crypto_bigint/uint/
add_mod.rs

1//! [`Uint`] addition modulus operations.
2
3use crate::{AddMod, Limb, Uint};
4
5impl<const LIMBS: usize> Uint<LIMBS> {
6    /// Computes `self + rhs mod p`.
7    ///
8    /// Assumes `self + rhs` as unbounded integer is `< 2p`.
9    pub const fn add_mod(&self, rhs: &Uint<LIMBS>, p: &Uint<LIMBS>) -> Uint<LIMBS> {
10        let (w, carry) = self.adc(rhs, Limb::ZERO);
11
12        // Attempt to subtract the modulus, to ensure the result is in the field.
13        let (w, borrow) = w.sbb(p, Limb::ZERO);
14        let (_, borrow) = carry.sbb(Limb::ZERO, borrow);
15
16        // If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise
17        // borrow = 0x000...000. Thus, we use it as a mask to conditionally add the
18        // modulus.
19        let mask = Uint::from_words([borrow.0; LIMBS]);
20
21        w.wrapping_add(&p.bitand(&mask))
22    }
23
24    /// Computes `self + rhs mod p` for the special modulus
25    /// `p = MAX+1-c` where `c` is small enough to fit in a single [`Limb`].
26    ///
27    /// Assumes `self + rhs` as unbounded integer is `< 2p`.
28    pub const fn add_mod_special(&self, rhs: &Self, c: Limb) -> Self {
29        // `Uint::adc` also works with a carry greater than 1.
30        let (out, carry) = self.adc(rhs, c);
31
32        // If overflow occurred, then above addition of `c` already accounts
33        // for the overflow. Otherwise, we need to subtract `c` again, which
34        // in that case cannot underflow.
35        let l = carry.0.wrapping_sub(1) & c.0;
36        out.wrapping_sub(&Uint::from_word(l))
37    }
38}
39
40impl<const LIMBS: usize> AddMod for Uint<LIMBS> {
41    type Output = Self;
42
43    fn add_mod(&self, rhs: &Self, p: &Self) -> Self {
44        debug_assert!(self < p);
45        debug_assert!(rhs < p);
46        self.add_mod(rhs, p)
47    }
48}
49
50#[cfg(all(test, feature = "rand"))]
51mod tests {
52    use crate::{Limb, NonZero, Random, RandomMod, Uint, U256};
53    use rand_core::SeedableRng;
54
55    // TODO(tarcieri): additional tests + proptests
56
57    #[test]
58    fn add_mod_nist_p256() {
59        let a =
60            U256::from_be_hex("44acf6b7e36c1342c2c5897204fe09504e1e2efb1a900377dbc4e7a6a133ec56");
61        let b =
62            U256::from_be_hex("d5777c45019673125ad240f83094d4252d829516fac8601ed01979ec1ec1a251");
63        let n =
64            U256::from_be_hex("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551");
65
66        let actual = a.add_mod(&b, &n);
67        let expected =
68            U256::from_be_hex("1a2472fde50286541d97ca6a3592dd75beb9c9646e40c511b82496cfc3926956");
69
70        assert_eq!(expected, actual);
71    }
72
73    macro_rules! test_add_mod_special {
74        ($size:expr, $test_name:ident) => {
75            #[test]
76            fn $test_name() {
77                let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
78                let moduli = [
79                    NonZero::<Limb>::random(&mut rng),
80                    NonZero::<Limb>::random(&mut rng),
81                ];
82
83                for special in &moduli {
84                    let p = &NonZero::new(Uint::ZERO.wrapping_sub(&Uint::from_word(special.0)))
85                        .unwrap();
86
87                    let minus_one = p.wrapping_sub(&Uint::ONE);
88
89                    let base_cases = [
90                        (Uint::ZERO, Uint::ZERO, Uint::ZERO),
91                        (Uint::ONE, Uint::ZERO, Uint::ONE),
92                        (Uint::ZERO, Uint::ONE, Uint::ONE),
93                        (minus_one, Uint::ONE, Uint::ZERO),
94                        (Uint::ONE, minus_one, Uint::ZERO),
95                    ];
96                    for (a, b, c) in &base_cases {
97                        let x = a.add_mod_special(b, *special.as_ref());
98                        assert_eq!(*c, x, "{} + {} mod {} = {} != {}", a, b, p, x, c);
99                    }
100
101                    for _i in 0..100 {
102                        let a = Uint::<$size>::random_mod(&mut rng, p);
103                        let b = Uint::<$size>::random_mod(&mut rng, p);
104
105                        let c = a.add_mod_special(&b, *special.as_ref());
106                        assert!(c < **p, "not reduced: {} >= {} ", c, p);
107
108                        let expected = a.add_mod(&b, p);
109                        assert_eq!(c, expected, "incorrect result");
110                    }
111                }
112            }
113        };
114    }
115
116    test_add_mod_special!(1, add_mod_special_1);
117    test_add_mod_special!(2, add_mod_special_2);
118    test_add_mod_special!(3, add_mod_special_3);
119    test_add_mod_special!(4, add_mod_special_4);
120    test_add_mod_special!(5, add_mod_special_5);
121    test_add_mod_special!(6, add_mod_special_6);
122    test_add_mod_special!(7, add_mod_special_7);
123    test_add_mod_special!(8, add_mod_special_8);
124    test_add_mod_special!(9, add_mod_special_9);
125    test_add_mod_special!(10, add_mod_special_10);
126    test_add_mod_special!(11, add_mod_special_11);
127    test_add_mod_special!(12, add_mod_special_12);
128}
crypto_bigint/uint/add_mod.rs

crypto_bigint/uint/
add_mod.rs
