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//! Variable-time modular addition of two [`U256`] values.
use super::U256;
impl U256 {
/// Computes `(self + other) mod modulus` using branching reduction.
///
/// Handles both reduced and unreduced inputs. Without overflow
/// (`sum < 2^256`), at most one subtraction is needed since
/// `sum < 2^256 < 2·modulus` for any modulus > 2^255. With
/// overflow, the wrapping subtraction consumes the 257th bit;
/// if the subtraction didn't underflow (sum was large enough),
/// one more subtraction finishes the reduction.
///
/// This is the fastest path but execution time depends on operand values.
/// Use `add_mod_ct` when constant-time behavior is required.
///
/// # 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_vt(&b, &P), U256::from_be_limbs([0, 0, 0, 30]));
/// ```
#[inline]
pub fn add_mod_vt(&self, other: &U256, modulus: &U256) -> U256 {
let (sum, overflow) = self.overflowing_add(other);
if overflow {
let (r, underflow) = sum.overflowing_sub(modulus);
if underflow {
r
} else {
r.overflowing_sub(modulus).0
}
} else if sum >= *modulus {
sum.overflowing_sub(modulus).0
} else {
sum
}
}
}
#[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_vt(&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_vt(&U256::ZERO, &P), a);
assert_eq!(U256::ZERO.add_mod_vt(&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_vt(&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_vt(&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_vt(&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_vt(&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_vt(&b, &P), b.add_mod_vt(&a, &P));
}
/// Inputs larger than modulus are reduced correctly.
#[test]
fn inputs_exceed_modulus() {
let max = U256::from_be_limbs([u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
assert_eq!(
max.add_mod_vt(&max, &P),
U256::from_be_limbs([0, 0, 0, 0x2000007A0]),
);
}
}
#[cfg(test)]
mod human_tests {
use super::*;
const P: U256 = U256::from_be_limbs([0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFEFFFFFC2F]);
/// (2^256 - 1) + (2^256 - 1) mod P exercises double-overflow reduction.
#[test]
fn all_ff_doubled() {
let a = U256::from_be_limbs([u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
let b = U256::from_be_limbs([u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
assert_eq!(
a.add_mod_vt(&b, &P),
U256::from_be_bytes([
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,
0, 0, 7, 160,
])
);
}
/// All 0xFF + all 0xAA overflows and reduces mod P.
#[test]
fn all_ff_plus_all_aa() {
let a = U256::from_be_bytes([0xFF; 32]);
let b = U256::from_be_bytes([0xAA; 32]);
assert_eq!(
a.add_mod_vt(&b, &P),
U256::from_be_bytes([
170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170,
170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 170, 171, 170, 170, 174, 122
])
);
}
}