bigint: Add a modpow fallback for even modulus
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@ -256,25 +256,39 @@ fn pow_bench(b: &mut Bencher) {
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});
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}
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/// This modulus is the prime from the 2048-bit MODP DH group:
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/// https://tools.ietf.org/html/rfc3526#section-3
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const RFC3526_2048BIT_MODP_GROUP: &'static str = "\
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FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
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29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
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EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
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E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
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EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
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C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
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83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
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670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
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E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
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DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
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15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF";
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#[bench]
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fn modpow(b: &mut Bencher) {
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let mut rng = get_rng();
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let base = rng.gen_biguint(2048);
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let e = rng.gen_biguint(2048);
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// This modulus is the prime from the 2048-bit MODP DH group:
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// https://tools.ietf.org/html/rfc3526#section-3
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let m = BigUint::from_str_radix("\
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FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
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29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
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EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
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E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
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EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
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C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
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83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
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670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
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E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
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DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
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15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF", 16).unwrap();
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let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap();
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b.iter(|| base.modpow(&e, &m));
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}
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#[bench]
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fn modpow_even(b: &mut Bencher) {
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let mut rng = get_rng();
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let base = rng.gen_biguint(2048);
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let e = rng.gen_biguint(2048);
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// Make the modulus even, so monty (base-2^32) doesn't apply.
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let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap() - 1u32;
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b.iter(|| base.modpow(&e, &m));
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}
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@ -1625,7 +1625,34 @@ impl BigUint {
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/// Returns `(self ^ exponent) % modulus`.
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pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self {
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monty_modpow(self, exponent, modulus)
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assert!(!modulus.is_zero(), "divide by zero!");
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// For an odd modulus, we can use Montgomery multiplication in base 2^32.
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if modulus.is_odd() {
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return monty_modpow(self, exponent, modulus);
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}
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// Otherwise do basically the same as `num::pow`, but with a modulus.
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let one = BigUint::one();
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if exponent.is_zero() { return one; }
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let mut base = self % modulus;
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let mut exp = exponent.clone();
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while exp.is_even() {
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base = &base * &base % modulus;
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exp >>= 1;
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}
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if exp == one { return base }
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let mut acc = base.clone();
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while exp > one {
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exp >>= 1;
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base = &base * &base % modulus;
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if exp.is_odd() {
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acc = acc * &base % modulus;
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}
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}
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acc
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}
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}
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@ -1098,6 +1098,11 @@ fn test_modpow() {
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let big_r = BigUint::from(r);
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assert_eq!(big_b.modpow(&big_e, &big_m), big_r);
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let even_m = &big_m << 1;
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let even_modpow = big_b.modpow(&big_e, &even_m);
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assert!(even_modpow < even_m);
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assert_eq!(even_modpow % big_m, big_r);
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}
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check(1, 0, 11, 1);
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@ -1160,6 +1165,11 @@ fn test_modpow_big() {
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109c4735_6e7db425_7b5d74c7_0b709508", 16).unwrap();
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assert_eq!(b.modpow(&e, &m), r);
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let even_m = &m << 1;
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let even_modpow = b.modpow(&e, &even_m);
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assert!(even_modpow < even_m);
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assert_eq!(even_modpow % m, r);
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}
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fn to_str_pairs() -> Vec<(BigUint, Vec<(u32, String)>)> {
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