From 3cd37a881d91663b2e3c5b488b554d26c2651904 Mon Sep 17 00:00:00 2001
From: Adam Wick <awick@uhsure.com>
Date: Wed, 4 Apr 2018 18:47:02 -0400
Subject: [PATCH] First whack at modular inverses.

---
 src/cryptonum/mod.rs    | 51 +++++++++++++++++++++++++++++++++++++++++
 src/cryptonum/signed.rs | 16 +++++++++++++
 2 files changed, 67 insertions(+)

diff --git a/src/cryptonum/mod.rs b/src/cryptonum/mod.rs
index c570101..27cf935 100644
--- a/src/cryptonum/mod.rs
+++ b/src/cryptonum/mod.rs
@@ -7,3 +7,54 @@ mod unsigned;
 
 pub use self::signed::SCN;
 pub use self::unsigned::UCN;
+
+use std::ops::Neg;
+
+pub fn modinv(e: &UCN, phi: &UCN) -> UCN {
+    let (_, mut x, _) = extended_euclidean(&e, &phi);
+    let int_phi = SCN::from(phi.clone());
+    while x.is_negative() {
+        x = x + &int_phi;
+    }
+    x.into()
+}
+
+fn extended_euclidean(a: &UCN, b: &UCN) -> (SCN, SCN, SCN) {
+    let posinta = SCN::from(a.clone());
+    let posintb = SCN::from(b.clone());
+    let (d, x, y) = egcd(posinta, posintb);
+
+    if d.is_negative() {
+        (d.neg(), x.neg(), y.neg())
+    } else {
+        (d, x, y)
+    }
+}
+
+fn egcd(a: SCN, b: SCN) -> (SCN, SCN, SCN) {
+    let mut s     = SCN::zero();
+    let mut old_s = SCN::from(1 as u8);
+    let mut t     = SCN::from(1 as u8);
+    let mut old_t = SCN::zero();
+    let mut r     = b;
+    let mut old_r = a;
+
+    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)
+}
+
diff --git a/src/cryptonum/signed.rs b/src/cryptonum/signed.rs
index 8f115dd..a5901cd 100644
--- a/src/cryptonum/signed.rs
+++ b/src/cryptonum/signed.rs
@@ -20,6 +20,10 @@ impl SCN {
         self.value.is_zero()
     }
 
+    pub fn is_negative(&self) -> bool {
+        self.negative
+    }
+
     pub fn from_str(x: &str) -> SCN {
         if x.get(0..1) == Some("-") {
             SCN{ negative: true, value: UCN::from_str(&x[1..]) }
@@ -59,6 +63,18 @@ define_signed_into!(SCN, i16, u16);
 define_signed_into!(SCN, i32, u32);
 define_signed_into!(SCN, i64, u64);
 
+impl From<UCN> for SCN {
+    fn from(x: UCN) -> SCN {
+        SCN{ negative: false, value: x }
+    }
+}
+
+impl Into<UCN> for SCN {
+    fn into(self) -> UCN {
+        self.value
+    }
+}
+
 //------------------------------------------------------------------------------
 //
 //  Comparisons