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#![allow(non_snake_case)]
use crate::backend::serial::curve_models::ProjectiveNielsPoint;
use crate::edwards::EdwardsPoint;
use crate::scalar::Scalar;
use crate::traits::Identity;
use crate::window::LookupTable;
/// Perform constant-time, variable-base scalar multiplication.
#[rustfmt::skip] // keep alignment of explanatory comments
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`.
// This decomposition requires s < 2^255, which is guaranteed by Scalar invariant #1.
let scalar_digits = scalar.as_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.as_projective(); // tmp2 = (prev) in P2 coords
tmp1 = tmp2.double(); // tmp1 = 2*(prev) in P1xP1 coords
tmp2 = tmp1.as_projective(); // tmp2 = 2*(prev) in P2 coords
tmp1 = tmp2.double(); // tmp1 = 4*(prev) in P1xP1 coords
tmp2 = tmp1.as_projective(); // tmp2 = 4*(prev) in P2 coords
tmp1 = tmp2.double(); // tmp1 = 8*(prev) in P1xP1 coords
tmp2 = tmp1.as_projective(); // tmp2 = 8*(prev) in P2 coords
tmp1 = tmp2.double(); // tmp1 = 16*(prev) in P1xP1 coords
tmp3 = tmp1.as_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.as_extended()
}