47 lines
2.0 KiB
Rust
47 lines
2.0 KiB
Rust
#![allow(non_snake_case)]
|
|
|
|
use traits::Identity;
|
|
use scalar::Scalar;
|
|
use edwards::EdwardsPoint;
|
|
use backend::serial::curve_models::{ProjectiveNielsPoint, ProjectivePoint};
|
|
use window::LookupTable;
|
|
|
|
/// Perform constant-time, variable-base scalar multiplication.
|
|
pub(crate) fn mul(point: &EdwardsPoint, scalar: &Scalar) -> EdwardsPoint {
|
|
// Construct a lookup table of [P,2P,3P,4P,5P,6P,7P,8P]
|
|
let lookup_table = LookupTable::<ProjectiveNielsPoint>::from(point);
|
|
// Setting s = scalar, compute
|
|
//
|
|
// s = s_0 + s_1*16^1 + ... + s_63*16^63,
|
|
//
|
|
// with `-8 ≤ s_i < 8` for `0 ≤ i < 63` and `-8 ≤ s_63 ≤ 8`.
|
|
let scalar_digits = scalar.to_radix_16();
|
|
// Compute s*P as
|
|
//
|
|
// s*P = P*(s_0 + s_1*16^1 + s_2*16^2 + ... + s_63*16^63)
|
|
// s*P = P*s_0 + P*s_1*16^1 + P*s_2*16^2 + ... + P*s_63*16^63
|
|
// s*P = P*s_0 + 16*(P*s_1 + 16*(P*s_2 + 16*( ... + P*s_63)...))
|
|
//
|
|
// We sum right-to-left.
|
|
|
|
// Unwrap first loop iteration to save computing 16*identity
|
|
let mut tmp2;
|
|
let mut tmp3 = EdwardsPoint::identity();
|
|
let mut tmp1 = &tmp3 + &lookup_table.select(scalar_digits[63]);
|
|
// Now tmp1 = s_63*P in P1xP1 coords
|
|
for i in (0..63).rev() {
|
|
tmp2 = tmp1.to_projective(); // tmp2 = (prev) in P2 coords
|
|
tmp1 = tmp2.double(); // tmp1 = 2*(prev) in P1xP1 coords
|
|
tmp2 = tmp1.to_projective(); // tmp2 = 2*(prev) in P2 coords
|
|
tmp1 = tmp2.double(); // tmp1 = 4*(prev) in P1xP1 coords
|
|
tmp2 = tmp1.to_projective(); // tmp2 = 4*(prev) in P2 coords
|
|
tmp1 = tmp2.double(); // tmp1 = 8*(prev) in P1xP1 coords
|
|
tmp2 = tmp1.to_projective(); // tmp2 = 8*(prev) in P2 coords
|
|
tmp1 = tmp2.double(); // tmp1 = 16*(prev) in P1xP1 coords
|
|
tmp3 = tmp1.to_extended(); // tmp3 = 16*(prev) in P3 coords
|
|
tmp1 = &tmp3 + &lookup_table.select(scalar_digits[i]);
|
|
// Now tmp1 = s_i*P + 16*(prev) in P1xP1 coords
|
|
}
|
|
tmp1.to_extended()
|
|
}
|