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static BIG_B: &str = "\
efac3c0a_0de55551_fee0bfe4_67fa017a_1a898fa1_6ca57cb1\
ca9e3248_cacc09a9_b99d6abc_38418d0f_82ae4238_d9a68832\
aadec7c1_ac5fed48_7a56a71b_67ac59d5_afb28022_20d9592d\
247c4efc_abbd9b75_586088ee_1dc00dc4_232a8e15_6e8191dd\
675b6ae0_c80f5164_752940bc_284b7cee_885c1e10_e495345b\
8fbe9cfd_e5233fe1_19459d0b_d64be53c_27de5a02_a829976b\
33096862_82dad291_bd38b6a9_be396646_ddaf8039_a2573c39\
1b14e8bc_2cb53e48_298c047e_d9879e9c_5a521076_f0e27df3\
990e1659_d3d8205b_6443ebc0_9918ebee_6764f668_9f2b2be3\
b59cbc76_d76d0dfc_d737c3ec_0ccf9c00_ad0554bf_17e776ad\
b4edf9cc_6ce540be_76229093_5c53893b";
static BIG_E: &str = "\
be0e6ea6_08746133_e0fbc1bf_82dba91e_e2b56231_a81888d2\
a833a1fc_f7ff002a_3c486a13_4f420bf3_a5435be9_1a5c8391\
774d6e6c_085d8357_b0c97d4d_2bb33f7c_34c68059_f78d2541\
eacc8832_426f1816_d3be001e_b69f9242_51c7708e_e10efe98\
449c9a4a_b55a0f23_9d797410_515da00d_3ea07970_4478a2ca\
c3d5043c_bd9be1b4_6dce479d_4302d344_84a939e6_0ab5ada7\
12ae34b2_30cc473c_9f8ee69d_2cac5970_29f5bf18_bc8203e4\
f3e895a2_13c94f1e_24c73d77_e517e801_53661fdd_a2ce9e47\
a73dd7f8_2f2adb1e_3f136bf7_8ae5f3b8_08730de1_a4eff678\
e77a06d0_19a522eb_cbefba2a_9caf7736_b157c5c6_2d192591\
17946850_2ddb1822_117b68a0_32f7db88";
// This modulus is the prime from the 2048-bit MODP DH group:
// https://tools.ietf.org/html/rfc3526#section-3
static BIG_M: &str = "\
FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF";
static BIG_R: &str = "\
a1468311_6e56edc9_7a98228b_5e924776_0dd7836e_caabac13\
eda5373b_4752aa65_a1454850_40dc770e_30aa8675_6be7d3a8\
9d3085e4_da5155cf_b451ef62_54d0da61_cf2b2c87_f495e096\
055309f7_77802bbb_37271ba8_1313f1b5_075c75d1_024b6c77\
fdb56f17_b05bce61_e527ebfd_2ee86860_e9907066_edd526e7\
93d289bf_6726b293_41b0de24_eff82424_8dfd374b_4ec59542\
35ced2b2_6b195c90_10042ffb_8f58ce21_bc10ec42_64fda779\
d352d234_3d4eaea6_a86111ad_a37e9555_43ca78ce_2885bed7\
5a30d182_f1cf6834_dc5b6e27_1a41ac34_a2e91e11_33363ff0\
f88a7b04_900227c9_f6e6d06b_7856b4bb_4e354d61_060db6c8\
109c4735_6e7db425_7b5d74c7_0b709508";
mod biguint {
use num_bigint::BigUint;
use num_integer::Integer;
use num_traits::Num;
fn check_modpow<T: Into<BigUint>>(b: T, e: T, m: T, r: T) {
let b: BigUint = b.into();
let e: BigUint = e.into();
let m: BigUint = m.into();
let r: BigUint = r.into();
assert_eq!(b.modpow(&e, &m), r);
let even_m = &m << 1;
let even_modpow = b.modpow(&e, &even_m);
assert!(even_modpow < even_m);
assert_eq!(even_modpow.mod_floor(&m), r);
}
#[test]
fn test_modpow_single() {
check_modpow::<u32>(1, 0, 11, 1);
check_modpow::<u32>(0, 15, 11, 0);
check_modpow::<u32>(3, 7, 11, 9);
check_modpow::<u32>(5, 117, 19, 1);
check_modpow::<u32>(20, 1, 2, 0);
check_modpow::<u32>(20, 1, 3, 2);
}
#[test]
fn test_modpow_small() {
for b in 0u64..11 {
for e in 0u64..11 {
for m in 1..11 {
check_modpow::<u64>(b, e, m, b.pow(e as u32) % m);
}
}
}
}
#[test]
fn test_modpow_big() {
let b = BigUint::from_str_radix(super::BIG_B, 16).unwrap();
let e = BigUint::from_str_radix(super::BIG_E, 16).unwrap();
let m = BigUint::from_str_radix(super::BIG_M, 16).unwrap();
let r = BigUint::from_str_radix(super::BIG_R, 16).unwrap();
assert_eq!(b.modpow(&e, &m), r);
let even_m = &m << 1;
let even_modpow = b.modpow(&e, &even_m);
assert!(even_modpow < even_m);
assert_eq!(even_modpow % m, r);
}
}
mod bigint {
use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{Num, One, Signed};
fn check_modpow<T: Into<BigInt>>(b: T, e: T, m: T, r: T) {
fn check(b: &BigInt, e: &BigInt, m: &BigInt, r: &BigInt) {
assert_eq!(&b.modpow(e, m), r, "{} ** {} (mod {}) != {}", b, e, m, r);
let even_m = m << 1u8;
let even_modpow = b.modpow(e, m);
assert!(even_modpow.abs() < even_m.abs());
assert_eq!(&even_modpow.mod_floor(m), r);
// the sign of the result follows the modulus like `mod_floor`, not `rem`
assert_eq!(b.modpow(&BigInt::one(), m), b.mod_floor(m));
}
let b: BigInt = b.into();
let e: BigInt = e.into();
let m: BigInt = m.into();
let r: BigInt = r.into();
let neg_b_r = if e.is_odd() {
(-&r).mod_floor(&m)
} else {
r.clone()
};
let neg_m_r = r.mod_floor(&-&m);
let neg_bm_r = neg_b_r.mod_floor(&-&m);
check(&b, &e, &m, &r);
check(&-&b, &e, &m, &neg_b_r);
check(&b, &e, &-&m, &neg_m_r);
check(&-b, &e, &-&m, &neg_bm_r);
}
#[test]
fn test_modpow() {
check_modpow(1, 0, 11, 1);
check_modpow(0, 15, 11, 0);
check_modpow(3, 7, 11, 9);
check_modpow(5, 117, 19, 1);
check_modpow(-20, 1, 2, 0);
check_modpow(-20, 1, 3, 1);
}
#[test]
fn test_modpow_small() {
for b in -10i64..11 {
for e in 0i64..11 {
for m in -10..11 {
if m == 0 {
continue;
}
check_modpow(b, e, m, b.pow(e as u32).mod_floor(&m));
}
}
}
}
#[test]
fn test_modpow_big() {
let b = BigInt::from_str_radix(super::BIG_B, 16).unwrap();
let e = BigInt::from_str_radix(super::BIG_E, 16).unwrap();
let m = BigInt::from_str_radix(super::BIG_M, 16).unwrap();
let r = BigInt::from_str_radix(super::BIG_R, 16).unwrap();
check_modpow(b, e, m, r);
}
}
|
