crypto_bigint/uint/
add_mod.rs

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1//! [`UInt`] addition modulus operations.
2
3use crate::{AddMod, Limb, UInt};
4
5impl<const LIMBS: usize> UInt<LIMBS> {
6    /// Computes `self + rhs mod p` in constant time.
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 mut i = 0;
20        let mut res = Self::ZERO;
21        let mut carry = Limb::ZERO;
22
23        while i < LIMBS {
24            let rhs = p.limbs[i].bitand(borrow);
25            let (limb, c) = w.limbs[i].adc(rhs, carry);
26            res.limbs[i] = limb;
27            carry = c;
28            i += 1;
29        }
30
31        res
32    }
33
34    /// Computes `self + rhs mod p` in constant time for the special modulus
35    /// `p = MAX+1-c` where `c` is small enough to fit in a single [`Limb`].
36    ///
37    /// Assumes `self + rhs` as unbounded integer is `< 2p`.
38    pub const fn add_mod_special(&self, rhs: &Self, c: Limb) -> Self {
39        // `UInt::adc` also works with a carry greater than 1.
40        let (out, carry) = self.adc(rhs, c);
41
42        // If overflow occurred, then above addition of `c` already accounts
43        // for the overflow. Otherwise, we need to subtract `c` again, which
44        // in that case cannot underflow.
45        let l = carry.0.wrapping_sub(1) & c.0;
46        let (out, _) = out.sbb(&UInt::from_word(l), Limb::ZERO);
47        out
48    }
49}
50
51impl<const LIMBS: usize> AddMod for UInt<LIMBS> {
52    type Output = Self;
53
54    fn add_mod(&self, rhs: &Self, p: &Self) -> Self {
55        debug_assert!(self < p);
56        debug_assert!(rhs < p);
57        self.add_mod(rhs, p)
58    }
59}
60
61#[cfg(all(test, feature = "rand"))]
62mod tests {
63    use crate::{Limb, NonZero, Random, RandomMod, UInt, U256};
64    use rand_core::SeedableRng;
65
66    // TODO(tarcieri): additional tests + proptests
67
68    #[test]
69    fn add_mod_nist_p256() {
70        let a =
71            U256::from_be_hex("44acf6b7e36c1342c2c5897204fe09504e1e2efb1a900377dbc4e7a6a133ec56");
72        let b =
73            U256::from_be_hex("d5777c45019673125ad240f83094d4252d829516fac8601ed01979ec1ec1a251");
74        let n =
75            U256::from_be_hex("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551");
76
77        let actual = a.add_mod(&b, &n);
78        let expected =
79            U256::from_be_hex("1a2472fde50286541d97ca6a3592dd75beb9c9646e40c511b82496cfc3926956");
80
81        assert_eq!(expected, actual);
82    }
83
84    macro_rules! test_add_mod_special {
85        ($size:expr, $test_name:ident) => {
86            #[test]
87            fn $test_name() {
88                let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
89                let moduli = [
90                    NonZero::<Limb>::random(&mut rng),
91                    NonZero::<Limb>::random(&mut rng),
92                ];
93
94                for special in &moduli {
95                    let p = &NonZero::new(UInt::ZERO.wrapping_sub(&UInt::from_word(special.0)))
96                        .unwrap();
97
98                    let minus_one = p.wrapping_sub(&UInt::ONE);
99
100                    let base_cases = [
101                        (UInt::ZERO, UInt::ZERO, UInt::ZERO),
102                        (UInt::ONE, UInt::ZERO, UInt::ONE),
103                        (UInt::ZERO, UInt::ONE, UInt::ONE),
104                        (minus_one, UInt::ONE, UInt::ZERO),
105                        (UInt::ONE, minus_one, UInt::ZERO),
106                    ];
107                    for (a, b, c) in &base_cases {
108                        let x = a.add_mod_special(b, *special.as_ref());
109                        assert_eq!(*c, x, "{} + {} mod {} = {} != {}", a, b, p, x, c);
110                    }
111
112                    for _i in 0..100 {
113                        let a = UInt::<$size>::random_mod(&mut rng, p);
114                        let b = UInt::<$size>::random_mod(&mut rng, p);
115
116                        let c = a.add_mod_special(&b, *special.as_ref());
117                        assert!(c < **p, "not reduced: {} >= {} ", c, p);
118
119                        let expected = a.add_mod(&b, p);
120                        assert_eq!(c, expected, "incorrect result");
121                    }
122                }
123            }
124        };
125    }
126
127    test_add_mod_special!(1, add_mod_special_1);
128    test_add_mod_special!(2, add_mod_special_2);
129    test_add_mod_special!(3, add_mod_special_3);
130    test_add_mod_special!(4, add_mod_special_4);
131    test_add_mod_special!(5, add_mod_special_5);
132    test_add_mod_special!(6, add_mod_special_6);
133    test_add_mod_special!(7, add_mod_special_7);
134    test_add_mod_special!(8, add_mod_special_8);
135    test_add_mod_special!(9, add_mod_special_9);
136    test_add_mod_special!(10, add_mod_special_10);
137    test_add_mod_special!(11, add_mod_special_11);
138    test_add_mod_special!(12, add_mod_special_12);
139}
crypto_bigint/uint/add_mod.rs

crypto_bigint/uint/
add_mod.rs
