Start staging some extended math functionality, including primality bits.

src/cryptonum/extended_math.rs

@@ -0,0 +1,71 @@
+use cryptonum::signed::Signed;
+use cryptonum::traits::*;
+use std::ops::*;
+
+pub fn modinv<'a,T>(e: &T, phi: &T) -> T
+  where
+   T: Clone + CryptoNumBase + Ord,
+   T: AddAssign + SubAssign + MulAssign + DivAssign,
+   T: Add<Output=T> + Sub<Output=T> + Mul<Output=T> + Div<Output=T>,
+   &'a T: Sub<Output=T>,
+   T: 'a
+{
+    let (_, mut x, _) = extended_euclidean(e, phi);
+    let int_phi = Signed::<T>::new(phi.clone());
+    while x.is_negative() {
+        x += &int_phi;
+    }
+    x.abs()
+}
+
+pub fn modexp<T>(b: &T, e: &T, m: &T) -> T
+{
+    panic!("modexp")
+}
+
+pub fn extended_euclidean<T>(a: &T, b: &T) -> (Signed<T>, Signed<T>, Signed<T>)
+  where
+    T: Clone + CryptoNumBase + Div + Mul + Sub
+{
+    let posinta = Signed::<T>::new(a.clone());
+    let posintb = Signed::<T>::new(b.clone());
+    let (mut d, mut x, mut y) = egcd(&posinta, &posintb);
+
+    if d.is_negative() {
+        d.negate();
+        x.negate();
+        y.negate();
+    }
+
+    (d, x, y)
+}
+
+pub fn egcd<T>(a: &Signed<T>, b: &Signed<T>) -> (Signed<T>,Signed<T>,Signed<T>)
+  where
+    T: Clone + CryptoNumBase + Div + Mul + Sub
+{
+    let mut s         = Signed::<T>::zero();
+    let mut old_s     = Signed::<T>::from_u8(1);
+    let mut t         = Signed::<T>::from_u8(1);
+    let mut old_t     = Signed::<T>::zero();
+    let mut r         = b.clone();
+    let mut old_r     = a.clone();
+
+    while !r.is_zero() {
+        let quotient = old_r.clone() / r.clone();
+
+        let prov_r = r.clone();
+        let prov_s = s.clone();
+        let prov_t = t.clone();
+
+        r = old_r - (r * &quotient);
+        s = old_s - (s * &quotient);
+        t = old_t - (t * &quotient);
+
+        old_r = prov_r;
+        old_s = prov_s;
+        old_t = prov_t;
+    }
+
+    (old_r, old_s, old_t)
+}

src/cryptonum/mod.rs

@@ -6,6 +6,8 @@
 mod core;
 #[macro_use]
 mod builder;
+//mod extended_math;
+// mod primes;
 mod traits;
 
 use self::core::*;

src/cryptonum/primes.rs

@@ -0,0 +1,129 @@
+use cryptonum::extended_math::modexp;
+use cryptonum::traits::*;
+use rand::Rng;
+use std::ops::*;
+
+static SMALL_PRIMES: [u64; 310] = [
+      2,     3,     5,     7,    11,    13,    17,    19,    23,    29,
+     31,    37,    41,    43,    47,    53,    59,    61,    67,    71,
+     73,    79,    83,    89,    97,   101,   103,   107,   109,   113,
+    127,   131,   137,   139,   149,   151,   157,   163,   167,   173,
+    179,   181,   191,   193,   197,   199,   211,   223,   227,   229,
+    233,   239,   241,   251,   257,   263,   269,   271,   277,   281,
+    283,   293,   307,   311,   313,   317,   331,   337,   347,   349,
+    353,   359,   367,   373,   379,   383,   389,   397,   401,   409,
+    419,   421,   431,   433,   439,   443,   449,   457,   461,   463,
+    467,   479,   487,   491,   499,   503,   509,   521,   523,   541,
+    547,   557,   563,   569,   571,   577,   587,   593,   599,   601,
+    607,   613,   617,   619,   631,   641,   643,   647,   653,   659,
+    661,   673,   677,   683,   691,   701,   709,   719,   727,   733,
+    739,   743,   751,   757,   761,   769,   773,   787,   797,   809,
+    811,   821,   823,   827,   829,   839,   853,   857,   859,   863,
+    877,   881,   883,   887,   907,   911,   919,   929,   937,   941,
+    947,   953,   967,   971,   977,   983,   991,   997,  1009,  1013,
+   1019,  1021,  1031,  1033,  1039,  1049,  1051,  1061,  1063,  1069,
+   1087,  1091,  1093,  1097,  1103,  1109,  1117,  1123,  1129,  1151,
+   1153,  1163,  1171,  1181,  1187,  1193,  1201,  1213,  1217,  1223,
+   1229,  1231,  1237,  1249,  1259,  1277,  1279,  1283,  1289,  1291,
+   1297,  1301,  1303,  1307,  1319,  1321,  1327,  1361,  1367,  1373,
+   1381,  1399,  1409,  1423,  1427,  1429,  1433,  1439,  1447,  1451,
+   1453,  1459,  1471,  1481,  1483,  1487,  1489,  1493,  1499,  1511,
+   1523,  1531,  1543,  1549,  1553,  1559,  1567,  1571,  1579,  1583,
+   1597,  1601,  1607,  1609,  1613,  1619,  1621,  1627,  1637,  1657,
+   1663,  1667,  1669,  1693,  1697,  1699,  1709,  1721,  1723,  1733,
+   1741,  1747,  1753,  1759,  1777,  1783,  1787,  1789,  1801,  1811,
+   1823,  1831,  1847,  1861,  1867,  1871,  1873,  1877,  1879,  1889,
+   1901,  1907,  1913,  1931,  1933,  1949,  1951,  1973,  1979,  1987,
+   1993,  1997,  1999,  2003,  2011,  2017,  2027,  2029,  2039,  2053];
+
+
+pub fn probably_prime<G,T>(x: &T, g: &mut G, iters: usize) -> bool
+  where
+   G: Rng,
+   T: Clone + PartialOrd + Rem + Sub,
+   T: CryptoNumBase + CryptoNumSerialization,
+{
+    for tester in SMALL_PRIMES.iter() {
+        if (x % T::from_u64(*tester)) == T::zero() {
+            return false;
+        }
+    }
+    miller_rabin(g, x, iters)
+}
+
+fn miller_rabin<G,T>(g: &mut G, n: T, iters: usize) -> bool
+  where
+   G: Rng,
+   T: Clone + PartialEq + PartialOrd + Sub,
+   T: CryptoNumBase + CryptoNumSerialization,
+{
+    let one = T::from_u8(1);
+    let two = T::from_u8(2);
+    let nm1 = n - one;
+    // Quoth Wikipedia:
+    // write n - 1 as 2^r*d with d odd by factoring powers of 2 from n - 1
+    let mut d = nm1.clone();
+    let mut r = 0;
+    while d.is_even() {
+        d >>= 1;
+        r += 1;
+        assert!(r < n.bit_size());
+    }
+    // WitnessLoop: repeat k times
+    'WitnessLoop: for _k in 0..iters {
+        // pick a random integer a in the range [2, n - 2]
+        let a = random_in_range(g, &two, &nm1);
+        // x <- a^d mod n
+        let mut x = modexp(&a, &d, &n);
+        // if x = 1 or x = n - 1 then
+        if (&x == &one) || (&x == &nm1) {
+            // continue WitnessLoop
+            continue 'WitnessLoop;
+        }
+        // repeat r - 1 times:
+        for _i in 0..r {
+            // x <- x^2 mod n
+            x = modexp(&x, &two, &n);
+            // if x = 1 then
+            if &x == &one {
+                // return composite
+                return false;
+            }
+            // if x = n - 1 then
+            if &x == &nm1 {
+                // continue WitnessLoop
+                continue 'WitnessLoop;
+            }
+        }
+        // return composite
+        return false;
+    }
+    // return probably prime
+    true
+}
+
+fn random_in_range<G,T>(rng: &mut G, min: &T, max: &T) -> T
+  where
+    G: Rng,
+    T: CryptoNumSerialization + PartialOrd
+{
+    assert_eq!(min.byte_size(), max.byte_size());
+    loop {
+        let candidate = random_number(rng, min.byte_size());
+
+        if (&candidate >= min) && (&candidate < max) {
+            return candidate;
+        }
+    }
+}
+
+fn random_number<G,T>(rng: &mut G, bytelen: usize) -> T
+  where
+    G: Rng,
+    T: CryptoNumSerialization
+{
+    let components: Vec<u8> = rng.gen_iter().take(bytelen).collect();
+    T::from_bytes(&components)
+}
+
+

src/lib.rs

@@ -14,6 +14,7 @@
 #[cfg(test)]
 #[macro_use]
 extern crate quickcheck;
+extern crate rand;
 
 /// The cryptonum module provides support for large numbers at fixed,
 /// cryptographically-relevant sizes.