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)
+}