||
var x20 uint64 = (x3 >> 8)
|
||||
var x21 uint8 = (uint8(x20) & 0xff)
|
||||
var x22 uint64 = (x20 >> 8)
|
||||
var x23 uint8 = (uint8(x22) & 0xff)
|
||||
var x24 uint64 = (x22 >> 8)
|
||||
var x25 uint8 = (uint8(x24) & 0xff)
|
||||
var x26 uint64 = (x24 >> 8)
|
||||
var x27 uint8 = (uint8(x26) & 0xff)
|
||||
var x28 uint64 = (x26 >> 8)
|
||||
var x29 uint8 = (uint8(x28) & 0xff)
|
||||
var x30 uint64 = (x28 >> 8)
|
||||
var x31 uint8 = (uint8(x30) & 0xff)
|
||||
var x32 uint8 = uint8((x30 >> 8))
|
||||
var x33 uint8 = (uint8(x2) & 0xff)
|
||||
var x34 uint64 = (x2 >> 8)
|
||||
var x35 uint8 = (uint8(x34) & 0xff)
|
||||
var x36 uint64 = (x34 >> 8)
|
||||
var x37 uint8 = (uint8(x36) & 0xff)
|
||||
var x38 uint64 = (x36 >> 8)
|
||||
var x39 uint8 = (uint8(x38) & 0xff)
|
||||
var x40 uint64 = (x38 >> 8)
|
||||
var x41 uint8 = (uint8(x40) & 0xff)
|
||||
var x42 uint64 = (x40 >> 8)
|
||||
var x43 uint8 = (uint8(x42) & 0xff)
|
||||
var x44 uint64 = (x42 >> 8)
|
||||
var x45 uint8 = (uint8(x44) & 0xff)
|
||||
var x46 uint8 = uint8((x44 >> 8))
|
||||
var x47 uint8 = (uint8(x1) & 0xff)
|
||||
var x48 uint64 = (x1 >> 8)
|
||||
var x49 uint8 = (uint8(x48) & 0xff)
|
||||
var x50 uint64 = (x48 >> 8)
|
||||
var x51 uint8 = (uint8(x50) & 0xff)
|
||||
var x52 uint64 = (x50 >> 8)
|
||||
var x53 uint8 = (uint8(x52) & 0xff)
|
||||
var x54 uint64 = (x52 >> 8)
|
||||
var x55 uint8 = (uint8(x54) & 0xff)
|
||||
var x56 uint64 = (x54 >> 8)
|
||||
var x57 uint8 = (uint8(x56) & 0xff)
|
||||
var x58 uint64 = (x56 >> 8)
|
||||
var x59 uint8 = (uint8(x58) & 0xff)
|
||||
var x60 uint8 = uint8((x58 >> 8))
|
||||
out1[0] = x5
|
||||
out1[1] = x7
|
||||
out1[2] = x9
|
||||
out1[3] = x11
|
||||
out1[4] = x13
|
||||
out1[5] = x15
|
||||
out1[6] = x17
|
||||
out1[7] = x18
|
||||
out1[8] = x19
|
||||
out1[9] = x21
|
||||
out1[10] = x23
|
||||
out1[11] = x25
|
||||
out1[12] = x27
|
||||
out1[13] = x29
|
||||
out1[14] = x31
|
||||
out1[15] = x32
|
||||
out1[16] = x33
|
||||
out1[17] = x35
|
||||
out1[18] = x37
|
||||
out1[19] = x39
|
||||
out1[20] = x41
|
||||
out1[21] = x43
|
||||
out1[22] = x45
|
||||
out1[23] = x46
|
||||
out1[24] = x47
|
||||
out1[25] = x49
|
||||
out1[26] = x51
|
||||
out1[27] = x53
|
||||
out1[28] = x55
|
||||
out1[29] = x57
|
||||
out1[30] = x59
|
||||
out1[31] = x60
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
|
||||
* Preconditions:
|
||||
* 0 ≤ bytes_eval arg1 < m
|
||||
* Postconditions:
|
||||
* eval out1 mod m = bytes_eval arg1 mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1f]]
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1fffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_from_bytes(out1 *[4]uint64, arg1 *[32]byte) {
|
||||
var x1 uint64 = (uint64((arg1[31])) << 56)
|
||||
var x2 uint64 = (uint64((arg1[30])) << 48)
|
||||
var x3 uint64 = (uint64((arg1[29])) << 40)
|
||||
var x4 uint64 = (uint64((arg1[28])) << 32)
|
||||
var x5 uint64 = (uint64((arg1[27])) << 24)
|
||||
var x6 uint64 = (uint64((arg1[26])) << 16)
|
||||
var x7 uint64 = (uint64((arg1[25])) << 8)
|
||||
var x8 uint8 = (arg1[24])
|
||||
var x9 uint64 = (uint64((arg1[23])) << 56)
|
||||
var x10 uint64 = (uint64((arg1[22])) << 48)
|
||||
var x11 uint64 = (uint64((arg1[21])) << 40)
|
||||
var x12 uint64 = (uint64((arg1[20])) << 32)
|
||||
var x13 uint64 = (uint64((arg1[19])) << 24)
|
||||
var x14 uint64 = (uint64((arg1[18])) << 16)
|
||||
var x15 uint64 = (uint64((arg1[17])) << 8)
|
||||
var x16 uint8 = (arg1[16])
|
||||
var x17 uint64 = (uint64((arg1[15])) << 56)
|
||||
var x18 uint64 = (uint64((arg1[14])) << 48)
|
||||
var x19 uint64 = (uint64((arg1[13])) << 40)
|
||||
var x20 uint64 = (uint64((arg1[12])) << 32)
|
||||
var x21 uint64 = (uint64((arg1[11])) << 24)
|
||||
var x22 uint64 = (uint64((arg1[10])) << 16)
|
||||
var x23 uint64 = (uint64((arg1[9])) << 8)
|
||||
var x24 uint8 = (arg1[8])
|
||||
var x25 uint64 = (uint64((arg1[7])) << 56)
|
||||
var x26 uint64 = (uint64((arg1[6])) << 48)
|
||||
var x27 uint64 = (uint64((arg1[5])) << 40)
|
||||
var x28 uint64 = (uint64((arg1[4])) << 32)
|
||||
var x29 uint64 = (uint64((arg1[3])) << 24)
|
||||
var x30 uint64 = (uint64((arg1[2])) << 16)
|
||||
var x31 uint64 = (uint64((arg1[1])) << 8)
|
||||
var x32 uint8 = (arg1[0])
|
||||
var x33 uint64 = (x31 + uint64(x32))
|
||||
var x34 uint64 = (x30 + x33)
|
||||
var x35 uint64 = (x29 + x34)
|
||||
var x36 uint64 = (x28 + x35)
|
||||
var x37 uint64 = (x27 + x36)
|
||||
var x38 uint64 = (x26 + x37)
|
||||
var x39 uint64 = (x25 + x38)
|
||||
var x40 uint64 = (x23 + uint64(x24))
|
||||
var x41 uint64 = (x22 + x40)
|
||||
var x42 uint64 = (x21 + x41)
|
||||
var x43 uint64 = (x20 + x42)
|
||||
var x44 uint64 = (x19 + x43)
|
||||
var x45 uint64 = (x18 + x44)
|
||||
var x46 uint64 = (x17 + x45)
|
||||
var x47 uint64 = (x15 + uint64(x16))
|
||||
var x48 uint64 = (x14 + x47)
|
||||
var x49 uint64 = (x13 + x48)
|
||||
var x50 uint64 = (x12 + x49)
|
||||
var x51 uint64 = (x11 + x50)
|
||||
var x52 uint64 = (x10 + x51)
|
||||
var x53 uint64 = (x9 + x52)
|
||||
var x54 uint64 = (x7 + uint64(x8))
|
||||
var x55 uint64 = (x6 + x54)
|
||||
var x56 uint64 = (x5 + x55)
|
||||
var x57 uint64 = (x4 + x56)
|
||||
var x58 uint64 = (x3 + x57)
|
||||
var x59 uint64 = (x2 + x58)
|
||||
var x60 uint64 = (x1 + x59)
|
||||
out1[0] = x39
|
||||
out1[1] = x46
|
||||
out1[2] = x53
|
||||
out1[3] = x60
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_set_one returns the field element one in the Montgomery domain.
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) mod m = 1 mod m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_set_one(out1 *[4]uint64) {
|
||||
out1[0] = 0xd6ec31748d98951d
|
||||
out1[1] = 0xc6ef5bf4737dcf70
|
||||
out1[2] = 0xfffffffffffffffe
|
||||
out1[3] = 0xfffffffffffffff
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_msat returns the saturated represtation of the prime modulus.
|
||||
* Postconditions:
|
||||
* twos_complement_eval out1 = m
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_msat(out1 *[5]uint64) {
|
||||
out1[0] = 0x5812631a5cf5d3ed
|
||||
out1[1] = 0x14def9dea2f79cd6
|
||||
out1[2] = uint64(0x0)
|
||||
out1[3] = 0x1000000000000000
|
||||
out1[4] = uint64(0x0)
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
|
||||
* Postconditions:
|
||||
* eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if (log2 m) + 1 < 46 then ⌊(49 * ((log2 m) + 1) + 80) / 17⌋ else ⌊(49 * ((log2 m) + 1) + 57) / 17⌋)
|
||||
* 0 ≤ eval out1 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* Output Bounds:
|
||||
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_divstep_precomp(out1 *[4]uint64) {
|
||||
out1[0] = 0xd70af84436a7cb92
|
||||
out1[1] = 0x5f71c978b0b8b159
|
||||
out1[2] = 0xe76d816974947f1a
|
||||
out1[3] = 0x19a2d36f193e4ff
|
||||
}
|
||||
|
||||
/*
|
||||
* The function fiat_sc255_divstep computes a divstep.
|
||||
* Preconditions:
|
||||
* 0 ≤ eval arg4 < m
|
||||
* 0 ≤ eval arg5 < m
|
||||
* Postconditions:
|
||||
* out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1)
|
||||
* twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2)
|
||||
* twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋)
|
||||
* eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m)
|
||||
* eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m)
|
||||
* 0 ≤ eval out5 < m
|
||||
* 0 ≤ eval out5 < m
|
||||
* 0 ≤ eval out2 < m
|
||||
* 0 ≤ eval out3 < m
|
||||
*
|
||||
* Input Bounds:
|
||||
* arg1: [0x0 ~> 0xffffffffffffffff]
|
||||
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* Output Bounds:
|
||||
* out1: [0x0 ~> 0xffffffffffffffff]
|
||||
* out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
* out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
|
||||
*/
|
||||
/*inline*/
|
||||
func fiat_sc255_divstep(out1 *uint64, out2 *[5]uint64, out3 *[5]uint64, out4 *[4]uint64, out5 *[4]uint64, arg1 uint64, arg2 *[5]uint64, arg3 *[5]uint64, arg4 *[4]uint64, arg5 *[4]uint64) {
|
||||
var x1 uint64
|
||||
x1, _ = fiat_sc255_addcarryx_u64((^arg1), uint64(0x1), 0x0)
|
||||
var x3 fiat_sc255_uint1 = (fiat_sc255_uint1((x1 >> 63)) & (fiat_sc255_uint1((arg3[0])) & 0x1))
|
||||
var x4 uint64
|
||||
x4, _ = fiat_sc255_addcarryx_u64((^arg1), uint64(0x1), 0x0)
|
||||
var x6 uint64
|
||||
fiat_sc255_cmovznz_u64(&x6, x3, arg1, x4)
|
||||
var x7 uint64
|
||||
fiat_sc255_cmovznz_u64(&x7, x3, (arg2[0]), (arg3[0]))
|
||||
var x8 uint64
|
||||
fiat_sc255_cmovznz_u64(&x8, x3, (arg2[1]), (arg3[1]))
|
||||
var x9 uint64
|
||||
fiat_sc255_cmovznz_u64(&x9, x3, (arg2[2]), (arg3[2]))
|
||||
var x10 uint64
|
||||
fiat_sc255_cmovznz_u64(&x10, x3, (arg2[3]), (arg3[3]))
|
||||
var x11 uint64
|
||||
fiat_sc255_cmovznz_u64(&x11, x3, (arg2[4]), (arg3[4]))
|
||||
var x12 uint64
|
||||
var x13 fiat_sc255_uint1
|
||||
x12, x13 = fiat_sc255_addcarryx_u64(uint64(0x1), (^(arg2[0])), 0x0)
|
||||
var x14 uint64
|
||||
var x15 fiat_sc255_uint1
|
||||
x14, x15 = fiat_sc255_addcarryx_u64(uint64(0x0), (^(arg2[1])), x13)
|
||||
var x16 uint64
|
||||
var x17 fiat_sc255_uint1
|
||||
x16, x17 = fiat_sc255_addcarryx_u64(uint64(0x0), (^(arg2[2])), x15)
|
||||
var x18 uint64
|
||||
var x19 fiat_sc255_uint1
|
||||
x18, x19 = fiat_sc255_addcarryx_u64(uint64(0x0), (^(arg2[3])), x17)
|
||||
var x20 uint64
|
||||
x20, _ = fiat_sc255_addcarryx_u64(uint64(0x0), (^(arg2[4])), x19)
|
||||
var x22 uint64
|
||||
fiat_sc255_cmovznz_u64(&x22, x3, (arg3[0]), x12)
|
||||
var x23 uint64
|
||||
fiat_sc255_cmovznz_u64(&x23, x3, (arg3[1]), x14)
|
||||
var x24 uint64
|
||||
fiat_sc255_cmovznz_u64(&x24, x3, (arg3[2]), x16)
|
||||
var x25 uint64
|
||||
fiat_sc255_cmovznz_u64(&x25, x3, (arg3[3]), x18)
|
||||
var x26 uint64
|
||||
fiat_sc255_cmovznz_u64(&x26, x3, (arg3[4]), x20)
|
||||
var x27 uint64
|
||||
fiat_sc255_cmovznz_u64(&x27, x3, (arg4[0]), (arg5[0]))
|
||||
var x28 uint64
|
||||
fiat_sc255_cmovznz_u64(&x28, x3, (arg4[1]), (arg5[1]))
|
||||
var x29 uint64
|
||||
fiat_sc255_cmovznz_u64(&x29, x3, (arg4[2]), (arg5[2]))
|
||||
var x30 uint64
|
||||
fiat_sc255_cmovznz_u64(&x30, x3, (arg4[3]), (arg5[3]))
|
||||
var x31 uint64
|
||||
var x32 fiat_sc255_uint1
|
||||
x31, x32 = fiat_sc255_addcarryx_u64(x27, x27, 0x0)
|
||||
var x33 uint64
|
||||
var x34 fiat_sc255_uint1
|
||||
x33, x34 = fiat_sc255_addcarryx_u64(x28, x28, x32)
|
||||
var x35 uint64
|
||||
var x36 fiat_sc255_uint1
|
||||
x35, x36 = fiat_sc255_addcarryx_u64(x29, x29, x34)
|
||||
var x37 uint64
|
||||
var x38 fiat_sc255_uint1
|
||||
x37, x38 = fiat_sc255_addcarryx_u64(x30, x30, x36)
|
||||
var x39 uint64
|
||||
var x40 fiat_sc255_uint1
|
||||
x39, x40 = fiat_sc255_subborrowx_u64(x31, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x41 uint64
|
||||
var x42 fiat_sc255_uint1
|
||||
x41, x42 = fiat_sc255_subborrowx_u64(x33, 0x14def9dea2f79cd6, x40)
|
||||
var x43 uint64
|
||||
var x44 fiat_sc255_uint1
|
||||
x43, x44 = fiat_sc255_subborrowx_u64(x35, uint64(0x0), x42)
|
||||
var x45 uint64
|
||||
var x46 fiat_sc255_uint1
|
||||
x45, x46 = fiat_sc255_subborrowx_u64(x37, 0x1000000000000000, x44)
|
||||
var x48 fiat_sc255_uint1
|
||||
_, x48 = fiat_sc255_subborrowx_u64(uint64(x38), uint64(0x0), x46)
|
||||
var x49 uint64 = (arg4[3])
|
||||
var x50 uint64 = (arg4[2])
|
||||
var x51 uint64 = (arg4[1])
|
||||
var x52 uint64 = (arg4[0])
|
||||
var x53 uint64
|
||||
var x54 fiat_sc255_uint1
|
||||
x53, x54 = fiat_sc255_subborrowx_u64(uint64(0x0), x52, 0x0)
|
||||
var x55 uint64
|
||||
var x56 fiat_sc255_uint1
|
||||
x55, x56 = fiat_sc255_subborrowx_u64(uint64(0x0), x51, x54)
|
||||
var x57 uint64
|
||||
var x58 fiat_sc255_uint1
|
||||
x57, x58 = fiat_sc255_subborrowx_u64(uint64(0x0), x50, x56)
|
||||
var x59 uint64
|
||||
var x60 fiat_sc255_uint1
|
||||
x59, x60 = fiat_sc255_subborrowx_u64(uint64(0x0), x49, x58)
|
||||
var x61 uint64
|
||||
fiat_sc255_cmovznz_u64(&x61, x60, uint64(0x0), 0xffffffffffffffff)
|
||||
var x62 uint64
|
||||
var x63 fiat_sc255_uint1
|
||||
x62, x63 = fiat_sc255_addcarryx_u64(x53, (x61 & 0x5812631a5cf5d3ed), 0x0)
|
||||
var x64 uint64
|
||||
var x65 fiat_sc255_uint1
|
||||
x64, x65 = fiat_sc255_addcarryx_u64(x55, (x61 & 0x14def9dea2f79cd6), x63)
|
||||
var x66 uint64
|
||||
var x67 fiat_sc255_uint1
|
||||
x66, x67 = fiat_sc255_addcarryx_u64(x57, uint64(0x0), x65)
|
||||
var x68 uint64
|
||||
x68, _ = fiat_sc255_addcarryx_u64(x59, (x61 & 0x1000000000000000), x67)
|
||||
var x70 uint64
|
||||
fiat_sc255_cmovznz_u64(&x70, x3, (arg5[0]), x62)
|
||||
var x71 uint64
|
||||
fiat_sc255_cmovznz_u64(&x71, x3, (arg5[1]), x64)
|
||||
var x72 uint64
|
||||
fiat_sc255_cmovznz_u64(&x72, x3, (arg5[2]), x66)
|
||||
var x73 uint64
|
||||
fiat_sc255_cmovznz_u64(&x73, x3, (arg5[3]), x68)
|
||||
var x74 fiat_sc255_uint1 = (fiat_sc255_uint1(x22) & 0x1)
|
||||
var x75 uint64
|
||||
fiat_sc255_cmovznz_u64(&x75, x74, uint64(0x0), x7)
|
||||
var x76 uint64
|
||||
fiat_sc255_cmovznz_u64(&x76, x74, uint64(0x0), x8)
|
||||
var x77 uint64
|
||||
fiat_sc255_cmovznz_u64(&x77, x74, uint64(0x0), x9)
|
||||
var x78 uint64
|
||||
fiat_sc255_cmovznz_u64(&x78, x74, uint64(0x0), x10)
|
||||
var x79 uint64
|
||||
fiat_sc255_cmovznz_u64(&x79, x74, uint64(0x0), x11)
|
||||
var x80 uint64
|
||||
var x81 fiat_sc255_uint1
|
||||
x80, x81 = fiat_sc255_addcarryx_u64(x22, x75, 0x0)
|
||||
var x82 uint64
|
||||
var x83 fiat_sc255_uint1
|
||||
x82, x83 = fiat_sc255_addcarryx_u64(x23, x76, x81)
|
||||
var x84 uint64
|
||||
var x85 fiat_sc255_uint1
|
||||
x84, x85 = fiat_sc255_addcarryx_u64(x24, x77, x83)
|
||||
var x86 uint64
|
||||
var x87 fiat_sc255_uint1
|
||||
x86, x87 = fiat_sc255_addcarryx_u64(x25, x78, x85)
|
||||
var x88 uint64
|
||||
x88, _ = fiat_sc255_addcarryx_u64(x26, x79, x87)
|
||||
var x90 uint64
|
||||
fiat_sc255_cmovznz_u64(&x90, x74, uint64(0x0), x27)
|
||||
var x91 uint64
|
||||
fiat_sc255_cmovznz_u64(&x91, x74, uint64(0x0), x28)
|
||||
var x92 uint64
|
||||
fiat_sc255_cmovznz_u64(&x92, x74, uint64(0x0), x29)
|
||||
var x93 uint64
|
||||
fiat_sc255_cmovznz_u64(&x93, x74, uint64(0x0), x30)
|
||||
var x94 uint64
|
||||
var x95 fiat_sc255_uint1
|
||||
x94, x95 = fiat_sc255_addcarryx_u64(x70, x90, 0x0)
|
||||
var x96 uint64
|
||||
var x97 fiat_sc255_uint1
|
||||
x96, x97 = fiat_sc255_addcarryx_u64(x71, x91, x95)
|
||||
var x98 uint64
|
||||
var x99 fiat_sc255_uint1
|
||||
x98, x99 = fiat_sc255_addcarryx_u64(x72, x92, x97)
|
||||
var x100 uint64
|
||||
var x101 fiat_sc255_uint1
|
||||
x100, x101 = fiat_sc255_addcarryx_u64(x73, x93, x99)
|
||||
var x102 uint64
|
||||
var x103 fiat_sc255_uint1
|
||||
x102, x103 = fiat_sc255_subborrowx_u64(x94, 0x5812631a5cf5d3ed, 0x0)
|
||||
var x104 uint64
|
||||
var x105 fiat_sc255_uint1
|
||||
x104, x105 = fiat_sc255_subborrowx_u64(x96, 0x14def9dea2f79cd6, x103)
|
||||
var x106 uint64
|
||||
var x107 fiat_sc255_uint1
|
||||
x106, x107 = fiat_sc255_subborrowx_u64(x98, uint64(0x0), x105)
|
||||
var x108 uint64
|
||||
var x109 fiat_sc255_uint1
|
||||
x108, x109 = fiat_sc255_subborrowx_u64(x100, 0x1000000000000000, x107)
|
||||
var x111 fiat_sc255_uint1
|
||||
_, x111 = fiat_sc255_subborrowx_u64(uint64(x101), uint64(0x0), x109)
|
||||
var x112 uint64
|
||||
x112, _ = fiat_sc255_addcarryx_u64(x6, uint64(0x1), 0x0)
|
||||
var x114 uint64 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff))
|
||||
var x115 uint64 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff))
|
||||
var x116 uint64 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff))
|
||||
var x117 uint64 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff))
|
||||
var x118 uint64 = ((x88 & 0x8000000000000000) | (x88 >> 1))
|
||||
var x119 uint64
|
||||
fiat_sc255_cmovznz_u64(&x119, x48, x39, x31)
|
||||
var x120 uint64
|
||||
fiat_sc255_cmovznz_u64(&x120, x48, x41, x33)
|
||||
var x121 uint64
|
||||
fiat_sc255_cmovznz_u64(&x121, x48, x43, x35)
|
||||
var x122 uint64
|
||||
fiat_sc255_cmovznz_u64(&x122, x48, x45, x37)
|
||||
var x123 uint64
|
||||
fiat_sc255_cmovznz_u64(&x123, x111, x102, x94)
|
||||
var x124 uint64
|
||||
fiat_sc255_cmovznz_u64(&x124, x111, x104, x96)
|
||||
var x125 uint64
|
||||
fiat_sc255_cmovznz_u64(&x125, x111, x106, x98)
|
||||
var x126 uint64
|
||||
fiat_sc255_cmovznz_u64(&x126, x111, x108, x100)
|
||||
*out1 = x112
|
||||
out2[0] = x7
|
||||
out2[1] = x8
|
||||
out2[2] = x9
|
||||
out2[3] = x10
|
||||
out2[4] = x11
|
||||
out3[0] = x114
|
||||
out3[1] = x115
|
||||
out3[2] = x116
|
||||
out3[3] = x117
|
||||
out3[4] = x118
|
||||
out4[0] = x119
|
||||
out4[1] = x120
|
||||
out4[2] = x121
|
||||
out4[3] = x122
|
||||
out5[0] = x123
|
||||
out5[1] = x124
|
||||
out5[2] = x125
|
||||
out5[3] = x126
|
||||
}
|
||||
115
scalar.go
115
scalar.go
|
|
@ -21,17 +21,18 @@ import (
|
|||
//
|
||||
// The zero value is a valid zero element.
|
||||
type Scalar struct {
|
||||
// s is the Scalar value in little-endian. The value is always reduced
|
||||
// modulo l between operations.
|
||||
s [32]byte
|
||||
// A Scalar is an integer modulo l = 2^252 + 27742317777372353535851937790883648493.
|
||||
// Internally, this implementation keeps the scalar in the Montgomery domain.
|
||||
s [4]uint64
|
||||
}
|
||||
|
||||
var (
|
||||
scZero = Scalar{[32]byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
|
||||
scZeroBytes = [32]byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
|
||||
scOneBytes = [32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
|
||||
scMinusOneBytes = [32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}
|
||||
|
||||
scOne = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
|
||||
|
||||
scMinusOne = Scalar{[32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}}
|
||||
scOne = Scalar{[4]uint64{0xd6ec31748d98951d, 0xc6ef5bf4737dcf70, 0xfffffffffffffffe, 0xfffffffffffffff}}
|
||||
scMinusOne = Scalar{[4]uint64{0x812631a5cf5d3ed0, 0x4def9dea2f79cd65, 1, 0}}
|
||||
)
|
||||
|
||||
// NewScalar returns a new zero Scalar.
|
||||
|
|
@ -39,37 +40,53 @@ func NewScalar() *Scalar {
|
|||
return &Scalar{}
|
||||
}
|
||||
|
||||
// MultiplyAdd sets s = x * y + z mod l, and returns s.
|
||||
// MultiplyAdd sets s = x * y + z mod l, and returns s. DEPRECATED. Use the individual Add and Multiply methods instead.
|
||||
func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar {
|
||||
scMulAdd(&s.s, &x.s, &y.s, &z.s)
|
||||
var tempFieldElement [4]uint64
|
||||
var xRepr, yRepr, zRepr, tempResult [32]byte
|
||||
|
||||
fiat_sc255_from_montgomery(&tempFieldElement, (*[4]uint64)(&x.s))
|
||||
fiat_sc255_to_bytes(&xRepr, &tempFieldElement)
|
||||
|
||||
fiat_sc255_from_montgomery(&tempFieldElement, (*[4]uint64)(&y.s))
|
||||
fiat_sc255_to_bytes(&yRepr, &tempFieldElement)
|
||||
|
||||
fiat_sc255_from_montgomery(&tempFieldElement, (*[4]uint64)(&z.s))
|
||||
fiat_sc255_to_bytes(&zRepr, &tempFieldElement)
|
||||
|
||||
scMulAdd(&tempResult, &xRepr, &yRepr, &zRepr)
|
||||
|
||||
fiat_sc255_from_bytes(&tempFieldElement, &tempResult)
|
||||
fiat_sc255_to_montgomery((*[4]uint64)(&s.s), &tempFieldElement)
|
||||
|
||||
return s
|
||||
}
|
||||
|
||||
// Add sets s = x + y mod l, and returns s.
|
||||
func (s *Scalar) Add(x, y *Scalar) *Scalar {
|
||||
// s = 1 * x + y mod l
|
||||
scMulAdd(&s.s, &scOne.s, &x.s, &y.s)
|
||||
fiat_sc255_add((*[4]uint64)(&s.s), (*[4]uint64)(&x.s), (*[4]uint64)(&y.s))
|
||||
return s
|
||||
}
|
||||
|
||||
// Subtract sets s = x - y mod l, and returns s.
|
||||
func (s *Scalar) Subtract(x, y *Scalar) *Scalar {
|
||||
// s = -1 * y + x mod l
|
||||
scMulAdd(&s.s, &scMinusOne.s, &y.s, &x.s)
|
||||
fiat_sc255_sub((*[4]uint64)(&s.s), (*[4]uint64)(&x.s), (*[4]uint64)(&y.s))
|
||||
return s
|
||||
}
|
||||
|
||||
// Negate sets s = -x mod l, and returns s.
|
||||
func (s *Scalar) Negate(x *Scalar) *Scalar {
|
||||
// s = -1 * x + 0 mod l
|
||||
scMulAdd(&s.s, &scMinusOne.s, &x.s, &scZero.s)
|
||||
fiat_sc255_opp((*[4]uint64)(&s.s), (*[4]uint64)(&x.s))
|
||||
return s
|
||||
}
|
||||
|
||||
// Multiply sets s = x * y mod l, and returns s.
|
||||
func (s *Scalar) Multiply(x, y *Scalar) *Scalar {
|
||||
// s = x * y + 0 mod l
|
||||
scMulAdd(&s.s, &x.s, &y.s, &scZero.s)
|
||||
fiat_sc255_mul((*[4]uint64)(&s.s), (*[4]uint64)(&x.s), (*[4]uint64)(&y.s))
|
||||
return s
|
||||
}
|
||||
|
||||
|
|
@ -91,7 +108,14 @@ func (s *Scalar) SetUniformBytes(x []byte) (*Scalar, error) {
|
|||
}
|
||||
var wideBytes [64]byte
|
||||
copy(wideBytes[:], x[:])
|
||||
scReduce(&s.s, &wideBytes)
|
||||
|
||||
// TODO: We should deprecate scReduce as well, but we retain it here for consistent behavior
|
||||
var reduced [32]byte
|
||||
scReduce(&reduced, &wideBytes)
|
||||
|
||||
fiat_sc255_from_bytes((*[4]uint64)(&s.s), &reduced)
|
||||
fiat_sc255_to_montgomery((*[4]uint64)(&s.s), (*[4]uint64)(&s.s))
|
||||
|
||||
return s, nil
|
||||
}
|
||||
|
||||
|
|
@ -102,22 +126,31 @@ func (s *Scalar) SetCanonicalBytes(x []byte) (*Scalar, error) {
|
|||
if len(x) != 32 {
|
||||
return nil, errors.New("invalid scalar length")
|
||||
}
|
||||
ss := &Scalar{}
|
||||
copy(ss.s[:], x)
|
||||
if !isReduced(ss) {
|
||||
|
||||
// Use bytes here because the original logic assumed the old 32-byte LE representation
|
||||
ss := [32]byte{}
|
||||
copy(ss[:], x)
|
||||
if !isReduced(ss[:]) {
|
||||
return nil, errors.New("invalid scalar encoding")
|
||||
}
|
||||
s.s = ss.s
|
||||
|
||||
fiat_sc255_from_bytes((*[4]uint64)(&s.s), &ss)
|
||||
fiat_sc255_to_montgomery((*[4]uint64)(&s.s), (*[4]uint64)(&s.s))
|
||||
|
||||
return s, nil
|
||||
}
|
||||
|
||||
// isReduced returns whether the given scalar is reduced modulo l.
|
||||
func isReduced(s *Scalar) bool {
|
||||
for i := len(s.s) - 1; i >= 0; i-- {
|
||||
// isReduced returns whether the given scalar in 32-byte little endian encoded form is reduced modulo l.
|
||||
func isReduced(s []byte) bool {
|
||||
if len(s) != 32 {
|
||||
return false
|
||||
}
|
||||
|
||||
for i := len(s) - 1; i >= 0; i-- {
|
||||
switch {
|
||||
case s.s[i] > scMinusOne.s[i]:
|
||||
case s[i] > scMinusOneBytes[i]:
|
||||
return false
|
||||
case s.s[i] < scMinusOne.s[i]:
|
||||
case s[i] < scMinusOneBytes[i]:
|
||||
return true
|
||||
}
|
||||
}
|
||||
|
|
@ -148,20 +181,34 @@ func (s *Scalar) SetBytesWithClamping(x []byte) (*Scalar, error) {
|
|||
wideBytes[0] &= 248
|
||||
wideBytes[31] &= 63
|
||||
wideBytes[31] |= 64
|
||||
scReduce(&s.s, &wideBytes)
|
||||
var reduced [32]byte
|
||||
scReduce(&reduced, &wideBytes)
|
||||
fiat_sc255_from_bytes((*[4]uint64)(&s.s), &reduced)
|
||||
fiat_sc255_to_montgomery((*[4]uint64)(&s.s), (*[4]uint64)(&s.s))
|
||||
return s, nil
|
||||
}
|
||||
|
||||
// Bytes returns the canonical 32-byte little-endian encoding of s.
|
||||
func (s *Scalar) Bytes() []byte {
|
||||
buf := make([]byte, 32)
|
||||
copy(buf, s.s[:])
|
||||
return buf
|
||||
// This pattern, called "outlining", allows this function to inline so the
|
||||
// allocations can occur on the caller stack rather than escaping to the heap.
|
||||
// See https://blog.filippo.io/efficient-go-apis-with-the-inliner for more details.
|
||||
var encoded [32]byte
|
||||
return s.bytes(&encoded)
|
||||
}
|
||||
|
||||
func (s *Scalar) bytes(out *[32]byte) []byte {
|
||||
var limbs [4]uint64
|
||||
fiat_sc255_from_montgomery(&limbs, (*[4]uint64)(&s.s))
|
||||
fiat_sc255_to_bytes(out, &limbs)
|
||||
return out[:]
|
||||
}
|
||||
|
||||
// Equal returns 1 if s and t are equal, and 0 otherwise.
|
||||
func (s *Scalar) Equal(t *Scalar) int {
|
||||
return subtle.ConstantTimeCompare(s.s[:], t.s[:])
|
||||
st := t.Bytes()
|
||||
ss := s.Bytes()
|
||||
return subtle.ConstantTimeCompare(ss[:], st[:])
|
||||
}
|
||||
|
||||
// scMulAdd and scReduce are ported from the public domain, “ref10”
|
||||
|
|
@ -950,7 +997,8 @@ func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {
|
|||
// This implementation is adapted from the one
|
||||
// in curve25519-dalek and is documented there:
|
||||
// https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/scalar.rs#L800-L871
|
||||
if s.s[31] > 127 {
|
||||
b := s.Bytes()
|
||||
if b[31] > 127 {
|
||||
panic("scalar has high bit set illegally")
|
||||
}
|
||||
if w < 2 {
|
||||
|
|
@ -963,7 +1011,7 @@ func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {
|
|||
var digits [5]uint64
|
||||
|
||||
for i := 0; i < 4; i++ {
|
||||
digits[i] = binary.LittleEndian.Uint64(s.s[i*8:])
|
||||
digits[i] = binary.LittleEndian.Uint64(b[i*8:])
|
||||
}
|
||||
|
||||
width := uint64(1 << w)
|
||||
|
|
@ -1011,7 +1059,8 @@ func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {
|
|||
}
|
||||
|
||||
func (s *Scalar) signedRadix16() [64]int8 {
|
||||
if s.s[31] > 127 {
|
||||
b := s.Bytes()
|
||||
if b[31] > 127 {
|
||||
panic("scalar has high bit set illegally")
|
||||
}
|
||||
|
||||
|
|
@ -1019,8 +1068,8 @@ func (s *Scalar) signedRadix16() [64]int8 {
|
|||
|
||||
// Compute unsigned radix-16 digits:
|
||||
for i := 0; i < 32; i++ {
|
||||
digits[2*i] = int8(s.s[i] & 15)
|
||||
digits[2*i+1] = int8((s.s[i] >> 4) & 15)
|
||||
digits[2*i] = int8(b[i] & 15)
|
||||
digits[2*i+1] = int8((b[i] >> 4) & 15)
|
||||
}
|
||||
|
||||
// Recenter coefficients:
|
||||
|
|
|
|||
|
|
@ -14,12 +14,12 @@ func TestScalarAliasing(t *testing.T) {
|
|||
x1, v1 := x, x
|
||||
|
||||
// Calculate a reference f(x) without aliasing.
|
||||
if out := f(&v, &x); out != &v || !isReduced(out) {
|
||||
if out := f(&v, &x); out != &v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Test aliasing the argument and the receiver.
|
||||
if out := f(&v1, &v1); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
|
|
@ -31,39 +31,39 @@ func TestScalarAliasing(t *testing.T) {
|
|||
x1, y1, v1 := x, y, Scalar{}
|
||||
|
||||
// Calculate a reference f(x, y) without aliasing.
|
||||
if out := f(&v, &x, &y); out != &v || !isReduced(out) {
|
||||
if out := f(&v, &x, &y); out != &v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Test aliasing the first argument and the receiver.
|
||||
v1 = x
|
||||
if out := f(&v1, &v1, &y); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &v1, &y); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
// Test aliasing the second argument and the receiver.
|
||||
v1 = y
|
||||
if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Calculate a reference f(x, x) without aliasing.
|
||||
if out := f(&v, &x, &x); out != &v || !isReduced(out) {
|
||||
if out := f(&v, &x, &x); out != &v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Test aliasing the first argument and the receiver.
|
||||
v1 = x
|
||||
if out := f(&v1, &v1, &x); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &v1, &x); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
// Test aliasing the second argument and the receiver.
|
||||
v1 = x
|
||||
if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
// Test aliasing both arguments and the receiver.
|
||||
v1 = x
|
||||
if out := f(&v1, &v1, &v1); out != &v1 || v1 != v || !isReduced(out) {
|
||||
if out := f(&v1, &v1, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
|
||||
return false
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -17,31 +17,36 @@ import (
|
|||
// Generate returns a valid (reduced modulo l) Scalar with a distribution
|
||||
// weighted towards high, low, and edge values.
|
||||
func (Scalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
|
||||
s := scZero
|
||||
s := scZeroBytes
|
||||
diceRoll := rand.Intn(100)
|
||||
switch {
|
||||
case diceRoll == 0:
|
||||
case diceRoll == 1:
|
||||
s = scOne
|
||||
s = scOneBytes
|
||||
case diceRoll == 2:
|
||||
s = scMinusOne
|
||||
s = scMinusOneBytes
|
||||
case diceRoll < 5:
|
||||
// Generate a low scalar in [0, 2^125).
|
||||
rand.Read(s.s[:16])
|
||||
s.s[15] &= (1 << 5) - 1
|
||||
rand.Read(s[:16])
|
||||
s[15] &= (1 << 5) - 1
|
||||
case diceRoll < 10:
|
||||
// Generate a high scalar in [2^252, 2^252 + 2^124).
|
||||
s.s[31] = 1 << 4
|
||||
rand.Read(s.s[:16])
|
||||
s.s[15] &= (1 << 4) - 1
|
||||
s[31] = 1 << 4
|
||||
rand.Read(s[:16])
|
||||
s[15] &= (1 << 4) - 1
|
||||
default:
|
||||
// Generate a valid scalar in [0, l) by returning [0, 2^252) which has a
|
||||
// negligibly different distribution (the former has a 2^-127.6 chance
|
||||
// of being out of the latter range).
|
||||
rand.Read(s.s[:])
|
||||
s.s[31] &= (1 << 4) - 1
|
||||
rand.Read(s[:])
|
||||
s[31] &= (1 << 4) - 1
|
||||
}
|
||||
return reflect.ValueOf(s)
|
||||
|
||||
val := Scalar{}
|
||||
fiat_sc255_from_bytes(&val.s, &s)
|
||||
fiat_sc255_to_montgomery(&val.s, &val.s)
|
||||
|
||||
return reflect.ValueOf(val)
|
||||
}
|
||||
|
||||
// quickCheckConfig1024 will make each quickcheck test run (1024 * -quickchecks)
|
||||
|
|
@ -50,7 +55,7 @@ var quickCheckConfig1024 = &quick.Config{MaxCountScale: 1 << 10}
|
|||
|
||||
func TestScalarGenerate(t *testing.T) {
|
||||
f := func(sc Scalar) bool {
|
||||
return isReduced(&sc)
|
||||
return isReduced(sc.Bytes())
|
||||
}
|
||||
if err := quick.Check(f, quickCheckConfig1024); err != nil {
|
||||
t.Errorf("generated unreduced scalar: %v", err)
|
||||
|
|
@ -64,7 +69,8 @@ func TestScalarSetCanonicalBytes(t *testing.T) {
|
|||
if _, err := sc.SetCanonicalBytes(in[:]); err != nil {
|
||||
return false
|
||||
}
|
||||
return bytes.Equal(in[:], sc.Bytes()) && isReduced(&sc)
|
||||
repr := sc.Bytes()
|
||||
return bytes.Equal(in[:], repr) && isReduced(repr)
|
||||
}
|
||||
if err := quick.Check(f1, quickCheckConfig1024); err != nil {
|
||||
t.Errorf("failed bytes->scalar->bytes round-trip: %v", err)
|
||||
|
|
@ -80,7 +86,7 @@ func TestScalarSetCanonicalBytes(t *testing.T) {
|
|||
t.Errorf("failed scalar->bytes->scalar round-trip: %v", err)
|
||||
}
|
||||
|
||||
b := scMinusOne.s
|
||||
b := scMinusOneBytes
|
||||
b[31] += 1
|
||||
s := scOne
|
||||
if out, err := s.SetCanonicalBytes(b[:]); err == nil {
|
||||
|
|
@ -97,10 +103,11 @@ func TestScalarSetUniformBytes(t *testing.T) {
|
|||
mod.Add(mod, new(big.Int).Lsh(big.NewInt(1), 252))
|
||||
f := func(in [64]byte, sc Scalar) bool {
|
||||
sc.SetUniformBytes(in[:])
|
||||
if !isReduced(&sc) {
|
||||
repr := sc.Bytes()
|
||||
if !isReduced(repr) {
|
||||
return false
|
||||
}
|
||||
scBig := bigIntFromLittleEndianBytes(sc.s[:])
|
||||
scBig := bigIntFromLittleEndianBytes(repr[:])
|
||||
inBig := bigIntFromLittleEndianBytes(in[:])
|
||||
return inBig.Mod(inBig, mod).Cmp(scBig) == 0
|
||||
}
|
||||
|
|
@ -159,7 +166,9 @@ func TestScalarMultiplyDistributesOverAdd(t *testing.T) {
|
|||
t3.Multiply(&y, &z)
|
||||
t2.Add(&t2, &t3)
|
||||
|
||||
return t1 == t2 && isReduced(&t1) && isReduced(&t3)
|
||||
reprT1, reprT2 := t1.Bytes(), t2.Bytes()
|
||||
|
||||
return t1 == t2 && isReduced(reprT1) && isReduced(reprT2)
|
||||
}
|
||||
|
||||
if err := quick.Check(multiplyDistributesOverAdd, quickCheckConfig1024); err != nil {
|
||||
|
|
@ -178,7 +187,7 @@ func TestScalarAddLikeSubNeg(t *testing.T) {
|
|||
t2.Negate(&y)
|
||||
t2.Add(&t2, &x)
|
||||
|
||||
return t1 == t2 && isReduced(&t1)
|
||||
return t1 == t2 && isReduced(t1.Bytes())
|
||||
}
|
||||
|
||||
if err := quick.Check(addLikeSubNeg, quickCheckConfig1024); err != nil {
|
||||
|
|
@ -187,12 +196,13 @@ func TestScalarAddLikeSubNeg(t *testing.T) {
|
|||
}
|
||||
|
||||
func TestScalarNonAdjacentForm(t *testing.T) {
|
||||
s := Scalar{[32]byte{
|
||||
s, _ := (&Scalar{}).SetCanonicalBytes([]byte{
|
||||
0x1a, 0x0e, 0x97, 0x8a, 0x90, 0xf6, 0x62, 0x2d,
|
||||
0x37, 0x47, 0x02, 0x3f, 0x8a, 0xd8, 0x26, 0x4d,
|
||||
0xa7, 0x58, 0xaa, 0x1b, 0x88, 0xe0, 0x40, 0xd1,
|
||||
0x58, 0x9e, 0x7b, 0x7f, 0x23, 0x76, 0xef, 0x09,
|
||||
}}
|
||||
})
|
||||
|
||||
expectedNaf := [256]int8{
|
||||
0, 13, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -11, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1,
|
||||
0, 0, 0, 0, 9, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 11, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0,
|
||||
|
|
@ -217,7 +227,8 @@ type notZeroScalar Scalar
|
|||
|
||||
func (notZeroScalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
|
||||
var s Scalar
|
||||
for s == scZero {
|
||||
var isNonZero uint64
|
||||
for fiat_sc255_nonzero(&isNonZero, (*[4]uint64)(&s.s)); isNonZero == 0; {
|
||||
s = Scalar{}.Generate(rand, size).Interface().(Scalar)
|
||||
}
|
||||
return reflect.ValueOf(notZeroScalar(s))
|
||||
|
|
|
|||
|
|
@ -15,7 +15,7 @@ var (
|
|||
quickCheckConfig32 = &quick.Config{MaxCountScale: 1 << 5}
|
||||
|
||||
// a random scalar generated using dalek.
|
||||
dalekScalar = Scalar{[32]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4}}
|
||||
dalekScalar, _ = (&Scalar{}).SetCanonicalBytes([]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4})
|
||||
// the above, times the edwards25519 basepoint.
|
||||
dalekScalarBasepoint, _ = new(Point).SetBytes([]byte{0xf4, 0xef, 0x7c, 0xa, 0x34, 0x55, 0x7b, 0x9f, 0x72, 0x3b, 0xb6, 0x1e, 0xf9, 0x46, 0x9, 0x91, 0x1c, 0xb9, 0xc0, 0x6c, 0x17, 0x28, 0x2d, 0x8b, 0x43, 0x2b, 0x5, 0x18, 0x6a, 0x54, 0x3e, 0x48})
|
||||
)
|
||||
|
|
@ -29,8 +29,8 @@ func TestScalarMultSmallScalars(t *testing.T) {
|
|||
}
|
||||
checkOnCurve(t, &p)
|
||||
|
||||
z = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
|
||||
p.ScalarMult(&z, B)
|
||||
scEight, _ := (&Scalar{}).SetCanonicalBytes([]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
|
||||
p.ScalarMult(scEight, B)
|
||||
if B.Equal(&p) != 1 {
|
||||
t.Error("1*B != 1")
|
||||
}
|
||||
|
|
@ -39,7 +39,7 @@ func TestScalarMultSmallScalars(t *testing.T) {
|
|||
|
||||
func TestScalarMultVsDalek(t *testing.T) {
|
||||
var p Point
|
||||
p.ScalarMult(&dalekScalar, B)
|
||||
p.ScalarMult(dalekScalar, B)
|
||||
if dalekScalarBasepoint.Equal(&p) != 1 {
|
||||
t.Error("Scalar mul does not match dalek")
|
||||
}
|
||||
|
|
@ -48,7 +48,7 @@ func TestScalarMultVsDalek(t *testing.T) {
|
|||
|
||||
func TestBaseMultVsDalek(t *testing.T) {
|
||||
var p Point
|
||||
p.ScalarBaseMult(&dalekScalar)
|
||||
p.ScalarBaseMult(dalekScalar)
|
||||
if dalekScalarBasepoint.Equal(&p) != 1 {
|
||||
t.Error("Scalar mul does not match dalek")
|
||||
}
|
||||
|
|
@ -58,12 +58,12 @@ func TestBaseMultVsDalek(t *testing.T) {
|
|||
func TestVarTimeDoubleBaseMultVsDalek(t *testing.T) {
|
||||
var p Point
|
||||
var z Scalar
|
||||
p.VarTimeDoubleScalarBaseMult(&dalekScalar, B, &z)
|
||||
p.VarTimeDoubleScalarBaseMult(dalekScalar, B, &z)
|
||||
if dalekScalarBasepoint.Equal(&p) != 1 {
|
||||
t.Error("VarTimeDoubleScalarBaseMult fails with b=0")
|
||||
}
|
||||
checkOnCurve(t, &p)
|
||||
p.VarTimeDoubleScalarBaseMult(&z, B, &dalekScalar)
|
||||
p.VarTimeDoubleScalarBaseMult(&z, B, dalekScalar)
|
||||
if dalekScalarBasepoint.Equal(&p) != 1 {
|
||||
t.Error("VarTimeDoubleScalarBaseMult fails with a=0")
|
||||
}
|
||||
|
|
@ -188,7 +188,7 @@ func BenchmarkScalarBaseMult(b *testing.B) {
|
|||
var p Point
|
||||
|
||||
for i := 0; i < b.N; i++ {
|
||||
p.ScalarBaseMult(&dalekScalar)
|
||||
p.ScalarBaseMult(dalekScalar)
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -196,7 +196,7 @@ func BenchmarkScalarMult(b *testing.B) {
|
|||
var p Point
|
||||
|
||||
for i := 0; i < b.N; i++ {
|
||||
p.ScalarMult(&dalekScalar, B)
|
||||
p.ScalarMult(dalekScalar, B)
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -204,6 +204,6 @@ func BenchmarkVarTimeDoubleScalarBaseMult(b *testing.B) {
|
|||
var p Point
|
||||
|
||||
for i := 0; i < b.N; i++ {
|
||||
p.VarTimeDoubleScalarBaseMult(&dalekScalar, B, &dalekScalar)
|
||||
p.VarTimeDoubleScalarBaseMult(dalekScalar, B, dalekScalar)
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue