From 62439387e5c78a09b86dd28fe1f47828ccc2cf6f Mon Sep 17 00:00:00 2001
From: Imbus <>
Date: Wed, 12 Feb 2025 20:51:51 +0100
Subject: [PATCH] Extended euclidean algorithm using recursion

---
 rsa.c | 17 +++++++++++++++++
 rsa.h | 15 +++++++++++++++
 2 files changed, 32 insertions(+)

diff --git a/rsa.c b/rsa.c
index b9c623a..06774fc 100644
--- a/rsa.c
+++ b/rsa.c
@@ -13,6 +13,23 @@ int gcd(int a, int b) {
     return a;
 }
 
+int extended_euclid(int a, int b, int *x, int *y) {
+    if (b == 0) {
+        *x = 1;
+        *y = 0;
+        return a;
+    }
+
+    int x1, y1;
+    int gcd = extended_euclid(b, a % b, &x1, &y1);
+
+    // Update x and y using results from recursive call
+    *x = y1;
+    *y = x1 - (a / b) * y1;
+
+    return gcd;
+}
+
 int totient(int n) {
     int result = n;
 
diff --git a/rsa.h b/rsa.h
index 9111722..690d0e3 100644
--- a/rsa.h
+++ b/rsa.h
@@ -65,3 +65,18 @@ bool is_prime(int n);
  * @return true if n is probably prime, false if n is composite.
  */
 bool miller_rabin(int n, int k);
+
+/**
+ * @brief Computes the greatest common divisor (GCD) of two integers a and b
+ * using the Extended Euclidean Algorithm. Also finds coefficients x and y such
+ * that ax + by = gcd(a, b).
+ *
+ * @param a The first integer.
+ * @param b The second integer.
+ * @param x Pointer to an integer to store the coefficient x in the equation ax
+ * + by = gcd(a, b).
+ * @param y Pointer to an integer to store the coefficient y in the equation ax
+ * + by = gcd(a, b).
+ * @return The greatest common divisor (gcd) of a and b.
+ */
+int extended_euclid(int a, int b, int *x, int *y);