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Combine differential_add and differential_double in Montgomery ladder.

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Isis Lovecruft 2017-12-18 01:02:55 +00:00
parent 06d802b986
commit 28f114f127
Failed to extract signature
1 changed files with 40 additions and 2 deletions
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42
src/montgomery.rs
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@ -31,6 +31,7 @@
use core::ops::{Mul, MulAssign};
use constants;
use constants::APLUS2_OVER_FOUR;
use field::FieldElement;
use edwards::{ExtendedPoint, CompressedEdwardsY};
use scalar::Scalar;
@ -379,6 +380,44 @@ impl MontgomeryPoint {
}
}
/// DOCDOC
fn differential_add_and_double(P: &mut MontgomeryPoint, Q: &mut MontgomeryPoint,
difference: &MontgomeryPoint) {
let t0 = &P.U + &P.W;
let t1 = &P.U - &P.W;
let t2 = &Q.U + &Q.W;
let t3 = &Q.U - &Q.W;
let t4 = t0.square(); // (U_P + W_P)^2 = U_P^2 + 2 U_P W_P + W_P^2
let t5 = t1.square(); // (U_P - W_P)^2 = U_P^2 - 2 U_P W_P + W_P^2
let t6 = &t4 - &t5; // 4 U_P W_P
let t7 = &t0 * &t3; // (U_P + W_P) (U_Q - W_Q) = U_P U_Q + W_P U_Q - U_P W_Q - W_P W_Q
let t8 = &t1 * &t2; // (U_P - W_P) (U_Q + W_Q) = U_P U_Q - W_P U_Q + U_P W_Q - W_P W_Q
let t9 = &t7 + &t8; // 2 (U_P U_Q - W_P W_Q)
let t10 = &t7 - &t8; // 2 (W_P U_Q - U_P W_Q)
let t11 = t9.square(); // 4 (U_P U_Q - W_P W_Q)^2
let t12 = t10.square(); // 4 (W_P U_Q - U_P W_Q)^2
let t13 = &APLUS2_OVER_FOUR * &t6; // (A + 2) U_P U_Q
let t14 = &t4 * &t5; // ((U_P + W_P)(U_P - W_P))^2 = (U_P^2 - W_P^2)^2 // P'_U
let t15 = &t13 + &t5; // (U_P - W_P)^2 + (A + 2) U_P W_P
let t16 = &t6 * &t15; // 4 (U_P W_P) ((U_P - W_P)^2 + (A + 2) U_P W_P) // P'_W
let t17 = &difference.U * &t12; // D_U * 4 (W_P U_Q - U_P W_Q)^2 // Q'_W
let t18 = &difference.W * &t11; // D_W * 4 (U_P U_Q - W_P W_Q)^2 // Q'_U
P.U = t14; // P'_U = (U_P + W_P)^2 (U_P - W_P)^2
P.W = t16; // P'_W = (4 U_P W_P) ((U_P - W_P)^2 + ((A + 2)/4) 4 U_P W_P)
Q.U = t18; // Q'_U = D_W * 4 (U_P U_Q - W_P W_Q)^2
Q.W = t17;
}
/// Multiply this `MontgomeryPoint` by a `Scalar`.
///
/// The reader is refered to §5.3 of ["Montgomery Curves and Their Arithmetic"
@ -399,8 +438,7 @@ impl<'a, 'b> Mul<&'b Scalar> for &'a MontgomeryPoint {
debug_assert!(mask == 0 || mask == 1);
x0.conditional_swap(&mut x1, mask);
x1 = x0.differential_add(&x1, &self);
x0 = x0.differential_double();
differential_add_and_double(&mut x0, &mut x1, &self);
}
x0.conditional_swap(&mut x1, bits[0] as u8);
x0