crypto-bigint 0.7.3

Pure Rust implementation of a big integer library which has been designed from the ground-up for use in cryptographic applications. Provides constant-time, no_std-friendly implementations of modern formulas using const generics.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149

//! Support for computing modular symbols.

use crate::{Int, JacobiSymbol, Odd, Uint, word};

impl<const LIMBS: usize> Int<LIMBS> {
    /// Compute the Jacobi symbol `(self|rhs)`.
    ///
    /// For prime `rhs`, this corresponds to the Legendre symbol and
    /// indicates whether `self` is quadratic residue modulo `rhs`.
    #[must_use]
    #[allow(clippy::cast_possible_truncation)]
    pub const fn jacobi_symbol<const RHS_LIMBS: usize>(
        &self,
        rhs: &Odd<Uint<RHS_LIMBS>>,
    ) -> JacobiSymbol {
        let (abs, sign) = self.abs_sign();
        let jacobi = abs.jacobi_symbol(rhs) as i64;
        // (-self|rhs) = -(self|rhs) iff rhs = 3 mod 4
        let swap = sign.and(word::choice_from_eq(rhs.as_ref().limbs[0].0 & 3, 3));
        JacobiSymbol::from_i8(swap.select_i64(jacobi, -jacobi) as i8)
    }

    /// Compute the Jacobi symbol `(self|rhs)`.
    ///
    /// For prime `rhs`, this corresponds to the Legendre symbol and
    /// indicates whether `self` is quadratic residue modulo `rhs`.
    ///
    /// This method executes in variable-time for the value of `self`.
    #[must_use]
    pub const fn jacobi_symbol_vartime<const RHS_LIMBS: usize>(
        &self,
        rhs: &Odd<Uint<RHS_LIMBS>>,
    ) -> JacobiSymbol {
        let (abs, sign) = self.abs_sign();
        let jacobi = abs.jacobi_symbol_vartime(rhs);
        JacobiSymbol::from_i8(
            if sign.to_bool_vartime() && rhs.as_ref().limbs[0].0 & 3 == 3 {
                -(jacobi as i8)
            } else {
                jacobi as i8
            },
        )
    }
}

#[cfg(test)]
mod tests {
    use crate::{I64, I256, JacobiSymbol, U64, U256};

    #[test]
    fn jacobi_quad_residue() {
        // Two semiprimes with no common factors, and
        // f is quadratic residue modulo g
        let f = I256::from(59i32 * 67);
        let g = U256::from(61u32 * 71).to_odd().unwrap();
        let res = f.jacobi_symbol(&g);
        let res_vartime = f.jacobi_symbol_vartime(&g);
        assert_eq!(res, JacobiSymbol::One);
        assert_eq!(res, res_vartime);
    }

    #[test]
    fn jacobi_non_quad_residue() {
        // f and g have no common factors, but
        // f is not quadratic residue modulo g
        let f = I256::from(59i32 * 67 + 2);
        let g = U256::from(61u32 * 71).to_odd().unwrap();
        let res = f.jacobi_symbol(&g);
        let res_vartime = f.jacobi_symbol_vartime(&g);
        assert_eq!(res, JacobiSymbol::MinusOne);
        assert_eq!(res, res_vartime);
    }

    #[test]
    fn jacobi_non_coprime() {
        let f = I256::from(4391633i32);
        let g = U256::from(2022161u32).to_odd().unwrap();
        let res = f.jacobi_symbol(&g);
        let res_vartime = f.jacobi_symbol_vartime(&g);
        assert_eq!(res, JacobiSymbol::Zero);
        assert_eq!(res, res_vartime);
    }

    #[test]
    fn jacobi_zero() {
        assert_eq!(
            I256::ZERO.jacobi_symbol(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            I256::ZERO.jacobi_symbol_vartime(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            I64::ZERO.jacobi_symbol_vartime(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            I256::ZERO.jacobi_symbol_vartime(&U64::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
    }

    #[test]
    fn jacobi_neg_one() {
        let f = I256::MINUS_ONE;
        assert_eq!(
            f.jacobi_symbol(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            f.jacobi_symbol_vartime(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            I64::MINUS_ONE.jacobi_symbol_vartime(&U256::ONE.to_odd().unwrap()),
            JacobiSymbol::One
        );
        assert_eq!(
            f.jacobi_symbol(&U256::from(3u8).to_odd().unwrap()),
            JacobiSymbol::MinusOne
        );
        assert_eq!(
            f.jacobi_symbol_vartime(&U256::from(3u8).to_odd().unwrap()),
            JacobiSymbol::MinusOne
        );
        assert_eq!(
            I64::MINUS_ONE.jacobi_symbol_vartime(&U256::from(3u8).to_odd().unwrap()),
            JacobiSymbol::MinusOne
        );
    }

    #[test]
    fn jacobi_int() {
        // Two semiprimes with no common factors, and
        // f is quadratic residue modulo g
        let f = I256::from(59i32 * 67);
        let g = U256::from(61u32 * 71).to_odd().unwrap();
        let res = f.jacobi_symbol(&g);
        let res_vartime = f.jacobi_symbol_vartime(&g);
        assert_eq!(res, JacobiSymbol::One);
        assert_eq!(res, res_vartime);

        let res = f.checked_neg().unwrap().jacobi_symbol(&g);
        let res_vartime = f.checked_neg().unwrap().jacobi_symbol_vartime(&g);
        assert_eq!(res, JacobiSymbol::MinusOne);
        assert_eq!(res, res_vartime);
    }
}