crypto_bigint/int/
invert_mod.rs

1//! Operations related to computing the inverse of an [`Int`] modulo a [`Uint`].
2
3use crate::{CtOption, Int, InvertMod, NonZero, Odd, Uint};
4
5impl<const LIMBS: usize> Int<LIMBS> {
6    /// Computes the multiplicative inverse of `self` mod `modulus`, where `modulus` is odd.
7    #[must_use]
8    pub fn invert_odd_mod(&self, modulus: &Odd<Uint<LIMBS>>) -> CtOption<Uint<LIMBS>> {
9        let (abs, sgn) = self.abs_sign();
10        let maybe_inv = abs.invert_odd_mod(modulus);
11        let abs_inv = maybe_inv.as_inner_unchecked();
12
13        // Note: when `self` is negative and modulus is non-zero, then
14        // self^{-1} % modulus = modulus - |self|^{-1} % modulus
15        CtOption::new(
16            Uint::select(abs_inv, &modulus.wrapping_sub(abs_inv), sgn),
17            maybe_inv.is_some(),
18        )
19    }
20
21    /// Computes the multiplicative inverse of `self` mod `modulus`.
22    ///
23    /// Returns some if an inverse exists, otherwise none.
24    #[must_use]
25    pub const fn invert_mod(&self, modulus: &NonZero<Uint<LIMBS>>) -> CtOption<Uint<LIMBS>> {
26        let (abs, sgn) = self.abs_sign();
27        let maybe_inv = abs.invert_mod(modulus);
28        let abs_inv = maybe_inv.as_inner_unchecked();
29
30        // Note: when `self` is negative and modulus is non-zero, then
31        // self^{-1} % modulus = modulus - |self|^{-1} % modulus
32        CtOption::new(
33            Uint::select(abs_inv, &modulus.as_ref().wrapping_sub(abs_inv), sgn),
34            maybe_inv.is_some(),
35        )
36    }
37}
38
39impl<const LIMBS: usize> InvertMod<NonZero<Uint<LIMBS>>> for Int<LIMBS>
40where
41    Uint<LIMBS>: InvertMod<Output = Uint<LIMBS>>,
42{
43    type Output = Uint<LIMBS>;
44
45    fn invert_mod(&self, modulus: &NonZero<Uint<LIMBS>>) -> CtOption<Self::Output> {
46        Self::invert_mod(self, modulus)
47    }
48}
49
50#[cfg(test)]
51mod tests {
52    use crate::{I1024, U1024};
53
54    #[test]
55    fn test_invert_odd() {
56        let a = I1024::from_be_hex(concat![
57            "FFFDDA166EAC4B985A4BAE6865C0BAE2510C4072939ADE2D05DB444E80D6ABB1",
58            "CB85BED4F9A48A5CAE1568E61DBCF2DB884EE3363063E5291211D934EA0B9C07",
59            "4338D107815CFD7716A5B75586DDD93136A6234F98D270627F5AB344157A3527",
60            "C7D13DDB214D0A87B19D2F33D07E3D1952EB145419B92989B4CF3CD47897767B"
61        ]);
62        let m = U1024::from_be_hex(concat![
63            "D509E7854ABDC81921F669F1DC6F61359523F3949803E58ED4EA8BC16483DC6F",
64            "37BFE27A9AC9EEA2969B357ABC5C0EE214BE16A7D4C58FC620D5B5A20AFF001A",
65            "D198D3155E5799DC4EA76652D64983A7E130B5EACEBAC768D28D589C36EC749C",
66            "558D0B64E37CD0775C0D0104AE7D98BA23C815185DD43CD8B16292FD94156767"
67        ])
68        .to_odd()
69        .unwrap();
70        let expected = U1024::from_be_hex(concat![
71            "24D3C45CFFAF0D5C7620A469C3DC2F3313DDE78A0987F0CEF7EABFF4A5407219",
72            "645BBF1E19580A3619798AAA545597FCA2496DAA2DF4685D313F98F52DD151C3",
73            "48BF956F72C8BDA32FC3F3E5F955226B8D9138C6E64AA568075BA2AEDBE58ED2",
74            "173B01FCA9E1905F9C74589FB3C36D55A4CBCB7FA86CC803BE979091D3F0C431"
75        ]);
76
77        let res = a.invert_odd_mod(&m).unwrap();
78        assert_eq!(res, expected);
79
80        // Even though it is less efficient, it still works
81        let res = a.invert_mod(&m.to_nz().unwrap()).unwrap();
82        assert_eq!(res, expected);
83    }
84
85    #[test]
86    fn test_invert_even() {
87        let a = I1024::from_be_hex(concat![
88            "FFFDDA166EAC4B985A4BAE6865C0BAE2510C4072939ADE2D05DB444E80D6ABB1",
89            "CB85BED4F9A48A5CAE1568E61DBCF2DB884EE3363063E5291211D934EA0B9C07",
90            "4338D107815CFD7716A5B75586DDD93136A6234F98D270627F5AB344157A3527",
91            "C7D13DDB214D0A87B19D2F33D07E3D1952EB145419B92989B4CF3CD47897767B",
92        ]);
93        let m = U1024::from_be_hex(concat![
94            "D509E7854ABDC81921F669F1DC6F61359523F3949803E58ED4EA8BC16483DC6F",
95            "37BFE27A9AC9EEA2969B357ABC5C0EE214BE16A7D4C58FC620D5B5A20AFF001A",
96            "D198D3155E5799DC4EA76652D64983A7E130B5EACEBAC768D28D589C36EC749C",
97            "558D0B64E37CD0775C0D0104AE7D98BA23C815185DD43CD8B16292FD94156000"
98        ])
99        .to_nz()
100        .unwrap();
101        let expected = U1024::from_be_hex(concat![
102            "B64AAE72443C49FD5BE587DDE82A265E8C1226D73E5AE3DC3081E6C5471EE917",
103            "5BC37EF8AE73B8D7F0365652BC335F9BC375EA303381B08D4A15E0CBBF92FDF4",
104            "D58AB97A48B1507553808DC84F9C6F656F39F81D9157AE2E1FD98C487D4D52F8",
105            "F9F1107F0F4064B074637B983CB6672DAD75067A02F0E455DBB6E2CE7D7ED8B3",
106        ]);
107
108        let res = a.invert_mod(&m).unwrap();
109        assert_eq!(res, expected);
110    }
111}
crypto_bigint/int/invert_mod.rs

crypto_bigint/int/
invert_mod.rs
