1
0
mirror of https://github.com/vlang/v.git synced 2023-08-10 21:13:21 +03:00
v/vlib/crypto/ed25519/internal/edwards25519/element.v

734 lines
21 KiB
V
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

module edwards25519
import math.bits
import math.unsigned
import encoding.binary
import crypto.internal.subtle
// embedded unsigned.Uint128
struct Uint128 {
unsigned.Uint128
}
// Element represents an element of the edwards25519 GF(2^255-19). Note that this
// is not a cryptographically secure group, and should only be used to interact
// with edwards25519.Point coordinates.
//
// 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.
pub struct Element {
mut:
// An element t represents the integer
// t.l0 + t.l1*2^51 + t.l2*2^102 + t.l3*2^153 + t.l4*2^204
//
// Between operations, all limbs are expected to be lower than 2^52.
l0 u64
l1 u64
l2 u64
l3 u64
l4 u64
}
const (
mask_low_51_bits = u64((1 << 51) - 1)
fe_zero = Element{
l0: 0
l1: 0
l2: 0
l3: 0
l4: 0
}
fe_one = Element{
l0: 1
l1: 0
l2: 0
l3: 0
l4: 0
}
// sqrt_m1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion.
sqrt_m1 = Element{
l0: 1718705420411056
l1: 234908883556509
l2: 2233514472574048
l3: 2117202627021982
l4: 765476049583133
}
)
// mul_64 returns a * b.
fn mul_64(a u64, b u64) Uint128 {
hi, lo := bits.mul_64(a, b)
return Uint128{
lo: lo
hi: hi
}
}
// add_mul_64 returns v + a * b.
fn add_mul_64(v Uint128, a u64, b u64) Uint128 {
mut hi, lo := bits.mul_64(a, b)
low, carry := bits.add_64(lo, v.lo, 0)
hi, _ = bits.add_64(hi, v.hi, carry)
return Uint128{
lo: low
hi: hi
}
}
// shift_right_by_51 returns a >> 51. a is assumed to be at most 115 bits.
fn shift_right_by_51(a Uint128) u64 {
return (a.hi << (64 - 51)) | (a.lo >> 51)
}
fn fe_mul_generic(a Element, b Element) Element {
a0 := a.l0
a1 := a.l1
a2 := a.l2
a3 := a.l3
a4 := a.l4
b0 := b.l0
b1 := b.l1
b2 := b.l2
b3 := b.l3
b4 := b.l4
// Limb multiplication works like pen-and-paper columnar multiplication, but
// with 51-bit limbs instead of digits.
//
// a4 a3 a2 a1 a0 x
// b4 b3 b2 b1 b0 =
// ------------------------
// a4b0 a3b0 a2b0 a1b0 a0b0 +
// a4b1 a3b1 a2b1 a1b1 a0b1 +
// a4b2 a3b2 a2b2 a1b2 a0b2 +
// a4b3 a3b3 a2b3 a1b3 a0b3 +
// a4b4 a3b4 a2b4 a1b4 a0b4 =
// ----------------------------------------------
// r8 r7 r6 r5 r4 r3 r2 r1 r0
//
// We can then use the reduction identity (a * 2²⁵⁵ + b = a * 19 + b) to
// reduce the limbs that would overflow 255 bits. r5 * 2²⁵⁵ becomes 19 * r5,
// r6 * 2³⁰⁶ becomes 19 * r6 * 2⁵¹, etc.
//
// Reduction can be carried out simultaneously to multiplication. For
// example, we do not compute r5: whenever the result of a multiplication
// belongs to r5, like a1b4, we multiply it by 19 and add the result to r0.
//
// a4b0 a3b0 a2b0 a1b0 a0b0 +
// a3b1 a2b1 a1b1 a0b1 19×a4b1 +
// a2b2 a1b2 a0b2 19×a4b2 19×a3b2 +
// a1b3 a0b3 19×a4b3 19×a3b3 19×a2b3 +
// a0b4 19×a4b4 19×a3b4 19×a2b4 19×a1b4 =
// --------------------------------------
// r4 r3 r2 r1 r0
//
// Finally we add up the columns into wide, overlapping limbs.
a1_19 := a1 * 19
a2_19 := a2 * 19
a3_19 := a3 * 19
a4_19 := a4 * 19
// r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
mut r0 := mul_64(a0, b0)
r0 = add_mul_64(r0, a1_19, b4)
r0 = add_mul_64(r0, a2_19, b3)
r0 = add_mul_64(r0, a3_19, b2)
r0 = add_mul_64(r0, a4_19, b1)
// r1 = a0×b1 + a1×b0 + 19×(a2×b4 + a3×b3 + a4×b2)
mut r1 := mul_64(a0, b1)
r1 = add_mul_64(r1, a1, b0)
r1 = add_mul_64(r1, a2_19, b4)
r1 = add_mul_64(r1, a3_19, b3)
r1 = add_mul_64(r1, a4_19, b2)
// r2 = a0×b2 + a1×b1 + a2×b0 + 19×(a3×b4 + a4×b3)
mut r2 := mul_64(a0, b2)
r2 = add_mul_64(r2, a1, b1)
r2 = add_mul_64(r2, a2, b0)
r2 = add_mul_64(r2, a3_19, b4)
r2 = add_mul_64(r2, a4_19, b3)
// r3 = a0×b3 + a1×b2 + a2×b1 + a3×b0 + 19×a4×b4
mut r3 := mul_64(a0, b3)
r3 = add_mul_64(r3, a1, b2)
r3 = add_mul_64(r3, a2, b1)
r3 = add_mul_64(r3, a3, b0)
r3 = add_mul_64(r3, a4_19, b4)
// r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
mut r4 := mul_64(a0, b4)
r4 = add_mul_64(r4, a1, b3)
r4 = add_mul_64(r4, a2, b2)
r4 = add_mul_64(r4, a3, b1)
r4 = add_mul_64(r4, a4, b0)
// After the multiplication, we need to reduce (carry) the five coefficients
// to obtain a result with limbs that are at most slightly larger than 2⁵¹,
// to respect the Element invariant.
//
// Overall, the reduction works the same as carryPropagate, except with
// wider inputs: we take the carry for each coefficient by shifting it right
// by 51, and add it to the limb above it. The top carry is multiplied by 19
// according to the reduction identity and added to the lowest limb.
//
// The largest coefficient (r0) will be at most 111 bits, which guarantees
// that all carries are at most 111 - 51 = 60 bits, which fits in a u64.
//
// r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
// r0 < 2⁵²×2⁵² + 19×(2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵²)
// r0 < (1 + 19 × 4) × 2⁵² × 2⁵²
// r0 < 2⁷ × 2⁵² × 2⁵²
// r0 < 2¹¹¹
//
// Moreover, the top coefficient (r4) is at most 107 bits, so c4 is at most
// 56 bits, and c4 * 19 is at most 61 bits, which again fits in a u64 and
// allows us to easily apply the reduction identity.
//
// r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
// r4 < 5 × 2⁵² × 2⁵²
// r4 < 2¹⁰⁷
//
c0 := shift_right_by_51(r0)
c1 := shift_right_by_51(r1)
c2 := shift_right_by_51(r2)
c3 := shift_right_by_51(r3)
c4 := shift_right_by_51(r4)
rr0 := r0.lo & edwards25519.mask_low_51_bits + c4 * 19
rr1 := r1.lo & edwards25519.mask_low_51_bits + c0
rr2 := r2.lo & edwards25519.mask_low_51_bits + c1
rr3 := r3.lo & edwards25519.mask_low_51_bits + c2
rr4 := r4.lo & edwards25519.mask_low_51_bits + c3
// Now all coefficients fit into 64-bit registers but are still too large to
// be passed around as a Element. We therefore do one last carry chain,
// where the carries will be small enough to fit in the wiggle room above 2⁵¹.
mut v := Element{
l0: rr0
l1: rr1
l2: rr2
l3: rr3
l4: rr4
}
// v.carryPropagate()
// using `carry_propagate_generic()` instead
v = v.carry_propagate_generic()
return v
}
// carry_propagate_generic brings the limbs below 52 bits by applying the reduction
// identity (a * 2²⁵⁵ + b = a * 19 + b) to the l4 carry.
fn (mut v Element) carry_propagate_generic() Element {
c0 := v.l0 >> 51
c1 := v.l1 >> 51
c2 := v.l2 >> 51
c3 := v.l3 >> 51
c4 := v.l4 >> 51
v.l0 = v.l0 & edwards25519.mask_low_51_bits + c4 * 19
v.l1 = v.l1 & edwards25519.mask_low_51_bits + c0
v.l2 = v.l2 & edwards25519.mask_low_51_bits + c1
v.l3 = v.l3 & edwards25519.mask_low_51_bits + c2
v.l4 = v.l4 & edwards25519.mask_low_51_bits + c3
return v
}
fn fe_square_generic(a Element) Element {
l0 := a.l0
l1 := a.l1
l2 := a.l2
l3 := a.l3
l4 := a.l4
// Squaring works precisely like multiplication above, but thanks to its
// symmetry we get to group a few terms together.
//
// l4 l3 l2 l1 l0 x
// l4 l3 l2 l1 l0 =
// ------------------------
// l4l0 l3l0 l2l0 l1l0 l0l0 +
// l4l1 l3l1 l2l1 l1l1 l0l1 +
// l4l2 l3l2 l2l2 l1l2 l0l2 +
// l4l3 l3l3 l2l3 l1l3 l0l3 +
// l4l4 l3l4 l2l4 l1l4 l0l4 =
// ----------------------------------------------
// r8 r7 r6 r5 r4 r3 r2 r1 r0
//
// l4l0 l3l0 l2l0 l1l0 l0l0 +
// l3l1 l2l1 l1l1 l0l1 19×l4l1 +
// l2l2 l1l2 l0l2 19×l4l2 19×l3l2 +
// l1l3 l0l3 19×l4l3 19×l3l3 19×l2l3 +
// l0l4 19×l4l4 19×l3l4 19×l2l4 19×l1l4 =
// --------------------------------------
// r4 r3 r2 r1 r0
//
// With precomputed 2×, 19×, and 2×19× terms, we can compute each limb with
// only three mul_64 and four Add64, instead of five and eight.
l0_2 := l0 * 2
l1_2 := l1 * 2
l1_38 := l1 * 38
l2_38 := l2 * 38
l3_38 := l3 * 38
l3_19 := l3 * 19
l4_19 := l4 * 19
// r0 = l0×l0 + 19×(l1×l4 + l2×l3 + l3×l2 + l4×l1) = l0×l0 + 19×2×(l1×l4 + l2×l3)
mut r0 := mul_64(l0, l0)
r0 = add_mul_64(r0, l1_38, l4)
r0 = add_mul_64(r0, l2_38, l3)
// r1 = l0×l1 + l1×l0 + 19×(l2×l4 + l3×l3 + l4×l2) = 2×l0×l1 + 19×2×l2×l4 + 19×l3×l3
mut r1 := mul_64(l0_2, l1)
r1 = add_mul_64(r1, l2_38, l4)
r1 = add_mul_64(r1, l3_19, l3)
// r2 = l0×l2 + l1×l1 + l2×l0 + 19×(l3×l4 + l4×l3) = 2×l0×l2 + l1×l1 + 19×2×l3×l4
mut r2 := mul_64(l0_2, l2)
r2 = add_mul_64(r2, l1, l1)
r2 = add_mul_64(r2, l3_38, l4)
// r3 = l0×l3 + l1×l2 + l2×l1 + l3×l0 + 19×l4×l4 = 2×l0×l3 + 2×l1×l2 + 19×l4×l4
mut r3 := mul_64(l0_2, l3)
r3 = add_mul_64(r3, l1_2, l2)
r3 = add_mul_64(r3, l4_19, l4)
// r4 = l0×l4 + l1×l3 + l2×l2 + l3×l1 + l4×l0 = 2×l0×l4 + 2×l1×l3 + l2×l2
mut r4 := mul_64(l0_2, l4)
r4 = add_mul_64(r4, l1_2, l3)
r4 = add_mul_64(r4, l2, l2)
c0 := shift_right_by_51(r0)
c1 := shift_right_by_51(r1)
c2 := shift_right_by_51(r2)
c3 := shift_right_by_51(r3)
c4 := shift_right_by_51(r4)
rr0 := r0.lo & edwards25519.mask_low_51_bits + c4 * 19
rr1 := r1.lo & edwards25519.mask_low_51_bits + c0
rr2 := r2.lo & edwards25519.mask_low_51_bits + c1
rr3 := r3.lo & edwards25519.mask_low_51_bits + c2
rr4 := r4.lo & edwards25519.mask_low_51_bits + c3
mut v := Element{
l0: rr0
l1: rr1
l2: rr2
l3: rr3
l4: rr4
}
v = v.carry_propagate_generic()
return v
}
// zero sets v = 0, and returns v.
pub fn (mut v Element) zero() Element {
v = edwards25519.fe_zero
return v
}
// one sets v = 1, and returns v.
pub fn (mut v Element) one() Element {
v = edwards25519.fe_one
return v
}
// reduce reduces v modulo 2^255 - 19 and returns it.
pub fn (mut v Element) reduce() Element {
v = v.carry_propagate_generic()
// After the light reduction we now have a edwards25519 element representation
// v < 2^255 + 2^13 * 19, but need v < 2^255 - 19.
// If v >= 2^255 - 19, then v + 19 >= 2^255, which would overflow 2^255 - 1,
// generating a carry. That is, c will be 0 if v < 2^255 - 19, and 1 otherwise.
mut c := (v.l0 + 19) >> 51
c = (v.l1 + c) >> 51
c = (v.l2 + c) >> 51
c = (v.l3 + c) >> 51
c = (v.l4 + c) >> 51
// If v < 2^255 - 19 and c = 0, this will be a no-op. Otherwise, it's
// effectively applying the reduction identity to the carry.
v.l0 += 19 * c
v.l1 += v.l0 >> 51
v.l0 = v.l0 & edwards25519.mask_low_51_bits
v.l2 += v.l1 >> 51
v.l1 = v.l1 & edwards25519.mask_low_51_bits
v.l3 += v.l2 >> 51
v.l2 = v.l2 & edwards25519.mask_low_51_bits
v.l4 += v.l3 >> 51
v.l3 = v.l3 & edwards25519.mask_low_51_bits
// no additional carry
v.l4 = v.l4 & edwards25519.mask_low_51_bits
return v
}
// add sets v = a + b, and returns v.
pub fn (mut v Element) add(a Element, b Element) Element {
v.l0 = a.l0 + b.l0
v.l1 = a.l1 + b.l1
v.l2 = a.l2 + b.l2
v.l3 = a.l3 + b.l3
v.l4 = a.l4 + b.l4
// Using the generic implementation here is actually faster than the
// assembly. Probably because the body of this function is so simple that
// the compiler can figure out better optimizations by inlining the carry
// propagation.
return v.carry_propagate_generic()
}
// subtract sets v = a - b, and returns v.
pub fn (mut v Element) subtract(a Element, b Element) Element {
// We first add 2 * p, to guarantee the subtraction won't underflow, and
// then subtract b (which can be up to 2^255 + 2^13 * 19).
v.l0 = (a.l0 + 0xFFFFFFFFFFFDA) - b.l0
v.l1 = (a.l1 + 0xFFFFFFFFFFFFE) - b.l1
v.l2 = (a.l2 + 0xFFFFFFFFFFFFE) - b.l2
v.l3 = (a.l3 + 0xFFFFFFFFFFFFE) - b.l3
v.l4 = (a.l4 + 0xFFFFFFFFFFFFE) - b.l4
return v.carry_propagate_generic()
}
// negate sets v = -a, and returns v.
pub fn (mut v Element) negate(a Element) Element {
return v.subtract(edwards25519.fe_zero, a)
}
// invert sets v = 1/z mod p, and returns v.
//
// If z == 0, invert returns v = 0.
pub fn (mut v Element) invert(z Element) Element {
// Inversion is implemented as exponentiation with exponent p 2. It uses the
// same sequence of 255 squarings and 11 multiplications as [Curve25519].
mut z2 := Element{}
mut z9 := Element{}
mut z11 := Element{}
mut z2_5_0 := Element{}
mut z2_10_0 := Element{}
mut z2_20_0 := Element{}
mut z2_50_0 := Element{}
mut z2_100_0 := Element{}
mut t := Element{}
z2.square(z) // 2
t.square(z2) // 4
t.square(t) // 8
z9.multiply(t, z) // 9
z11.multiply(z9, z2) // 11
t.square(z11) // 22
z2_5_0.multiply(t, z9) // 31 = 2^5 - 2^0
t.square(z2_5_0) // 2^6 - 2^1
for i := 0; i < 4; i++ {
t.square(t) // 2^10 - 2^5
}
z2_10_0.multiply(t, z2_5_0) // 2^10 - 2^0
t.square(z2_10_0) // 2^11 - 2^1
for i := 0; i < 9; i++ {
t.square(t) // 2^20 - 2^10
}
z2_20_0.multiply(t, z2_10_0) // 2^20 - 2^0
t.square(z2_20_0) // 2^21 - 2^1
for i := 0; i < 19; i++ {
t.square(t) // 2^40 - 2^20
}
t.multiply(t, z2_20_0) // 2^40 - 2^0
t.square(t) // 2^41 - 2^1
for i := 0; i < 9; i++ {
t.square(t) // 2^50 - 2^10
}
z2_50_0.multiply(t, z2_10_0) // 2^50 - 2^0
t.square(z2_50_0) // 2^51 - 2^1
for i := 0; i < 49; i++ {
t.square(t) // 2^100 - 2^50
}
z2_100_0.multiply(t, z2_50_0) // 2^100 - 2^0
t.square(z2_100_0) // 2^101 - 2^1
for i := 0; i < 99; i++ {
t.square(t) // 2^200 - 2^100
}
t.multiply(t, z2_100_0) // 2^200 - 2^0
t.square(t) // 2^201 - 2^1
for i := 0; i < 49; i++ {
t.square(t) // 2^250 - 2^50
}
t.multiply(t, z2_50_0) // 2^250 - 2^0
t.square(t) // 2^251 - 2^1
t.square(t) // 2^252 - 2^2
t.square(t) // 2^253 - 2^3
t.square(t) // 2^254 - 2^4
t.square(t) // 2^255 - 2^5
return v.multiply(t, z11) // 2^255 - 21
}
// square sets v = x * x, and returns v.
pub fn (mut v Element) square(x Element) Element {
v = fe_square_generic(x)
return v
}
// multiply sets v = x * y, and returns v.
pub fn (mut v Element) multiply(x Element, y Element) Element {
v = fe_mul_generic(x, y)
return v
}
// mul_51 returns lo + hi * 2⁵¹ = a * b.
fn mul_51(a u64, b u32) (u64, u64) {
mh, ml := bits.mul_64(a, u64(b))
lo := ml & edwards25519.mask_low_51_bits
hi := (mh << 13) | (ml >> 51)
return lo, hi
}
// pow_22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3.
pub fn (mut v Element) pow_22523(x Element) Element {
mut t0, mut t1, mut t2 := Element{}, Element{}, Element{}
t0.square(x) // x^2
t1.square(t0) // x^4
t1.square(t1) // x^8
t1.multiply(x, t1) // x^9
t0.multiply(t0, t1) // x^11
t0.square(t0) // x^22
t0.multiply(t1, t0) // x^31
t1.square(t0) // x^62
for i := 1; i < 5; i++ { // x^992
t1.square(t1)
}
t0.multiply(t1, t0) // x^1023 -> 1023 = 2^10 - 1
t1.square(t0) // 2^11 - 2
for i := 1; i < 10; i++ { // 2^20 - 2^10
t1.square(t1)
}
t1.multiply(t1, t0) // 2^20 - 1
t2.square(t1) // 2^21 - 2
for i := 1; i < 20; i++ { // 2^40 - 2^20
t2.square(t2)
}
t1.multiply(t2, t1) // 2^40 - 1
t1.square(t1) // 2^41 - 2
for i := 1; i < 10; i++ { // 2^50 - 2^10
t1.square(t1)
}
t0.multiply(t1, t0) // 2^50 - 1
t1.square(t0) // 2^51 - 2
for i := 1; i < 50; i++ { // 2^100 - 2^50
t1.square(t1)
}
t1.multiply(t1, t0) // 2^100 - 1
t2.square(t1) // 2^101 - 2
for i := 1; i < 100; i++ { // 2^200 - 2^100
t2.square(t2)
}
t1.multiply(t2, &t1) // 2^200 - 1
t1.square(t1) // 2^201 - 2
for i := 1; i < 50; i++ { // 2^250 - 2^50
t1.square(t1)
}
t0.multiply(t1, t0) // 2^250 - 1
t0.square(t0) // 2^251 - 2
t0.square(t0) // 2^252 - 4
return v.multiply(t0, x) // 2^252 - 3 -> x^(2^252-3)
}
// sqrt_ratio sets r to the non-negative square root of the ratio of u and v.
//
// If u/v is square, sqrt_ratio returns r and 1. If u/v is not square, sqrt_ratio
// sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00,
// and returns r and 0.
pub fn (mut r Element) sqrt_ratio(u Element, v Element) (Element, int) {
mut a, mut b := Element{}, Element{}
// r = (u * v3) * (u * v7)^((p-5)/8)
v2 := a.square(v)
uv3 := b.multiply(u, b.multiply(v2, v))
uv7 := a.multiply(uv3, a.square(v2))
r.multiply(uv3, r.pow_22523(uv7))
mut check := a.multiply(v, a.square(r)) // check = v * r^2
mut uneg := b.negate(u)
correct_sign_sqrt := check.equal(u)
flipped_sign_sqrt := check.equal(uneg)
flipped_sign_sqrt_i := check.equal(uneg.multiply(uneg, edwards25519.sqrt_m1))
rprime := b.multiply(r, edwards25519.sqrt_m1) // r_prime = SQRT_M1 * r
// r = CT_selected(r_prime IF flipped_sign_sqrt | flipped_sign_sqrt_i ELSE r)
r.selected(rprime, r, flipped_sign_sqrt | flipped_sign_sqrt_i)
r.absolute(r) // Choose the nonnegative square root.
return r, correct_sign_sqrt | flipped_sign_sqrt
}
// mask_64_bits returns 0xffffffff if cond is 1, and 0 otherwise.
fn mask_64_bits(cond int) u64 {
// in go, `^` operates on bit mean NOT, flip bit
// in v, its a ~ bitwise NOT
return ~(u64(cond) - 1)
}
// selected sets v to a if cond == 1, and to b if cond == 0.
pub fn (mut v Element) selected(a Element, b Element, cond int) Element {
// see above notes
m := mask_64_bits(cond)
v.l0 = (m & a.l0) | (~m & b.l0)
v.l1 = (m & a.l1) | (~m & b.l1)
v.l2 = (m & a.l2) | (~m & b.l2)
v.l3 = (m & a.l3) | (~m & b.l3)
v.l4 = (m & a.l4) | (~m & b.l4)
return v
}
// is_negative returns 1 if v is negative, and 0 otherwise.
pub fn (mut v Element) is_negative() int {
return int(v.bytes()[0] & 1)
}
// absolute sets v to |u|, and returns v.
pub fn (mut v Element) absolute(u Element) Element {
mut e := Element{}
mut uk := u
return v.selected(e.negate(uk), uk, uk.is_negative())
}
// set sets v = a, and returns v.
pub fn (mut v Element) set(a Element) Element {
v = a
return v
}
// set_bytes sets v to x, where x is a 32-byte little-endian encoding. If x is
// not of the right length, SetUniformBytes returns an error, and the
// receiver is unchanged.
//
// Consistent with RFC 7748, the most significant bit (the high bit of the
// last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1)
// are accepted. Note that this is laxer than specified by RFC 8032.
pub fn (mut v Element) set_bytes(x []byte) ?Element {
if x.len != 32 {
return error('edwards25519: invalid edwards25519 element input size')
}
// Bits 0:51 (bytes 0:8, bits 0:64, shift 0, mask 51).
v.l0 = binary.little_endian_u64(x[0..8])
v.l0 &= edwards25519.mask_low_51_bits
// Bits 51:102 (bytes 6:14, bits 48:112, shift 3, mask 51).
v.l1 = binary.little_endian_u64(x[6..14]) >> 3
v.l1 &= edwards25519.mask_low_51_bits
// Bits 102:153 (bytes 12:20, bits 96:160, shift 6, mask 51).
v.l2 = binary.little_endian_u64(x[12..20]) >> 6
v.l2 &= edwards25519.mask_low_51_bits
// Bits 153:204 (bytes 19:27, bits 152:216, shift 1, mask 51).
v.l3 = binary.little_endian_u64(x[19..27]) >> 1
v.l3 &= edwards25519.mask_low_51_bits
// Bits 204:251 (bytes 24:32, bits 192:256, shift 12, mask 51).
// Note: not bytes 25:33, shift 4, to avoid overread.
v.l4 = binary.little_endian_u64(x[24..32]) >> 12
v.l4 &= edwards25519.mask_low_51_bits
return v
}
// bytes returns the canonical 32-byte little-endian encoding of v.
pub fn (mut v Element) bytes() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
// out := v.bytes_generic()
return v.bytes_generic()
}
fn (mut v Element) bytes_generic() []byte {
mut out := []byte{len: 32}
v = v.reduce()
mut buf := []byte{len: 8}
idxs := [v.l0, v.l1, v.l2, v.l3, v.l4]
for i, l in idxs {
bits_offset := i * 51
binary.little_endian_put_u64(mut buf, l << u32(bits_offset % 8))
for j, bb in buf {
off := bits_offset / 8 + j
if off >= out.len {
break
}
out[off] |= bb
}
}
return out
}
// equal returns 1 if v and u are equal, and 0 otherwise.
pub fn (mut v Element) equal(ue Element) int {
mut u := ue
sa := u.bytes()
sv := v.bytes()
return subtle.constant_time_compare(sa, sv)
}
// swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v.
pub fn (mut v Element) swap(mut u Element, cond int) {
// mut u := ue
m := mask_64_bits(cond)
mut t := m & (v.l0 ^ u.l0)
v.l0 ^= t
u.l0 ^= t
t = m & (v.l1 ^ u.l1)
v.l1 ^= t
u.l1 ^= t
t = m & (v.l2 ^ u.l2)
v.l2 ^= t
u.l2 ^= t
t = m & (v.l3 ^ u.l3)
v.l3 ^= t
u.l3 ^= t
t = m & (v.l4 ^ u.l4)
v.l4 ^= t
u.l4 ^= t
}
// mult_32 sets v = x * y, and returns v.
pub fn (mut v Element) mult_32(x Element, y u32) Element {
x0lo, x0hi := mul_51(x.l0, y)
x1lo, x1hi := mul_51(x.l1, y)
x2lo, x2hi := mul_51(x.l2, y)
x3lo, x3hi := mul_51(x.l3, y)
x4lo, x4hi := mul_51(x.l4, y)
v.l0 = x0lo + 19 * x4hi // carried over per the reduction identity
v.l1 = x1lo + x0hi
v.l2 = x2lo + x1hi
v.l3 = x3lo + x2hi
v.l4 = x4lo + x3hi
// The hi portions are going to be only 32 bits, plus any previous excess,
// so we can skip the carry propagation.
return v
}
fn swap_endianness(mut buf []byte) []byte {
for i := 0; i < buf.len / 2; i++ {
buf[i], buf[buf.len - i - 1] = buf[buf.len - i - 1], buf[i]
}
return buf
}