1174 lines
29 KiB
V
1174 lines
29 KiB
V
module edwards25519
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import rand
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import encoding.binary
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import crypto.internal.subtle
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// A Scalar is an integer modulo
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//
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// l = 2^252 + 27742317777372353535851937790883648493
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//
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// which is the prime order of the edwards25519 group.
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//
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// This type works similarly to math/big.Int, and all arguments and
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// receivers are allowed to alias.
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//
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// The zero value is a valid zero element.
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struct Scalar {
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mut:
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// s is the Scalar value in little-endian. The value is always reduced
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// between operations.
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s [32]u8
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}
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pub const (
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sc_zero = Scalar{
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s: [u8(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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0, 0, 0, 0, 0]!
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}
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sc_one = Scalar{
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s: [u8(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,
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0, 0, 0, 0, 0]!
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}
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sc_minus_one = Scalar{
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s: [u8(236), 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16]!
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}
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)
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// new_scalar return new zero scalar
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pub fn new_scalar() Scalar {
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return Scalar{}
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}
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// add sets s = x + y mod l, and returns s.
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pub fn (mut s Scalar) add(x Scalar, y Scalar) Scalar {
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// s = 1 * x + y mod l
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sc_mul_add(mut s.s, edwards25519.sc_one.s, x.s, y.s)
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return s
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}
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// multiply_add sets s = x * y + z mod l, and returns s.
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pub fn (mut s Scalar) multiply_add(x Scalar, y Scalar, z Scalar) Scalar {
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sc_mul_add(mut s.s, x.s, y.s, z.s)
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return s
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}
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// subtract sets s = x - y mod l, and returns s.
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pub fn (mut s Scalar) subtract(x Scalar, y Scalar) Scalar {
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// s = -1 * y + x mod l
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sc_mul_add(mut s.s, edwards25519.sc_minus_one.s, y.s, x.s)
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return s
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}
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// negate sets s = -x mod l, and returns s.
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pub fn (mut s Scalar) negate(x Scalar) Scalar {
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// s = -1 * x + 0 mod l
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sc_mul_add(mut s.s, edwards25519.sc_minus_one.s, x.s, edwards25519.sc_zero.s)
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return s
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}
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// multiply sets s = x * y mod l, and returns s.
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pub fn (mut s Scalar) multiply(x Scalar, y Scalar) Scalar {
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// s = x * y + 0 mod l
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sc_mul_add(mut s.s, x.s, y.s, edwards25519.sc_zero.s)
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return s
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}
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// set sets s = x, and returns s.
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pub fn (mut s Scalar) set(x Scalar) Scalar {
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s = x
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return s
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}
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// set_uniform_bytes sets s to an uniformly distributed value given 64 uniformly
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// distributed random bytes. If x is not of the right length, set_uniform_bytes
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// returns an error, and the receiver is unchanged.
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pub fn (mut s Scalar) set_uniform_bytes(x []u8) ?Scalar {
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if x.len != 64 {
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return error('edwards25519: invalid set_uniform_bytes input length')
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}
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mut wide_bytes := []u8{len: 64}
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copy(mut wide_bytes, x)
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// for i, item in x {
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// wide_bytes[i] = item
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//}
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sc_reduce(mut s.s, mut wide_bytes)
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return s
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}
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// set_canonical_bytes sets s = x, where x is a 32-byte little-endian encoding of
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// s, and returns s. If x is not a canonical encoding of s, set_canonical_bytes
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// returns an error, and the receiver is unchanged.
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pub fn (mut s Scalar) set_canonical_bytes(x []u8) ?Scalar {
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if x.len != 32 {
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return error('invalid scalar length')
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}
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// mut bb := []u8{len:32}
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mut ss := Scalar{}
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for i, item in x {
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ss.s[i] = item
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}
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//_ := copy(mut ss.s[..], x) //its not working
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if !is_reduced(ss) {
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return error('invalid scalar encoding')
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}
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s.s = ss.s
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return s
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}
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// is_reduced returns whether the given scalar is reduced modulo l.
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fn is_reduced(s Scalar) bool {
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for i := s.s.len - 1; i >= 0; i-- {
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if s.s[i] > edwards25519.sc_minus_one.s[i] {
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return false
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}
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if s.s[i] < edwards25519.sc_minus_one.s[i] {
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return true
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}
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/*
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switch {
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case s.s[i] > sc_minus_one.s[i]:
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return false
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case s.s[i] < sc_minus_one.s[i]:
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return true
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}
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*/
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}
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return true
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}
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// set_bytes_with_clamping applies the buffer pruning described in RFC 8032,
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// Section 5.1.5 (also known as clamping) and sets s to the result. The input
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// must be 32 bytes, and it is not modified. If x is not of the right length,
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// `set_bytes_with_clamping` returns an error, and the receiver is unchanged.
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//
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// Note that since Scalar values are always reduced modulo the prime order of
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// the curve, the resulting value will not preserve any of the cofactor-clearing
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// properties that clamping is meant to provide. It will however work as
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// expected as long as it is applied to points on the prime order subgroup, like
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// in Ed25519. In fact, it is lost to history why RFC 8032 adopted the
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// irrelevant RFC 7748 clamping, but it is now required for compatibility.
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pub fn (mut s Scalar) set_bytes_with_clamping(x []u8) ?Scalar {
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// The description above omits the purpose of the high bits of the clamping
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// for brevity, but those are also lost to reductions, and are also
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// irrelevant to edwards25519 as they protect against a specific
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// implementation bug that was once observed in a generic Montgomery ladder.
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if x.len != 32 {
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return error('edwards25519: invalid set_bytes_with_clamping input length')
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}
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mut wide_bytes := []u8{len: 64, cap: 64}
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copy(mut wide_bytes, x)
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// for i, item in x {
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// wide_bytes[i] = item
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//}
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wide_bytes[0] &= 248
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wide_bytes[31] &= 63
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wide_bytes[31] |= 64
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sc_reduce(mut s.s, mut wide_bytes)
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return s
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}
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// bytes returns the canonical 32-byte little-endian encoding of s.
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pub fn (mut s Scalar) bytes() []u8 {
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mut buf := []u8{len: 32}
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copy(mut buf, s.s[..])
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return buf
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}
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// equal returns 1 if s and t are equal, and 0 otherwise.
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pub fn (s Scalar) equal(t Scalar) int {
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return subtle.constant_time_compare(s.s[..], t.s[..])
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}
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// sc_mul_add and sc_reduce are ported from the public domain, “ref10”
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// implementation of ed25519 from SUPERCOP.
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fn load3(inp []u8) i64 {
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mut r := i64(inp[0])
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r |= i64(inp[1]) * 256 // << 8
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r |= i64(inp[2]) * 65536 // << 16
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return r
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}
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fn load4(inp []u8) i64 {
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mut r := i64(inp[0])
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r |= i64(inp[1]) * 256
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r |= i64(inp[2]) * 65536
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r |= i64(inp[3]) * 16777216
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return r
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}
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// Input:
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// a[0]+256*a[1]+...+256^31*a[31] = a
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// b[0]+256*b[1]+...+256^31*b[31] = b
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// c[0]+256*c[1]+...+256^31*c[31] = c
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//
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// Output:
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// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
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// where l = 2^252 + 27742317777372353535851937790883648493.
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fn sc_mul_add(mut s [32]u8, a [32]u8, b [32]u8, c [32]u8) {
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a0 := 2097151 & load3(a[..])
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a1 := 2097151 & (load4(a[2..]) >> 5)
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a2 := 2097151 & (load3(a[5..]) >> 2)
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a3 := 2097151 & (load4(a[7..]) >> 7)
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a4 := 2097151 & (load4(a[10..]) >> 4)
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a5 := 2097151 & (load3(a[13..]) >> 1)
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a6 := 2097151 & (load4(a[15..]) >> 6)
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a7 := 2097151 & (load3(a[18..]) >> 3)
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a8 := 2097151 & load3(a[21..])
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a9 := 2097151 & (load4(a[23..]) >> 5)
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a10 := 2097151 & (load3(a[26..]) >> 2)
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a11 := (load4(a[28..]) >> 7)
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b0 := 2097151 & load3(b[..])
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b1 := 2097151 & (load4(b[2..]) >> 5)
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b2 := 2097151 & (load3(b[5..]) >> 2)
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b3 := 2097151 & (load4(b[7..]) >> 7)
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b4 := 2097151 & (load4(b[10..]) >> 4)
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b5 := 2097151 & (load3(b[13..]) >> 1)
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b6 := 2097151 & (load4(b[15..]) >> 6)
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b7 := 2097151 & (load3(b[18..]) >> 3)
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b8 := 2097151 & load3(b[21..])
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b9 := 2097151 & (load4(b[23..]) >> 5)
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b10 := 2097151 & (load3(b[26..]) >> 2)
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b11 := (load4(b[28..]) >> 7)
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c0 := 2097151 & load3(c[..])
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c1 := 2097151 & (load4(c[2..]) >> 5)
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c2 := 2097151 & (load3(c[5..]) >> 2)
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c3 := 2097151 & (load4(c[7..]) >> 7)
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c4 := 2097151 & (load4(c[10..]) >> 4)
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c5 := 2097151 & (load3(c[13..]) >> 1)
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c6 := 2097151 & (load4(c[15..]) >> 6)
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c7 := 2097151 & (load3(c[18..]) >> 3)
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c8 := 2097151 & load3(c[21..])
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c9 := 2097151 & (load4(c[23..]) >> 5)
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c10 := 2097151 & (load3(c[26..]) >> 2)
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c11 := (load4(c[28..]) >> 7)
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mut carry := [23]i64{} // original one
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// mut carry := [23]u64{}
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mut s0 := c0 + a0 * b0
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mut s1 := c1 + a0 * b1 + a1 * b0
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mut s2 := c2 + a0 * b2 + a1 * b1 + a2 * b0
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mut s3 := c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0
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mut s4 := c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0
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mut s5 := c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0
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mut s6 := c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0
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mut s7 := c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0
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mut s8 := c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 +
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a8 * b0
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mut s9 := c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 +
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a8 * b1 + a9 * b0
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mut s10 := c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 +
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a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0
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mut s11 := c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 +
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a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0
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mut s12 := a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 +
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a9 * b3 + a10 * b2 + a11 * b1
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mut s13 := a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 +
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a10 * b3 + a11 * b2
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mut s14 := a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 +
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a11 * b3
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mut s15 := a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4
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mut s16 := a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5
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mut s17 := a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6
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mut s18 := a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7
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mut s19 := a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8
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mut s20 := a9 * b11 + a10 * b10 + a11 * b9
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mut s21 := a10 * b11 + a11 * b10
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mut s22 := a11 * b11
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mut s23 := i64(0) // original
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// mut s23 := u64(0)
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// carry[0] = (s0 + (1048576)) >> 21
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carry[0] = (s0 + (1048576)) >> 21
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s1 += carry[0]
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s0 -= carry[0] * 2097152
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carry[2] = (s2 + (1048576)) >> 21
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s3 += carry[2]
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s2 -= carry[2] * 2097152
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carry[4] = (s4 + (1048576)) >> 21
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s5 += carry[4]
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s4 -= carry[4] * 2097152
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carry[6] = (s6 + (1048576)) >> 21
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s7 += carry[6]
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s6 -= carry[6] * 2097152
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carry[8] = (s8 + (1048576)) >> 21
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s9 += carry[8]
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s8 -= carry[8] * 2097152
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carry[10] = (s10 + (1048576)) >> 21
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s11 += carry[10]
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s10 -= carry[10] * 2097152
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carry[12] = (s12 + (1048576)) >> 21
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s13 += carry[12]
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s12 -= carry[12] * 2097152
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carry[14] = (s14 + (1048576)) >> 21
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s15 += carry[14]
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s14 -= carry[14] * 2097152
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carry[16] = (s16 + (1048576)) >> 21
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s17 += carry[16]
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s16 -= carry[16] * 2097152
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carry[18] = (s18 + (1048576)) >> 21
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s19 += carry[18]
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s18 -= carry[18] * 2097152
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carry[20] = (s20 + (1048576)) >> 21
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s21 += carry[20]
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s20 -= carry[20] * 2097152
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carry[22] = (s22 + (1048576)) >> 21
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s23 += carry[22]
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s22 -= carry[22] * 2097152
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carry[1] = (s1 + (1048576)) >> 21
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s2 += carry[1]
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s1 -= carry[1] * 2097152
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carry[3] = (s3 + (1048576)) >> 21
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s4 += carry[3]
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s3 -= carry[3] * 2097152
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carry[5] = (s5 + (1048576)) >> 21
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s6 += carry[5]
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s5 -= carry[5] * 2097152
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carry[7] = (s7 + (1048576)) >> 21
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s8 += carry[7]
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s7 -= carry[7] * 2097152
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carry[9] = (s9 + (1048576)) >> 21
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s10 += carry[9]
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s9 -= carry[9] * 2097152
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carry[11] = (s11 + (1048576)) >> 21
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s12 += carry[11]
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s11 -= carry[11] * 2097152
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carry[13] = (s13 + (1048576)) >> 21
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s14 += carry[13]
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s13 -= carry[13] * 2097152
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carry[15] = (s15 + (1048576)) >> 21
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s16 += carry[15]
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s15 -= carry[15] * 2097152
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carry[17] = (s17 + (1048576)) >> 21
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s18 += carry[17]
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s17 -= carry[17] * 2097152
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carry[19] = (s19 + (1048576)) >> 21
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s20 += carry[19]
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s19 -= carry[19] * 2097152
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carry[21] = (s21 + (1048576)) >> 21
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s22 += carry[21]
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s21 -= carry[21] * 2097152
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s11 += s23 * 666643
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s12 += s23 * 470296
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s13 += s23 * 654183
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s14 -= s23 * 997805
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s15 += s23 * 136657
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s16 -= s23 * 683901
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s23 = 0
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s10 += s22 * 666643
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s11 += s22 * 470296
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s12 += s22 * 654183
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s13 -= s22 * 997805
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s14 += s22 * 136657
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s15 -= s22 * 683901
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s22 = 0
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s9 += s21 * 666643
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s10 += s21 * 470296
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s11 += s21 * 654183
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s12 -= s21 * 997805
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s13 += s21 * 136657
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s14 -= s21 * 683901
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s21 = 0
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s8 += s20 * 666643
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s9 += s20 * 470296
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s10 += s20 * 654183
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s11 -= s20 * 997805
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s12 += s20 * 136657
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s13 -= s20 * 683901
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s20 = 0
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s7 += s19 * 666643
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s8 += s19 * 470296
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s9 += s19 * 654183
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s10 -= s19 * 997805
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s11 += s19 * 136657
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s12 -= s19 * 683901
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s19 = 0
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s6 += s18 * 666643
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s7 += s18 * 470296
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s8 += s18 * 654183
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s9 -= s18 * 997805
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s10 += s18 * 136657
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s11 -= s18 * 683901
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s18 = 0
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carry[6] = (s6 + (1048576)) >> 21
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s7 += carry[6]
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|
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] = u8(s0 >> 0)
|
|
s[1] = u8(s0 >> 8)
|
|
s[2] = u8((s0 >> 16) | (s1 * 32))
|
|
s[3] = u8(s1 >> 3)
|
|
s[4] = u8(s1 >> 11)
|
|
s[5] = u8((s1 >> 19) | (s2 * 4))
|
|
s[6] = u8(s2 >> 6)
|
|
s[7] = u8((s2 >> 14) | (s3 * 128))
|
|
s[8] = u8(s3 >> 1)
|
|
s[9] = u8(s3 >> 9)
|
|
s[10] = u8((s3 >> 17) | (s4 * 16))
|
|
s[11] = u8(s4 >> 4)
|
|
s[12] = u8(s4 >> 12)
|
|
s[13] = u8((s4 >> 20) | (s5 * 2))
|
|
s[14] = u8(s5 >> 7)
|
|
s[15] = u8((s5 >> 15) | (s6 * 64))
|
|
s[16] = u8(s6 >> 2)
|
|
s[17] = u8(s6 >> 10)
|
|
s[18] = u8((s6 >> 18) | (s7 * 8))
|
|
s[19] = u8(s7 >> 5)
|
|
s[20] = u8(s7 >> 13)
|
|
s[21] = u8(s8 >> 0)
|
|
s[22] = u8(s8 >> 8)
|
|
s[23] = u8((s8 >> 16) | (s9 * 32))
|
|
s[24] = u8(s9 >> 3)
|
|
s[25] = u8(s9 >> 11)
|
|
s[26] = u8((s9 >> 19) | (s10 * 4))
|
|
s[27] = u8(s10 >> 6)
|
|
s[28] = u8((s10 >> 14) | (s11 * 128))
|
|
s[29] = u8(s11 >> 1)
|
|
s[30] = u8(s11 >> 9)
|
|
s[31] = u8(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]u8, mut s []u8) {
|
|
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] = u8(s0 >> 0)
|
|
out[1] = u8(s0 >> 8)
|
|
out[2] = u8((s0 >> 16) | (s1 * 32))
|
|
out[3] = u8(s1 >> 3)
|
|
out[4] = u8(s1 >> 11)
|
|
out[5] = u8((s1 >> 19) | (s2 * 4))
|
|
out[6] = u8(s2 >> 6)
|
|
out[7] = u8((s2 >> 14) | (s3 * 128))
|
|
out[8] = u8(s3 >> 1)
|
|
out[9] = u8(s3 >> 9)
|
|
out[10] = u8((s3 >> 17) | (s4 * 16))
|
|
out[11] = u8(s4 >> 4)
|
|
out[12] = u8(s4 >> 12)
|
|
out[13] = u8((s4 >> 20) | (s5 * 2))
|
|
out[14] = u8(s5 >> 7)
|
|
out[15] = u8((s5 >> 15) | (s6 * 64))
|
|
out[16] = u8(s6 >> 2)
|
|
out[17] = u8(s6 >> 10)
|
|
out[18] = u8((s6 >> 18) | (s7 * 8))
|
|
out[19] = u8(s7 >> 5)
|
|
out[20] = u8(s7 >> 13)
|
|
out[21] = u8(s8 >> 0)
|
|
out[22] = u8(s8 >> 8)
|
|
out[23] = u8((s8 >> 16) | (s9 * 32))
|
|
out[24] = u8(s9 >> 3)
|
|
out[25] = u8(s9 >> 11)
|
|
out[26] = u8((s9 >> 19) | (s10 * 4))
|
|
out[27] = u8(s10 >> 6)
|
|
out[28] = u8((s10 >> 14) | (s11 * 128))
|
|
out[29] = u8(s11 >> 1)
|
|
out[30] = u8(s11 >> 9)
|
|
out[31] = u8(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(mut 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(mut 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(mut 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)
|
|
}
|