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//! Constant-time modular addition of two [`U256`] values.
use super::U256;
impl U256 {
/// Computes `(self + other) mod modulus` in constant time.
///
/// Both operands must be in `[0, modulus)` (reduced). For reduced inputs
/// the sum is at most `2 * modulus - 2`, so a single conditional
/// subtraction always suffices. The subtraction is always executed and
/// the result selected via branchless bitmask (`ct_select`), ensuring
/// execution time is independent of the operand values.
///
/// # Examples
///
/// ```
/// use cnfy_uint::u256::U256;
/// let P = U256::from_be_limbs([
/// 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,
/// 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFEFFFFFC2F,
/// ]);
///
/// let a = U256::from_be_limbs([0, 0, 0, 10]);
/// let b = U256::from_be_limbs([0, 0, 0, 20]);
/// assert_eq!(a.add_mod_ct(&b, &P), U256::from_be_limbs([0, 0, 0, 30]));
/// ```
#[inline]
pub fn add_mod_ct(&self, other: &U256, modulus: &U256) -> U256 {
let (sum, carry) = self.overflowing_add(other);
let (reduced, borrow) = sum.overflowing_sub(modulus);
// Subtraction is valid when carry absorbs the borrow (overflow case)
// or when sum >= modulus (no borrow). One subtraction always suffices
// for reduced inputs (both < modulus), since their sum < 2 * modulus.
reduced.ct_select(&sum, carry | !borrow)
}
}
#[cfg(test)]
mod ai_tests {
use super::*;
const P: U256 = U256::from_be_limbs([0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFEFFFFFC2F]);
/// Adding zero to zero yields zero.
#[test]
fn zero_plus_zero() {
assert_eq!(U256::ZERO.add_mod_ct(&U256::ZERO, &P), U256::ZERO);
}
/// Adding zero is the identity operation.
#[test]
fn additive_identity() {
let a = U256::from_be_limbs([0, 0, 0, 42]);
assert_eq!(a.add_mod_ct(&U256::ZERO, &P), a);
assert_eq!(U256::ZERO.add_mod_ct(&a, &P), a);
}
/// Small values that don't require reduction.
#[test]
fn small_no_reduction() {
let a = U256::from_be_limbs([
0x0202020202020202,
0x0202020202020202,
0x0202020202020202,
0x0202020202020202,
]);
let expected = U256::from_be_limbs([
0x0404040404040404,
0x0404040404040404,
0x0404040404040404,
0x0404040404040404,
]);
assert_eq!(a.add_mod_ct(&a, &P), expected);
}
/// Adding one to P-1 wraps to zero (exact modulus hit).
#[test]
fn p_minus_one_plus_one() {
let p_minus_1 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]);
assert_eq!(p_minus_1.add_mod_ct(&U256::ONE, &P), U256::ZERO);
}
/// Adding two to P-1 wraps to one.
#[test]
fn p_minus_one_plus_two() {
let p_minus_1 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]);
let two = U256::from_be_limbs([0, 0, 0, 2]);
assert_eq!(p_minus_1.add_mod_ct(&two, &P), U256::ONE);
}
/// (P-1) + (P-1) mod P = P-2. Exercises 257-bit overflow path.
#[test]
fn p_minus_one_doubled() {
let p_minus_1 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]);
let p_minus_2 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2D,
]);
assert_eq!(p_minus_1.add_mod_ct(&p_minus_1, &P), p_minus_2);
}
/// Commutativity: a + b = b + a.
#[test]
fn commutative() {
let a = U256::from_be_limbs([0, 0x1234, 0, 0x5678]);
let b = U256::from_be_limbs([0, 0xABCD, 0, 0xEF01]);
assert_eq!(a.add_mod_ct(&b, &P), b.add_mod_ct(&a, &P));
}
/// Two large reduced values whose sum overflows 256 bits.
#[test]
fn large_reduced_overflow() {
let p_minus_1 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]);
let p_minus_2 = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2D,
]);
let expected = U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2C,
]);
assert_eq!(p_minus_1.add_mod_ct(&p_minus_2, &P), expected);
}
/// CT version matches VT version for all reduced inputs.
#[test]
fn matches_vt() {
let cases = [
(U256::ZERO, U256::ZERO),
(U256::ONE, U256::ONE),
(
U256::from_be_limbs([0, 0x1234, 0, 0x5678]),
U256::from_be_limbs([0, 0xABCD, 0, 0xEF01]),
),
(
U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]),
U256::from_be_limbs([
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFEFFFFFC2E,
]),
),
(
U256::from_be_limbs([
0x79BE667EF9DCBBAC,
0x55A06295CE870B07,
0x029BFCDB2DCE28D9,
0x59F2815B16F81798,
]),
U256::from_be_limbs([
0x483ADA7726A3C465,
0x5DA4FBFC0E1108A8,
0xFD17B448A6855419,
0x9C47D08FFB10D4B8,
]),
),
];
for (a, b) in &cases {
assert_eq!(
a.add_mod_ct(b, &P),
a.add_mod_vt(b, &P),
"CT/VT mismatch for {a:?} + {b:?}"
);
}
}
}