530 lines
22 KiB
Rust
530 lines
22 KiB
Rust
//! Arithmetic mod 2^252 + 27742317777372353535851937790883648493
|
||
//! with 9 29-bit unsigned limbs
|
||
//!
|
||
//! To see that this is safe for intermediate results, note that
|
||
//! the largest limb in a 9 by 9 product of 29-bit limbs will be
|
||
//! (0x1fffffff^2) * 9 = 0x23fffffdc0000009 (62 bits).
|
||
//!
|
||
//! For a one level Karatsuba decomposition, the specific ranges
|
||
//! depend on how the limbs are combined, but will stay within
|
||
//! -0x1ffffffe00000008 (62 bits with sign bit) to
|
||
//! 0x43fffffbc0000011 (63 bits), which is still safe.
|
||
|
||
use core::fmt::Debug;
|
||
use core::ops::{Index, IndexMut};
|
||
|
||
use zeroize::Zeroize;
|
||
|
||
use constants;
|
||
|
||
/// The `Scalar29` struct represents an element in ℤ/lℤ as 9 29-bit limbs
|
||
#[derive(Copy,Clone)]
|
||
pub struct Scalar29(pub [u32; 9]);
|
||
|
||
impl Debug for Scalar29 {
|
||
fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
|
||
write!(f, "Scalar29: {:?}", &self.0[..])
|
||
}
|
||
}
|
||
|
||
impl Zeroize for Scalar29 {
|
||
fn zeroize(&mut self) {
|
||
self.0.zeroize();
|
||
}
|
||
}
|
||
|
||
impl Index<usize> for Scalar29 {
|
||
type Output = u32;
|
||
fn index(&self, _index: usize) -> &u32 {
|
||
&(self.0[_index])
|
||
}
|
||
}
|
||
|
||
impl IndexMut<usize> for Scalar29 {
|
||
fn index_mut(&mut self, _index: usize) -> &mut u32 {
|
||
&mut (self.0[_index])
|
||
}
|
||
}
|
||
|
||
/// u32 * u32 = u64 multiply helper
|
||
#[inline(always)]
|
||
fn m(x: u32, y: u32) -> u64 {
|
||
(x as u64) * (y as u64)
|
||
}
|
||
|
||
impl Scalar29 {
|
||
/// Return the zero scalar.
|
||
pub fn zero() -> Scalar29 {
|
||
Scalar29([0,0,0,0,0,0,0,0,0])
|
||
}
|
||
|
||
/// Unpack a 32 byte / 256 bit scalar into 9 29-bit limbs.
|
||
pub fn from_bytes(bytes: &[u8; 32]) -> Scalar29 {
|
||
let mut words = [0u32; 8];
|
||
for i in 0..8 {
|
||
for j in 0..4 {
|
||
words[i] |= (bytes[(i * 4) + j] as u32) << (j * 8);
|
||
}
|
||
}
|
||
|
||
let mask = (1u32 << 29) - 1;
|
||
let top_mask = (1u32 << 24) - 1;
|
||
let mut s = Scalar29::zero();
|
||
|
||
s[ 0] = words[0] & mask;
|
||
s[ 1] = ((words[0] >> 29) | (words[1] << 3)) & mask;
|
||
s[ 2] = ((words[1] >> 26) | (words[2] << 6)) & mask;
|
||
s[ 3] = ((words[2] >> 23) | (words[3] << 9)) & mask;
|
||
s[ 4] = ((words[3] >> 20) | (words[4] << 12)) & mask;
|
||
s[ 5] = ((words[4] >> 17) | (words[5] << 15)) & mask;
|
||
s[ 6] = ((words[5] >> 14) | (words[6] << 18)) & mask;
|
||
s[ 7] = ((words[6] >> 11) | (words[7] << 21)) & mask;
|
||
s[ 8] = (words[7] >> 8) & top_mask;
|
||
|
||
s
|
||
}
|
||
|
||
/// Reduce a 64 byte / 512 bit scalar mod l.
|
||
pub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar29 {
|
||
let mut words = [0u32; 16];
|
||
for i in 0..16 {
|
||
for j in 0..4 {
|
||
words[i] |= (bytes[(i * 4) + j] as u32) << (j * 8);
|
||
}
|
||
}
|
||
|
||
let mask = (1u32 << 29) - 1;
|
||
let mut lo = Scalar29::zero();
|
||
let mut hi = Scalar29::zero();
|
||
|
||
lo[0] = words[ 0] & mask;
|
||
lo[1] = ((words[ 0] >> 29) | (words[ 1] << 3)) & mask;
|
||
lo[2] = ((words[ 1] >> 26) | (words[ 2] << 6)) & mask;
|
||
lo[3] = ((words[ 2] >> 23) | (words[ 3] << 9)) & mask;
|
||
lo[4] = ((words[ 3] >> 20) | (words[ 4] << 12)) & mask;
|
||
lo[5] = ((words[ 4] >> 17) | (words[ 5] << 15)) & mask;
|
||
lo[6] = ((words[ 5] >> 14) | (words[ 6] << 18)) & mask;
|
||
lo[7] = ((words[ 6] >> 11) | (words[ 7] << 21)) & mask;
|
||
lo[8] = ((words[ 7] >> 8) | (words[ 8] << 24)) & mask;
|
||
hi[0] = ((words[ 8] >> 5) | (words[ 9] << 27)) & mask;
|
||
hi[1] = (words[ 9] >> 2) & mask;
|
||
hi[2] = ((words[ 9] >> 31) | (words[10] << 1)) & mask;
|
||
hi[3] = ((words[10] >> 28) | (words[11] << 4)) & mask;
|
||
hi[4] = ((words[11] >> 25) | (words[12] << 7)) & mask;
|
||
hi[5] = ((words[12] >> 22) | (words[13] << 10)) & mask;
|
||
hi[6] = ((words[13] >> 19) | (words[14] << 13)) & mask;
|
||
hi[7] = ((words[14] >> 16) | (words[15] << 16)) & mask;
|
||
hi[8] = words[15] >> 13 ;
|
||
|
||
lo = Scalar29::montgomery_mul(&lo, &constants::R); // (lo * R) / R = lo
|
||
hi = Scalar29::montgomery_mul(&hi, &constants::RR); // (hi * R^2) / R = hi * R
|
||
|
||
Scalar29::add(&hi, &lo) // (hi * R) + lo
|
||
}
|
||
|
||
/// Pack the limbs of this `Scalar29` into 32 bytes.
|
||
pub fn to_bytes(&self) -> [u8; 32] {
|
||
let mut s = [0u8; 32];
|
||
|
||
s[0] = (self.0[ 0] >> 0) as u8;
|
||
s[1] = (self.0[ 0] >> 8) as u8;
|
||
s[2] = (self.0[ 0] >> 16) as u8;
|
||
s[3] = ((self.0[ 0] >> 24) | (self.0[ 1] << 5)) as u8;
|
||
s[4] = (self.0[ 1] >> 3) as u8;
|
||
s[5] = (self.0[ 1] >> 11) as u8;
|
||
s[6] = (self.0[ 1] >> 19) as u8;
|
||
s[7] = ((self.0[ 1] >> 27) | (self.0[ 2] << 2)) as u8;
|
||
s[8] = (self.0[ 2] >> 6) as u8;
|
||
s[9] = (self.0[ 2] >> 14) as u8;
|
||
s[10] = ((self.0[ 2] >> 22) | (self.0[ 3] << 7)) as u8;
|
||
s[11] = (self.0[ 3] >> 1) as u8;
|
||
s[12] = (self.0[ 3] >> 9) as u8;
|
||
s[13] = (self.0[ 3] >> 17) as u8;
|
||
s[14] = ((self.0[ 3] >> 25) | (self.0[ 4] << 4)) as u8;
|
||
s[15] = (self.0[ 4] >> 4) as u8;
|
||
s[16] = (self.0[ 4] >> 12) as u8;
|
||
s[17] = (self.0[ 4] >> 20) as u8;
|
||
s[18] = ((self.0[ 4] >> 28) | (self.0[ 5] << 1)) as u8;
|
||
s[19] = (self.0[ 5] >> 7) as u8;
|
||
s[20] = (self.0[ 5] >> 15) as u8;
|
||
s[21] = ((self.0[ 5] >> 23) | (self.0[ 6] << 6)) as u8;
|
||
s[22] = (self.0[ 6] >> 2) as u8;
|
||
s[23] = (self.0[ 6] >> 10) as u8;
|
||
s[24] = (self.0[ 6] >> 18) as u8;
|
||
s[25] = ((self.0[ 6] >> 26) | (self.0[ 7] << 3)) as u8;
|
||
s[26] = (self.0[ 7] >> 5) as u8;
|
||
s[27] = (self.0[ 7] >> 13) as u8;
|
||
s[28] = (self.0[ 7] >> 21) as u8;
|
||
s[29] = (self.0[ 8] >> 0) as u8;
|
||
s[30] = (self.0[ 8] >> 8) as u8;
|
||
s[31] = (self.0[ 8] >> 16) as u8;
|
||
|
||
s
|
||
}
|
||
|
||
/// Compute `a + b` (mod l).
|
||
pub fn add(a: &Scalar29, b: &Scalar29) -> Scalar29 {
|
||
let mut sum = Scalar29::zero();
|
||
let mask = (1u32 << 29) - 1;
|
||
|
||
// a + b
|
||
let mut carry: u32 = 0;
|
||
for i in 0..9 {
|
||
carry = a[i] + b[i] + (carry >> 29);
|
||
sum[i] = carry & mask;
|
||
}
|
||
|
||
// subtract l if the sum is >= l
|
||
Scalar29::sub(&sum, &constants::L)
|
||
}
|
||
|
||
/// Compute `a - b` (mod l).
|
||
pub fn sub(a: &Scalar29, b: &Scalar29) -> Scalar29 {
|
||
let mut difference = Scalar29::zero();
|
||
let mask = (1u32 << 29) - 1;
|
||
|
||
// a - b
|
||
let mut borrow: u32 = 0;
|
||
for i in 0..9 {
|
||
borrow = a[i].wrapping_sub(b[i] + (borrow >> 31));
|
||
difference[i] = borrow & mask;
|
||
}
|
||
|
||
// conditionally add l if the difference is negative
|
||
let underflow_mask = ((borrow >> 31) ^ 1).wrapping_sub(1);
|
||
let mut carry: u32 = 0;
|
||
for i in 0..9 {
|
||
carry = (carry >> 29) + difference[i] + (constants::L[i] & underflow_mask);
|
||
difference[i] = carry & mask;
|
||
}
|
||
|
||
difference
|
||
}
|
||
|
||
/// Compute `a * b`.
|
||
///
|
||
/// This is implemented with a one-level refined Karatsuba decomposition
|
||
#[inline(always)]
|
||
pub (crate) fn mul_internal(a: &Scalar29, b: &Scalar29) -> [u64; 17] {
|
||
let mut z = [0u64; 17];
|
||
|
||
z[0] = m(a[0],b[0]); // c00
|
||
z[1] = m(a[0],b[1]) + m(a[1],b[0]); // c01
|
||
z[2] = m(a[0],b[2]) + m(a[1],b[1]) + m(a[2],b[0]); // c02
|
||
z[3] = m(a[0],b[3]) + m(a[1],b[2]) + m(a[2],b[1]) + m(a[3],b[0]); // c03
|
||
z[4] = m(a[0],b[4]) + m(a[1],b[3]) + m(a[2],b[2]) + m(a[3],b[1]) + m(a[4],b[0]); // c04
|
||
z[5] = m(a[1],b[4]) + m(a[2],b[3]) + m(a[3],b[2]) + m(a[4],b[1]); // c05
|
||
z[6] = m(a[2],b[4]) + m(a[3],b[3]) + m(a[4],b[2]); // c06
|
||
z[7] = m(a[3],b[4]) + m(a[4],b[3]); // c07
|
||
z[8] = (m(a[4],b[4])).wrapping_sub(z[3]); // c08 - c03
|
||
|
||
z[10] = z[5].wrapping_sub(m(a[5],b[5])); // c05mc10
|
||
z[11] = z[6].wrapping_sub(m(a[5],b[6]) + m(a[6],b[5])); // c06mc11
|
||
z[12] = z[7].wrapping_sub(m(a[5],b[7]) + m(a[6],b[6]) + m(a[7],b[5])); // c07mc12
|
||
z[13] = m(a[5],b[8]) + m(a[6],b[7]) + m(a[7],b[6]) + m(a[8],b[5]); // c13
|
||
z[14] = m(a[6],b[8]) + m(a[7],b[7]) + m(a[8],b[6]); // c14
|
||
z[15] = m(a[7],b[8]) + m(a[8],b[7]); // c15
|
||
z[16] = m(a[8],b[8]); // c16
|
||
|
||
z[ 5] = z[10].wrapping_sub(z[ 0]); // c05mc10 - c00
|
||
z[ 6] = z[11].wrapping_sub(z[ 1]); // c06mc11 - c01
|
||
z[ 7] = z[12].wrapping_sub(z[ 2]); // c07mc12 - c02
|
||
z[ 8] = z[ 8].wrapping_sub(z[13]); // c08mc13 - c03
|
||
z[ 9] = z[14].wrapping_add(z[ 4]); // c14 + c04
|
||
z[10] = z[15].wrapping_add(z[10]); // c15 + c05mc10
|
||
z[11] = z[16].wrapping_add(z[11]); // c16 + c06mc11
|
||
|
||
let aa = [
|
||
a[0]+a[5],
|
||
a[1]+a[6],
|
||
a[2]+a[7],
|
||
a[3]+a[8]
|
||
];
|
||
|
||
let bb = [
|
||
b[0]+b[5],
|
||
b[1]+b[6],
|
||
b[2]+b[7],
|
||
b[3]+b[8]
|
||
];
|
||
|
||
z[ 5] = (m(aa[0],bb[0])) .wrapping_add(z[ 5]); // c20 + c05mc10 - c00
|
||
z[ 6] = (m(aa[0],bb[1]) + m(aa[1],bb[0])) .wrapping_add(z[ 6]); // c21 + c06mc11 - c01
|
||
z[ 7] = (m(aa[0],bb[2]) + m(aa[1],bb[1]) + m(aa[2],bb[0])) .wrapping_add(z[ 7]); // c22 + c07mc12 - c02
|
||
z[ 8] = (m(aa[0],bb[3]) + m(aa[1],bb[2]) + m(aa[2],bb[1]) + m(aa[3],bb[0])) .wrapping_add(z[ 8]); // c23 + c08mc13 - c03
|
||
z[ 9] = (m(aa[0], b[4]) + m(aa[1],bb[3]) + m(aa[2],bb[2]) + m(aa[3],bb[1]) + m(a[4],bb[0])).wrapping_sub(z[ 9]); // c24 - c14 - c04
|
||
z[10] = ( m(aa[1], b[4]) + m(aa[2],bb[3]) + m(aa[3],bb[2]) + m(a[4],bb[1])).wrapping_sub(z[10]); // c25 - c15 - c05mc10
|
||
z[11] = ( m(aa[2], b[4]) + m(aa[3],bb[3]) + m(a[4],bb[2])).wrapping_sub(z[11]); // c26 - c16 - c06mc11
|
||
z[12] = ( m(aa[3], b[4]) + m(a[4],bb[3])).wrapping_sub(z[12]); // c27 - c07mc12
|
||
|
||
z
|
||
}
|
||
|
||
/// Compute `a^2`.
|
||
#[inline(always)]
|
||
fn square_internal(a: &Scalar29) -> [u64; 17] {
|
||
let aa = [
|
||
a[0]*2,
|
||
a[1]*2,
|
||
a[2]*2,
|
||
a[3]*2,
|
||
a[4]*2,
|
||
a[5]*2,
|
||
a[6]*2,
|
||
a[7]*2
|
||
];
|
||
|
||
[
|
||
m( a[0],a[0]),
|
||
m(aa[0],a[1]),
|
||
m(aa[0],a[2]) + m( a[1],a[1]),
|
||
m(aa[0],a[3]) + m(aa[1],a[2]),
|
||
m(aa[0],a[4]) + m(aa[1],a[3]) + m( a[2],a[2]),
|
||
m(aa[0],a[5]) + m(aa[1],a[4]) + m(aa[2],a[3]),
|
||
m(aa[0],a[6]) + m(aa[1],a[5]) + m(aa[2],a[4]) + m( a[3],a[3]),
|
||
m(aa[0],a[7]) + m(aa[1],a[6]) + m(aa[2],a[5]) + m(aa[3],a[4]),
|
||
m(aa[0],a[8]) + m(aa[1],a[7]) + m(aa[2],a[6]) + m(aa[3],a[5]) + m( a[4],a[4]),
|
||
m(aa[1],a[8]) + m(aa[2],a[7]) + m(aa[3],a[6]) + m(aa[4],a[5]),
|
||
m(aa[2],a[8]) + m(aa[3],a[7]) + m(aa[4],a[6]) + m( a[5],a[5]),
|
||
m(aa[3],a[8]) + m(aa[4],a[7]) + m(aa[5],a[6]),
|
||
m(aa[4],a[8]) + m(aa[5],a[7]) + m( a[6],a[6]),
|
||
m(aa[5],a[8]) + m(aa[6],a[7]),
|
||
m(aa[6],a[8]) + m( a[7],a[7]),
|
||
m(aa[7],a[8]),
|
||
m( a[8],a[8]),
|
||
]
|
||
}
|
||
|
||
/// Compute `limbs/R` (mod l), where R is the Montgomery modulus 2^261
|
||
#[inline(always)]
|
||
pub (crate) fn montgomery_reduce(limbs: &[u64; 17]) -> Scalar29 {
|
||
|
||
#[inline(always)]
|
||
fn part1(sum: u64) -> (u64, u32) {
|
||
let p = (sum as u32).wrapping_mul(constants::LFACTOR) & ((1u32 << 29) - 1);
|
||
((sum + m(p,constants::L[0])) >> 29, p)
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn part2(sum: u64) -> (u64, u32) {
|
||
let w = (sum as u32) & ((1u32 << 29) - 1);
|
||
(sum >> 29, w)
|
||
}
|
||
|
||
// note: l5,l6,l7 are zero, so their multiplies can be skipped
|
||
let l = &constants::L;
|
||
|
||
// the first half computes the Montgomery adjustment factor n, and begins adding n*l to make limbs divisible by R
|
||
let (carry, n0) = part1( limbs[ 0]);
|
||
let (carry, n1) = part1(carry + limbs[ 1] + m(n0,l[1]));
|
||
let (carry, n2) = part1(carry + limbs[ 2] + m(n0,l[2]) + m(n1,l[1]));
|
||
let (carry, n3) = part1(carry + limbs[ 3] + m(n0,l[3]) + m(n1,l[2]) + m(n2,l[1]));
|
||
let (carry, n4) = part1(carry + limbs[ 4] + m(n0,l[4]) + m(n1,l[3]) + m(n2,l[2]) + m(n3,l[1]));
|
||
let (carry, n5) = part1(carry + limbs[ 5] + m(n1,l[4]) + m(n2,l[3]) + m(n3,l[2]) + m(n4,l[1]));
|
||
let (carry, n6) = part1(carry + limbs[ 6] + m(n2,l[4]) + m(n3,l[3]) + m(n4,l[2]) + m(n5,l[1]));
|
||
let (carry, n7) = part1(carry + limbs[ 7] + m(n3,l[4]) + m(n4,l[3]) + m(n5,l[2]) + m(n6,l[1]));
|
||
let (carry, n8) = part1(carry + limbs[ 8] + m(n0,l[8]) + m(n4,l[4]) + m(n5,l[3]) + m(n6,l[2]) + m(n7,l[1]));
|
||
|
||
// limbs is divisible by R now, so we can divide by R by simply storing the upper half as the result
|
||
let (carry, r0) = part2(carry + limbs[ 9] + m(n1,l[8]) + m(n5,l[4]) + m(n6,l[3]) + m(n7,l[2]) + m(n8,l[1]));
|
||
let (carry, r1) = part2(carry + limbs[10] + m(n2,l[8]) + m(n6,l[4]) + m(n7,l[3]) + m(n8,l[2]));
|
||
let (carry, r2) = part2(carry + limbs[11] + m(n3,l[8]) + m(n7,l[4]) + m(n8,l[3]));
|
||
let (carry, r3) = part2(carry + limbs[12] + m(n4,l[8]) + m(n8,l[4]));
|
||
let (carry, r4) = part2(carry + limbs[13] + m(n5,l[8]) );
|
||
let (carry, r5) = part2(carry + limbs[14] + m(n6,l[8]) );
|
||
let (carry, r6) = part2(carry + limbs[15] + m(n7,l[8]) );
|
||
let (carry, r7) = part2(carry + limbs[16] + m(n8,l[8]));
|
||
let r8 = carry as u32;
|
||
|
||
// result may be >= l, so attempt to subtract l
|
||
Scalar29::sub(&Scalar29([r0,r1,r2,r3,r4,r5,r6,r7,r8]), l)
|
||
}
|
||
|
||
/// Compute `a * b` (mod l).
|
||
#[inline(never)]
|
||
pub fn mul(a: &Scalar29, b: &Scalar29) -> Scalar29 {
|
||
let ab = Scalar29::montgomery_reduce(&Scalar29::mul_internal(a, b));
|
||
Scalar29::montgomery_reduce(&Scalar29::mul_internal(&ab, &constants::RR))
|
||
}
|
||
|
||
/// Compute `a^2` (mod l).
|
||
#[inline(never)]
|
||
#[allow(dead_code)] // XXX we don't expose square() via the Scalar API
|
||
pub fn square(&self) -> Scalar29 {
|
||
let aa = Scalar29::montgomery_reduce(&Scalar29::square_internal(self));
|
||
Scalar29::montgomery_reduce(&Scalar29::mul_internal(&aa, &constants::RR))
|
||
}
|
||
|
||
/// Compute `(a * b) / R` (mod l), where R is the Montgomery modulus 2^261
|
||
#[inline(never)]
|
||
pub fn montgomery_mul(a: &Scalar29, b: &Scalar29) -> Scalar29 {
|
||
Scalar29::montgomery_reduce(&Scalar29::mul_internal(a, b))
|
||
}
|
||
|
||
/// Compute `(a^2) / R` (mod l) in Montgomery form, where R is the Montgomery modulus 2^261
|
||
#[inline(never)]
|
||
pub fn montgomery_square(&self) -> Scalar29 {
|
||
Scalar29::montgomery_reduce(&Scalar29::square_internal(self))
|
||
}
|
||
|
||
/// Puts a Scalar29 in to Montgomery form, i.e. computes `a*R (mod l)`
|
||
#[inline(never)]
|
||
pub fn to_montgomery(&self) -> Scalar29 {
|
||
Scalar29::montgomery_mul(self, &constants::RR)
|
||
}
|
||
|
||
/// Takes a Scalar29 out of Montgomery form, i.e. computes `a/R (mod l)`
|
||
pub fn from_montgomery(&self) -> Scalar29 {
|
||
let mut limbs = [0u64; 17];
|
||
for i in 0..9 {
|
||
limbs[i] = self[i] as u64;
|
||
}
|
||
Scalar29::montgomery_reduce(&limbs)
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod test {
|
||
use super::*;
|
||
|
||
/// Note: x is 2^253-1 which is slightly larger than the largest scalar produced by
|
||
/// this implementation (l-1), and should verify there are no overflows for valid scalars
|
||
///
|
||
/// x = 2^253-1 = 14474011154664524427946373126085988481658748083205070504932198000989141204991
|
||
/// x = 7237005577332262213973186563042994240801631723825162898930247062703686954002 mod l
|
||
/// x = 5147078182513738803124273553712992179887200054963030844803268920753008712037*R mod l in Montgomery form
|
||
pub static X: Scalar29 = Scalar29(
|
||
[0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff,
|
||
0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff,
|
||
0x001fffff]);
|
||
|
||
/// x^2 = 3078544782642840487852506753550082162405942681916160040940637093560259278169 mod l
|
||
pub static XX: Scalar29 = Scalar29(
|
||
[0x00217559, 0x000b3401, 0x103ff43b, 0x1462a62c,
|
||
0x1d6f9f38, 0x18e7a42f, 0x09a3dcee, 0x008dbe18,
|
||
0x0006ce65]);
|
||
|
||
/// x^2 = 2912514428060642753613814151688322857484807845836623976981729207238463947987*R mod l in Montgomery form
|
||
pub static XX_MONT: Scalar29 = Scalar29(
|
||
[0x152b4d2e, 0x0571d53b, 0x1da6d964, 0x188663b6,
|
||
0x1d1b5f92, 0x19d50e3f, 0x12306c29, 0x0c6f26fe,
|
||
0x00030edb]);
|
||
|
||
/// y = 6145104759870991071742105800796537629880401874866217824609283457819451087098
|
||
pub static Y: Scalar29 = Scalar29(
|
||
[0x1e1458fa, 0x165ba838, 0x1d787b36, 0x0e577f3a,
|
||
0x1d2baf06, 0x1d689a19, 0x1fff3047, 0x117704ab,
|
||
0x000d9601]);
|
||
|
||
/// x*y = 36752150652102274958925982391442301741
|
||
pub static XY: Scalar29 = Scalar29(
|
||
[0x0ba7632d, 0x017736bb, 0x15c76138, 0x0c69daa1,
|
||
0x000001ba, 0x00000000, 0x00000000, 0x00000000,
|
||
0x00000000]);
|
||
|
||
/// x*y = 3783114862749659543382438697751927473898937741870308063443170013240655651591*R mod l in Montgomery form
|
||
pub static XY_MONT: Scalar29 = Scalar29(
|
||
[0x077b51e1, 0x1c64e119, 0x02a19ef5, 0x18d2129e,
|
||
0x00de0430, 0x045a7bc8, 0x04cfc7c9, 0x1c002681,
|
||
0x000bdc1c]);
|
||
|
||
/// a = 2351415481556538453565687241199399922945659411799870114962672658845158063753
|
||
pub static A: Scalar29 = Scalar29(
|
||
[0x07b3be89, 0x02291b60, 0x14a99f03, 0x07dc3787,
|
||
0x0a782aae, 0x16262525, 0x0cfdb93f, 0x13f5718d,
|
||
0x000532da]);
|
||
|
||
/// b = 4885590095775723760407499321843594317911456947580037491039278279440296187236
|
||
pub static B: Scalar29 = Scalar29(
|
||
[0x15421564, 0x1e69fd72, 0x093d9692, 0x161785be,
|
||
0x1587d69f, 0x09d9dada, 0x130246c0, 0x0c0a8e72,
|
||
0x000acd25]);
|
||
|
||
/// a+b = 0
|
||
/// a-b = 4702830963113076907131374482398799845891318823599740229925345317690316127506
|
||
pub static AB: Scalar29 = Scalar29(
|
||
[0x0f677d12, 0x045236c0, 0x09533e06, 0x0fb86f0f,
|
||
0x14f0555c, 0x0c4c4a4a, 0x19fb727f, 0x07eae31a,
|
||
0x000a65b5]);
|
||
|
||
// c = (2^512 - 1) % l = 1627715501170711445284395025044413883736156588369414752970002579683115011840
|
||
pub static C: Scalar29 = Scalar29(
|
||
[0x049c0f00, 0x00308f1a, 0x0164d1e9, 0x1c374ed1,
|
||
0x1be65d00, 0x19e90bfa, 0x08f73bb1, 0x036f8613,
|
||
0x00039941]);
|
||
|
||
#[test]
|
||
fn mul_max() {
|
||
let res = Scalar29::mul(&X, &X);
|
||
for i in 0..9 {
|
||
assert!(res[i] == XX[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn square_max() {
|
||
let res = X.square();
|
||
for i in 0..9 {
|
||
assert!(res[i] == XX[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn montgomery_mul_max() {
|
||
let res = Scalar29::montgomery_mul(&X, &X);
|
||
for i in 0..9 {
|
||
assert!(res[i] == XX_MONT[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn montgomery_square_max() {
|
||
let res = X.montgomery_square();
|
||
for i in 0..9 {
|
||
assert!(res[i] == XX_MONT[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn mul() {
|
||
let res = Scalar29::mul(&X, &Y);
|
||
for i in 0..9 {
|
||
assert!(res[i] == XY[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn montgomery_mul() {
|
||
let res = Scalar29::montgomery_mul(&X, &Y);
|
||
for i in 0..9 {
|
||
assert!(res[i] == XY_MONT[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn add() {
|
||
let res = Scalar29::add(&A, &B);
|
||
let zero = Scalar29::zero();
|
||
for i in 0..9 {
|
||
assert!(res[i] == zero[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn sub() {
|
||
let res = Scalar29::sub(&A, &B);
|
||
for i in 0..9 {
|
||
assert!(res[i] == AB[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn from_bytes_wide() {
|
||
let bignum = [255u8; 64]; // 2^512 - 1
|
||
let reduced = Scalar29::from_bytes_wide(&bignum);
|
||
for i in 0..9 {
|
||
assert!(reduced[i] == C[i]);
|
||
}
|
||
}
|
||
}
|