v/vlib/crypto/ed25519/internal/edwards25519/scalar.v

1174 lines
29 KiB
V

module edwards25519
import rand
import encoding.binary
import crypto.internal.subtle
// A Scalar is an integer modulo
//
// l = 2^252 + 27742317777372353535851937790883648493
//
// which is the prime order of the edwards25519 group.
//
// This type works similarly to math/big.Int, and all arguments and
// receivers are allowed to alias.
//
// The zero value is a valid zero element.
struct Scalar {
mut:
// s is the Scalar value in little-endian. The value is always reduced
// between operations.
s [32]byte
}
pub const (
sc_zero = Scalar{
s: [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]!
}
sc_one = Scalar{
s: [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]!
}
sc_minus_one = Scalar{
s: [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]!
}
)
// new_scalar return new zero scalar
pub fn new_scalar() Scalar {
return Scalar{}
}
// add sets s = x + y mod l, and returns s.
pub fn (mut s Scalar) add(x Scalar, y Scalar) Scalar {
// s = 1 * x + y mod l
sc_mul_add(mut s.s, edwards25519.sc_one.s, x.s, y.s)
return s
}
// multiply_add sets s = x * y + z mod l, and returns s.
pub fn (mut s Scalar) multiply_add(x Scalar, y Scalar, z Scalar) Scalar {
sc_mul_add(mut s.s, x.s, y.s, z.s)
return s
}
// subtract sets s = x - y mod l, and returns s.
pub fn (mut s Scalar) subtract(x Scalar, y Scalar) Scalar {
// s = -1 * y + x mod l
sc_mul_add(mut s.s, edwards25519.sc_minus_one.s, y.s, x.s)
return s
}
// negate sets s = -x mod l, and returns s.
pub fn (mut s Scalar) negate(x Scalar) Scalar {
// s = -1 * x + 0 mod l
sc_mul_add(mut s.s, edwards25519.sc_minus_one.s, x.s, edwards25519.sc_zero.s)
return s
}
// multiply sets s = x * y mod l, and returns s.
pub fn (mut s Scalar) multiply(x Scalar, y Scalar) Scalar {
// s = x * y + 0 mod l
sc_mul_add(mut s.s, x.s, y.s, edwards25519.sc_zero.s)
return s
}
// set sets s = x, and returns s.
pub fn (mut s Scalar) set(x Scalar) Scalar {
s = x
return s
}
// set_uniform_bytes sets s to an uniformly distributed value given 64 uniformly
// distributed random bytes. If x is not of the right length, set_uniform_bytes
// returns an error, and the receiver is unchanged.
pub fn (mut s Scalar) set_uniform_bytes(x []byte) ?Scalar {
if x.len != 64 {
return error('edwards25519: invalid set_uniform_bytes input length')
}
mut wide_bytes := []byte{len: 64}
copy(wide_bytes, x)
// for i, item in x {
// wide_bytes[i] = item
//}
sc_reduce(mut s.s, mut wide_bytes)
return s
}
// set_canonical_bytes sets s = x, where x is a 32-byte little-endian encoding of
// s, and returns s. If x is not a canonical encoding of s, set_canonical_bytes
// returns an error, and the receiver is unchanged.
pub fn (mut s Scalar) set_canonical_bytes(x []byte) ?Scalar {
if x.len != 32 {
return error('invalid scalar length')
}
// mut bb := []byte{len:32}
mut ss := Scalar{}
for i, item in x {
ss.s[i] = item
}
//_ := copy(ss.s[..], x) //its not working
if !is_reduced(ss) {
return error('invalid scalar encoding')
}
s.s = ss.s
return s
}
// is_reduced returns whether the given scalar is reduced modulo l.
fn is_reduced(s Scalar) bool {
for i := s.s.len - 1; i >= 0; i-- {
if s.s[i] > edwards25519.sc_minus_one.s[i] {
return false
}
if s.s[i] < edwards25519.sc_minus_one.s[i] {
return true
}
/*
switch {
case s.s[i] > sc_minus_one.s[i]:
return false
case s.s[i] < sc_minus_one.s[i]:
return true
}
*/
}
return true
}
// set_bytes_with_clamping applies the buffer pruning described in RFC 8032,
// Section 5.1.5 (also known as clamping) and sets s to the result. The input
// must be 32 bytes, and it is not modified. If x is not of the right length,
// `set_bytes_with_clamping` returns an error, and the receiver is unchanged.
//
// Note that since Scalar values are always reduced modulo the prime order of
// the curve, the resulting value will not preserve any of the cofactor-clearing
// properties that clamping is meant to provide. It will however work as
// expected as long as it is applied to points on the prime order subgroup, like
// in Ed25519. In fact, it is lost to history why RFC 8032 adopted the
// irrelevant RFC 7748 clamping, but it is now required for compatibility.
pub fn (mut s Scalar) set_bytes_with_clamping(x []byte) ?Scalar {
// The description above omits the purpose of the high bits of the clamping
// for brevity, but those are also lost to reductions, and are also
// irrelevant to edwards25519 as they protect against a specific
// implementation bug that was once observed in a generic Montgomery ladder.
if x.len != 32 {
return error('edwards25519: invalid set_bytes_with_clamping input length')
}
mut wide_bytes := []byte{len: 64, cap: 64}
copy(wide_bytes, x)
// for i, item in x {
// wide_bytes[i] = item
//}
wide_bytes[0] &= 248
wide_bytes[31] &= 63
wide_bytes[31] |= 64
sc_reduce(mut s.s, mut wide_bytes)
return s
}
// bytes returns the canonical 32-byte little-endian encoding of s.
pub fn (mut s Scalar) bytes() []byte {
mut buf := []byte{len: 32}
copy(buf, s.s[..])
return buf
}
// equal returns 1 if s and t are equal, and 0 otherwise.
pub fn (s Scalar) equal(t Scalar) int {
return subtle.constant_time_compare(s.s[..], t.s[..])
}
// sc_mul_add and sc_reduce are ported from the public domain, “ref10”
// implementation of ed25519 from SUPERCOP.
fn load3(inp []byte) i64 {
mut r := i64(inp[0])
r |= i64(inp[1]) * 256 // << 8
r |= i64(inp[2]) * 65536 // << 16
return r
}
fn load4(inp []byte) i64 {
mut r := i64(inp[0])
r |= i64(inp[1]) * 256
r |= i64(inp[2]) * 65536
r |= i64(inp[3]) * 16777216
return r
}
// Input:
// a[0]+256*a[1]+...+256^31*a[31] = a
// b[0]+256*b[1]+...+256^31*b[31] = b
// c[0]+256*c[1]+...+256^31*c[31] = c
//
// Output:
// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
// where l = 2^252 + 27742317777372353535851937790883648493.
fn sc_mul_add(mut s [32]byte, a [32]byte, b [32]byte, c [32]byte) {
a0 := 2097151 & load3(a[..])
a1 := 2097151 & (load4(a[2..]) >> 5)
a2 := 2097151 & (load3(a[5..]) >> 2)
a3 := 2097151 & (load4(a[7..]) >> 7)
a4 := 2097151 & (load4(a[10..]) >> 4)
a5 := 2097151 & (load3(a[13..]) >> 1)
a6 := 2097151 & (load4(a[15..]) >> 6)
a7 := 2097151 & (load3(a[18..]) >> 3)
a8 := 2097151 & load3(a[21..])
a9 := 2097151 & (load4(a[23..]) >> 5)
a10 := 2097151 & (load3(a[26..]) >> 2)
a11 := (load4(a[28..]) >> 7)
b0 := 2097151 & load3(b[..])
b1 := 2097151 & (load4(b[2..]) >> 5)
b2 := 2097151 & (load3(b[5..]) >> 2)
b3 := 2097151 & (load4(b[7..]) >> 7)
b4 := 2097151 & (load4(b[10..]) >> 4)
b5 := 2097151 & (load3(b[13..]) >> 1)
b6 := 2097151 & (load4(b[15..]) >> 6)
b7 := 2097151 & (load3(b[18..]) >> 3)
b8 := 2097151 & load3(b[21..])
b9 := 2097151 & (load4(b[23..]) >> 5)
b10 := 2097151 & (load3(b[26..]) >> 2)
b11 := (load4(b[28..]) >> 7)
c0 := 2097151 & load3(c[..])
c1 := 2097151 & (load4(c[2..]) >> 5)
c2 := 2097151 & (load3(c[5..]) >> 2)
c3 := 2097151 & (load4(c[7..]) >> 7)
c4 := 2097151 & (load4(c[10..]) >> 4)
c5 := 2097151 & (load3(c[13..]) >> 1)
c6 := 2097151 & (load4(c[15..]) >> 6)
c7 := 2097151 & (load3(c[18..]) >> 3)
c8 := 2097151 & load3(c[21..])
c9 := 2097151 & (load4(c[23..]) >> 5)
c10 := 2097151 & (load3(c[26..]) >> 2)
c11 := (load4(c[28..]) >> 7)
mut carry := [23]i64{} // original one
// mut carry := [23]u64{}
mut s0 := c0 + a0 * b0
mut s1 := c1 + a0 * b1 + a1 * b0
mut s2 := c2 + a0 * b2 + a1 * b1 + a2 * b0
mut s3 := c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0
mut s4 := c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0
mut s5 := c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0
mut s6 := c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0
mut s7 := c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0
mut s8 := c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 +
a8 * b0
mut s9 := c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 +
a8 * b1 + a9 * b0
mut s10 := c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 +
a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0
mut s11 := c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 +
a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0
mut s12 := a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 +
a9 * b3 + a10 * b2 + a11 * b1
mut s13 := a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 +
a10 * b3 + a11 * b2
mut s14 := a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 +
a11 * b3
mut s15 := a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4
mut s16 := a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5
mut s17 := a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6
mut s18 := a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7
mut s19 := a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8
mut s20 := a9 * b11 + a10 * b10 + a11 * b9
mut s21 := a10 * b11 + a11 * b10
mut s22 := a11 * b11
mut s23 := i64(0) // original
// mut s23 := u64(0)
// carry[0] = (s0 + (1048576)) >> 21
carry[0] = (s0 + (1048576)) >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[2] = (s2 + (1048576)) >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[4] = (s4 + (1048576)) >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[6] = (s6 + (1048576)) >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[8] = (s8 + (1048576)) >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[10] = (s10 + (1048576)) >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[12] = (s12 + (1048576)) >> 21
s13 += carry[12]
s12 -= carry[12] * 2097152
carry[14] = (s14 + (1048576)) >> 21
s15 += carry[14]
s14 -= carry[14] * 2097152
carry[16] = (s16 + (1048576)) >> 21
s17 += carry[16]
s16 -= carry[16] * 2097152
carry[18] = (s18 + (1048576)) >> 21
s19 += carry[18]
s18 -= carry[18] * 2097152
carry[20] = (s20 + (1048576)) >> 21
s21 += carry[20]
s20 -= carry[20] * 2097152
carry[22] = (s22 + (1048576)) >> 21
s23 += carry[22]
s22 -= carry[22] * 2097152
carry[1] = (s1 + (1048576)) >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[3] = (s3 + (1048576)) >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[5] = (s5 + (1048576)) >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[7] = (s7 + (1048576)) >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[9] = (s9 + (1048576)) >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[11] = (s11 + (1048576)) >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
carry[13] = (s13 + (1048576)) >> 21
s14 += carry[13]
s13 -= carry[13] * 2097152
carry[15] = (s15 + (1048576)) >> 21
s16 += carry[15]
s15 -= carry[15] * 2097152
carry[17] = (s17 + (1048576)) >> 21
s18 += carry[17]
s17 -= carry[17] * 2097152
carry[19] = (s19 + (1048576)) >> 21
s20 += carry[19]
s19 -= carry[19] * 2097152
carry[21] = (s21 + (1048576)) >> 21
s22 += carry[21]
s21 -= carry[21] * 2097152
s11 += s23 * 666643
s12 += s23 * 470296
s13 += s23 * 654183
s14 -= s23 * 997805
s15 += s23 * 136657
s16 -= s23 * 683901
s23 = 0
s10 += s22 * 666643
s11 += s22 * 470296
s12 += s22 * 654183
s13 -= s22 * 997805
s14 += s22 * 136657
s15 -= s22 * 683901
s22 = 0
s9 += s21 * 666643
s10 += s21 * 470296
s11 += s21 * 654183
s12 -= s21 * 997805
s13 += s21 * 136657
s14 -= s21 * 683901
s21 = 0
s8 += s20 * 666643
s9 += s20 * 470296
s10 += s20 * 654183
s11 -= s20 * 997805
s12 += s20 * 136657
s13 -= s20 * 683901
s20 = 0
s7 += s19 * 666643
s8 += s19 * 470296
s9 += s19 * 654183
s10 -= s19 * 997805
s11 += s19 * 136657
s12 -= s19 * 683901
s19 = 0
s6 += s18 * 666643
s7 += s18 * 470296
s8 += s18 * 654183
s9 -= s18 * 997805
s10 += s18 * 136657
s11 -= s18 * 683901
s18 = 0
carry[6] = (s6 + (1048576)) >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[8] = (s8 + (1048576)) >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[10] = (s10 + (1048576)) >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[12] = (s12 + (1048576)) >> 21
s13 += carry[12]
s12 -= carry[12] * 2097152
carry[14] = (s14 + (1048576)) >> 21
s15 += carry[14]
s14 -= carry[14] * 2097152
carry[16] = (s16 + (1048576)) >> 21
s17 += carry[16]
s16 -= carry[16] * 2097152
carry[7] = (s7 + (1048576)) >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[9] = (s9 + (1048576)) >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[11] = (s11 + (1048576)) >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
carry[13] = (s13 + (1048576)) >> 21
s14 += carry[13]
s13 -= carry[13] * 2097152
carry[15] = (s15 + (1048576)) >> 21
s16 += carry[15]
s15 -= carry[15] * 2097152
s5 += s17 * 666643
s6 += s17 * 470296
s7 += s17 * 654183
s8 -= s17 * 997805
s9 += s17 * 136657
s10 -= s17 * 683901
s17 = 0
s4 += s16 * 666643
s5 += s16 * 470296
s6 += s16 * 654183
s7 -= s16 * 997805
s8 += s16 * 136657
s9 -= s16 * 683901
s16 = 0
s3 += s15 * 666643
s4 += s15 * 470296
s5 += s15 * 654183
s6 -= s15 * 997805
s7 += s15 * 136657
s8 -= s15 * 683901
s15 = 0
s2 += s14 * 666643
s3 += s14 * 470296
s4 += s14 * 654183
s5 -= s14 * 997805
s6 += s14 * 136657
s7 -= s14 * 683901
s14 = 0
s1 += s13 * 666643
s2 += s13 * 470296
s3 += s13 * 654183
s4 -= s13 * 997805
s5 += s13 * 136657
s6 -= s13 * 683901
s13 = 0
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = (s0 + (1048576)) >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[2] = (s2 + (1048576)) >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[4] = (s4 + (1048576)) >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[6] = (s6 + (1048576)) >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[8] = (s8 + (1048576)) >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[10] = (s10 + (1048576)) >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[1] = (s1 + (1048576)) >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[3] = (s3 + (1048576)) >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[5] = (s5 + (1048576)) >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[7] = (s7 + (1048576)) >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[9] = (s9 + (1048576)) >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[11] = (s11 + (1048576)) >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = s0 >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[1] = s1 >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[2] = s2 >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[3] = s3 >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[4] = s4 >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[5] = s5 >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[6] = s6 >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[7] = s7 >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[8] = s8 >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[9] = s9 >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[10] = s10 >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[11] = s11 >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = s0 >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[1] = s1 >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[2] = s2 >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[3] = s3 >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[4] = s4 >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[5] = s5 >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[6] = s6 >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[7] = s7 >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[8] = s8 >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[9] = s9 >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[10] = s10 >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
s[0] = byte(s0 >> 0)
s[1] = byte(s0 >> 8)
s[2] = byte((s0 >> 16) | (s1 * 32))
s[3] = byte(s1 >> 3)
s[4] = byte(s1 >> 11)
s[5] = byte((s1 >> 19) | (s2 * 4))
s[6] = byte(s2 >> 6)
s[7] = byte((s2 >> 14) | (s3 * 128))
s[8] = byte(s3 >> 1)
s[9] = byte(s3 >> 9)
s[10] = byte((s3 >> 17) | (s4 * 16))
s[11] = byte(s4 >> 4)
s[12] = byte(s4 >> 12)
s[13] = byte((s4 >> 20) | (s5 * 2))
s[14] = byte(s5 >> 7)
s[15] = byte((s5 >> 15) | (s6 * 64))
s[16] = byte(s6 >> 2)
s[17] = byte(s6 >> 10)
s[18] = byte((s6 >> 18) | (s7 * 8))
s[19] = byte(s7 >> 5)
s[20] = byte(s7 >> 13)
s[21] = byte(s8 >> 0)
s[22] = byte(s8 >> 8)
s[23] = byte((s8 >> 16) | (s9 * 32))
s[24] = byte(s9 >> 3)
s[25] = byte(s9 >> 11)
s[26] = byte((s9 >> 19) | (s10 * 4))
s[27] = byte(s10 >> 6)
s[28] = byte((s10 >> 14) | (s11 * 128))
s[29] = byte(s11 >> 1)
s[30] = byte(s11 >> 9)
s[31] = byte(s11 >> 17)
}
// Input:
// s[0]+256*s[1]+...+256^63*s[63] = s
//
// Output:
// s[0]+256*s[1]+...+256^31*s[31] = s mod l
// where l = 2^252 + 27742317777372353535851937790883648493.
fn sc_reduce(mut out [32]byte, mut s []byte) {
assert out.len == 32
assert s.len == 64
mut s0 := 2097151 & load3(s[..])
mut s1 := 2097151 & (load4(s[2..]) >> 5)
mut s2 := 2097151 & (load3(s[5..]) >> 2)
mut s3 := 2097151 & (load4(s[7..]) >> 7)
mut s4 := 2097151 & (load4(s[10..]) >> 4)
mut s5 := 2097151 & (load3(s[13..]) >> 1)
mut s6 := 2097151 & (load4(s[15..]) >> 6)
mut s7 := 2097151 & (load3(s[18..]) >> 3)
mut s8 := 2097151 & load3(s[21..])
mut s9 := 2097151 & (load4(s[23..]) >> 5)
mut s10 := 2097151 & (load3(s[26..]) >> 2)
mut s11 := 2097151 & (load4(s[28..]) >> 7)
mut s12 := 2097151 & (load4(s[31..]) >> 4)
mut s13 := 2097151 & (load3(s[34..]) >> 1)
mut s14 := 2097151 & (load4(s[36..]) >> 6)
mut s15 := 2097151 & (load3(s[39..]) >> 3)
mut s16 := 2097151 & load3(s[42..])
mut s17 := 2097151 & (load4(s[44..]) >> 5)
mut s18 := 2097151 & (load3(s[47..]) >> 2)
mut s19 := 2097151 & (load4(s[49..]) >> 7)
mut s20 := 2097151 & (load4(s[52..]) >> 4)
mut s21 := 2097151 & (load3(s[55..]) >> 1)
mut s22 := 2097151 & (load4(s[57..]) >> 6)
mut s23 := (load4(s[60..]) >> 3)
s11 += s23 * 666643
s12 += s23 * 470296
s13 += s23 * 654183
s14 -= s23 * 997805
s15 += s23 * 136657
s16 -= s23 * 683901
s23 = 0
s10 += s22 * 666643
s11 += s22 * 470296
s12 += s22 * 654183
s13 -= s22 * 997805
s14 += s22 * 136657
s15 -= s22 * 683901
s22 = 0
s9 += s21 * 666643
s10 += s21 * 470296
s11 += s21 * 654183
s12 -= s21 * 997805
s13 += s21 * 136657
s14 -= s21 * 683901
s21 = 0
s8 += s20 * 666643
s9 += s20 * 470296
s10 += s20 * 654183
s11 -= s20 * 997805
s12 += s20 * 136657
s13 -= s20 * 683901
s20 = 0
s7 += s19 * 666643
s8 += s19 * 470296
s9 += s19 * 654183
s10 -= s19 * 997805
s11 += s19 * 136657
s12 -= s19 * 683901
s19 = 0
s6 += s18 * 666643
s7 += s18 * 470296
s8 += s18 * 654183
s9 -= s18 * 997805
s10 += s18 * 136657
s11 -= s18 * 683901
s18 = 0
mut carry := [17]i64{} // original one
// mut carry := [17]u64{}
carry[6] = (s6 + (1048576)) >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[8] = (s8 + (1048576)) >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[10] = (s10 + (1048576)) >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[12] = (s12 + (1048576)) >> 21
s13 += carry[12]
s12 -= carry[12] * 2097152
carry[14] = (s14 + (1048576)) >> 21
s15 += carry[14]
s14 -= carry[14] * 2097152
carry[16] = (s16 + (1048576)) >> 21
s17 += carry[16]
s16 -= carry[16] * 2097152
carry[7] = (s7 + (1048576)) >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[9] = (s9 + (1048576)) >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[11] = (s11 + (1048576)) >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
carry[13] = (s13 + (1048576)) >> 21
s14 += carry[13]
s13 -= carry[13] * 2097152
carry[15] = (s15 + (1048576)) >> 21
s16 += carry[15]
s15 -= carry[15] * 2097152
s5 += s17 * 666643
s6 += s17 * 470296
s7 += s17 * 654183
s8 -= s17 * 997805
s9 += s17 * 136657
s10 -= s17 * 683901
s17 = 0
s4 += s16 * 666643
s5 += s16 * 470296
s6 += s16 * 654183
s7 -= s16 * 997805
s8 += s16 * 136657
s9 -= s16 * 683901
s16 = 0
s3 += s15 * 666643
s4 += s15 * 470296
s5 += s15 * 654183
s6 -= s15 * 997805
s7 += s15 * 136657
s8 -= s15 * 683901
s15 = 0
s2 += s14 * 666643
s3 += s14 * 470296
s4 += s14 * 654183
s5 -= s14 * 997805
s6 += s14 * 136657
s7 -= s14 * 683901
s14 = 0
s1 += s13 * 666643
s2 += s13 * 470296
s3 += s13 * 654183
s4 -= s13 * 997805
s5 += s13 * 136657
s6 -= s13 * 683901
s13 = 0
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = (s0 + (1048576)) >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[2] = (s2 + (1048576)) >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[4] = (s4 + (1048576)) >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[6] = (s6 + (1048576)) >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[8] = (s8 + (1048576)) >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[10] = (s10 + (1048576)) >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[1] = (s1 + (1048576)) >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[3] = (s3 + (1048576)) >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[5] = (s5 + (1048576)) >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[7] = (s7 + (1048576)) >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[9] = (s9 + (1048576)) >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[11] = (s11 + (1048576)) >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = s0 >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[1] = s1 >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[2] = s2 >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[3] = s3 >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[4] = s4 >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[5] = s5 >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[6] = s6 >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[7] = s7 >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[8] = s8 >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[9] = s9 >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[10] = s10 >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
carry[11] = s11 >> 21
s12 += carry[11]
s11 -= carry[11] * 2097152
s0 += s12 * 666643
s1 += s12 * 470296
s2 += s12 * 654183
s3 -= s12 * 997805
s4 += s12 * 136657
s5 -= s12 * 683901
s12 = 0
carry[0] = s0 >> 21
s1 += carry[0]
s0 -= carry[0] * 2097152
carry[1] = s1 >> 21
s2 += carry[1]
s1 -= carry[1] * 2097152
carry[2] = s2 >> 21
s3 += carry[2]
s2 -= carry[2] * 2097152
carry[3] = s3 >> 21
s4 += carry[3]
s3 -= carry[3] * 2097152
carry[4] = s4 >> 21
s5 += carry[4]
s4 -= carry[4] * 2097152
carry[5] = s5 >> 21
s6 += carry[5]
s5 -= carry[5] * 2097152
carry[6] = s6 >> 21
s7 += carry[6]
s6 -= carry[6] * 2097152
carry[7] = s7 >> 21
s8 += carry[7]
s7 -= carry[7] * 2097152
carry[8] = s8 >> 21
s9 += carry[8]
s8 -= carry[8] * 2097152
carry[9] = s9 >> 21
s10 += carry[9]
s9 -= carry[9] * 2097152
carry[10] = s10 >> 21
s11 += carry[10]
s10 -= carry[10] * 2097152
out[0] = byte(s0 >> 0)
out[1] = byte(s0 >> 8)
out[2] = byte((s0 >> 16) | (s1 * 32))
out[3] = byte(s1 >> 3)
out[4] = byte(s1 >> 11)
out[5] = byte((s1 >> 19) | (s2 * 4))
out[6] = byte(s2 >> 6)
out[7] = byte((s2 >> 14) | (s3 * 128))
out[8] = byte(s3 >> 1)
out[9] = byte(s3 >> 9)
out[10] = byte((s3 >> 17) | (s4 * 16))
out[11] = byte(s4 >> 4)
out[12] = byte(s4 >> 12)
out[13] = byte((s4 >> 20) | (s5 * 2))
out[14] = byte(s5 >> 7)
out[15] = byte((s5 >> 15) | (s6 * 64))
out[16] = byte(s6 >> 2)
out[17] = byte(s6 >> 10)
out[18] = byte((s6 >> 18) | (s7 * 8))
out[19] = byte(s7 >> 5)
out[20] = byte(s7 >> 13)
out[21] = byte(s8 >> 0)
out[22] = byte(s8 >> 8)
out[23] = byte((s8 >> 16) | (s9 * 32))
out[24] = byte(s9 >> 3)
out[25] = byte(s9 >> 11)
out[26] = byte((s9 >> 19) | (s10 * 4))
out[27] = byte(s10 >> 6)
out[28] = byte((s10 >> 14) | (s11 * 128))
out[29] = byte(s11 >> 1)
out[30] = byte(s11 >> 9)
out[31] = byte(s11 >> 17)
}
// non_adjacent_form computes a width-w non-adjacent form for this scalar.
//
// w must be between 2 and 8, or non_adjacent_form will panic.
pub fn (mut s Scalar) non_adjacent_form(w u32) []i8 {
// 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 {
panic('scalar has high bit set illegally')
}
if w < 2 {
panic('w must be at least 2 by the definition of NAF')
} else if w > 8 {
panic('NAF digits must fit in i8')
}
mut naf := []i8{len: 256}
mut digits := [5]u64{}
for i := 0; i < 4; i++ {
digits[i] = binary.little_endian_u64(s.s[i * 8..])
}
width := u64(1 << w)
window_mask := u64(width - 1)
mut pos := u32(0)
mut carry := u64(0)
for pos < 256 {
idx_64 := pos / 64
idx_bit := pos % 64
mut bitbuf := u64(0)
if idx_bit < 64 - w {
// This window's bits are contained in a single u64
bitbuf = digits[idx_64] >> idx_bit
} else {
// Combine the current 64 bits with bits from the next 64
bitbuf = (digits[idx_64] >> idx_bit) | (digits[1 + idx_64] << (64 - idx_bit))
}
// Add carry into the current window
window := carry + (bitbuf & window_mask)
if window & 1 == 0 {
// If the window value is even, preserve the carry and continue.
// Why is the carry preserved?
// If carry == 0 and window & 1 == 0,
// then the next carry should be 0
// If carry == 1 and window & 1 == 0,
// then bit_buf & 1 == 1 so the next carry should be 1
pos += 1
continue
}
if window < width / 2 {
carry = 0
naf[pos] = i8(window)
} else {
carry = 1
naf[pos] = i8(window) - i8(width)
}
pos += w
}
return naf
}
fn (mut s Scalar) signed_radix16() []i8 {
if s.s[31] > 127 {
panic('scalar has high bit set illegally')
}
mut digits := []i8{len: 64}
// Compute unsigned radix-16 digits:
for i := 0; i < 32; i++ {
digits[2 * i] = i8(s.s[i] & 15)
digits[2 * i + 1] = i8((s.s[i] >> 4) & 15)
}
// Recenter coefficients:
for i := 0; i < 63; i++ {
mut carry := (digits[i] + 8) >> 4
// digits[i] -= unsafe { carry * 16 } // original one
digits[i] -= unsafe { carry * 16 } // carry * 16 == carry *
digits[i + 1] += carry
}
return digits
}
// utility function
// generate returns a valid (reduced modulo l) Scalar with a distribution
// weighted towards high, low, and edge values.
fn generate_scalar(size int) ?Scalar {
/*
s := scZero
diceRoll := rand.Intn(100)
switch {
case diceRoll == 0:
case diceRoll == 1:
s = scOne
case diceRoll == 2:
s = scMinusOne
case diceRoll < 5:
// Generate a low scalar in [0, 2^125).
rand.Read(s.s[:16])
s.s[15] &= (1 * 32) - 1
case diceRoll < 10:
// Generate a high scalar in [2^252, 2^252 + 2^124).
s.s[31] = 1 * 16
rand.Read(s.s[:16])
s.s[15] &= (1 * 16) - 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 * 16) - 1
}
return reflect.ValueOf(s)
*/
mut s := edwards25519.sc_zero
diceroll := rand.intn(100) or { 0 }
match true {
/*
case diceroll == 0:
case diceroll == 1:
*/
diceroll == 0 || diceroll == 1 {
s = edwards25519.sc_one
}
diceroll == 2 {
s = edwards25519.sc_minus_one
}
diceroll < 5 {
// rand.Read(s.s[:16]) // read random bytes and fill buf
// using builtin rand.read([]buf)
rand.read(mut s.s[..16])
// buf := rand.read(s.s[..16].len) ?
// copy(s.s[..16], buf)
/*
for i, item in buf {
s.s[i] = item
}
*/
s.s[15] &= (1 * 32) - 1
// generate a low scalar in [0, 2^125).
}
diceroll < 10 {
// generate a high scalar in [2^252, 2^252 + 2^124).
s.s[31] = 1 * 16
// Read generates len(p) random bytes and writes them into p
// rand.Read(s.s[:16])
rand.read(mut s.s[..16])
// buf := rand.read(s.s[..16].len) ?
// copy(s.s[..16], buf)
/*
for i, item in buf {
s.s[i] = item
}
*/
s.s[15] &= (1 * 16) - 1
}
else {
// 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[:])
rand.read(mut s.s[..])
// buf := crand.read(s.s.len) ?
// copy(s.s[..], buf)
/*
for i, item in buf {
s.s[i] = item
}
*/
s.s[31] &= (1 * 16) - 1
}
}
return s
}
type NotZeroScalar = Scalar
fn generate_notzero_scalar(size int) ?NotZeroScalar {
mut s := Scalar{}
for s == edwards25519.sc_zero {
s = generate_scalar(size) ?
}
return NotZeroScalar(s)
}