Using 64 bit integers

rsa.c

@@ -3,13 +3,12 @@
 #include <stdbool.h>
 #include <stdint.h>
 
-int gcd(int a, int b) {
+uint64_t gcd(uint64_t a, uint64_t b) {
     while (b != 0) {
-        int temp = b;
+        uint64_t temp = b;
         b = a % b;
         a = temp;
     }
-
     return a;
 }
 
@@ -71,7 +70,7 @@ uint64_t modexp(uint64_t a, uint64_t b, uint64_t m) {
 
 uint64_t gen_prime(uint64_t min, uint64_t max) {
     uint64_t cand = 0;
-    while (!miller_rabin(cand, 10)) cand = prand_range(min, max);
+    while (!miller_rabin(cand, 5)) cand = prand_range(min, max);
 
     return cand;
 }
@@ -88,26 +87,26 @@ bool is_prime(int n) {
     return true;
 }
 
-bool miller_rabin(int n, int k) {
+bool miller_rabin(uint64_t n, uint64_t k) {
     if (n < 2)
         return false;
 
-    int d = n - 1;
-    int s = 0;
+    uint64_t d = n - 1;
+    uint64_t s = 0;
 
     while (d % 2 == 0) {
         d /= 2;
         s++;
     }
 
-    for (int i = 0; i < k; i++) {
-        int a = prand_range(2, n - 2);
-        int x = modexp(a, d, n);
+    for (uint64_t i = 0; i < k; i++) {
+        uint64_t a = prand_range(2, n - 2);
+        uint64_t x = modexp(a, d, n);
 
         if (x == 1 || x == n - 1)
             continue;
 
-        for (int r = 1; r < s; r++) {
+        for (uint64_t r = 1; r < s; r++) {
             x = modexp(x, 2, n);
             if (x == n - 1)
                 break;
@@ -120,11 +119,31 @@ bool miller_rabin(int n, int k) {
     return true; // Likely prime
 }
 
-int mod_inverse(int e, int phi) {
-    for (int d = 0; d < phi; d++) {
-        if ((d * e) % phi == 1)
-            return d;
+int mod_inverse(int a, int m) {
+    int m0 = m;
+    int y = 0, x = 1;
+
+    if (m == 1)
+        return 0;
+
+    while (a > 1) {
+        // q is quotient
+        int q = a / m;
+        int t = m;
+
+        // m is remainder now
+        m = a % m;
+        a = t;
+        t = y;
+
+        // Update x and y
+        y = x - q * y;
+        x = t;
     }
 
-    return 0;
+    // Make x positive
+    if (x < 0)
+        x += m0;
+
+    return x;
 }

rsa.h

@@ -10,7 +10,7 @@
  * @param b Second number
  * @return The greatest common divider
  */
-int gcd(int a, int b);
+uint64_t gcd(uint64_t a, uint64_t b);
 
 /**
  * @brief Computes Euler's Totient function φ(n), which counts the number of
@@ -31,13 +31,13 @@ int totient(int n);
 uint64_t modexp(uint64_t a, uint64_t b, uint64_t m);
 
 /**
- * @brief Computes the modular inverse of e modulo phi.
+ * @brief Computes the modular inverse of a modulo m.
  *
- * @param e The integer whose modular inverse is to be found.
- * @param phi The modulus.
- * @return The modular inverse of e modulo phi, or -1 if no inverse exists.
+ * @param a The integer whose modular inverse is to be found.
+ * @param m The modulus.
+ * @return The modular inverse of a modulo m, or -1 if no inverse exists.
  */
-int mod_inverse(int e, int phi);
+int mod_inverse(int a, int m);
 
 /**
  * @brief Generates a random prime number within the given range.
@@ -64,7 +64,7 @@ bool is_prime(int n);
  * @param k The number of rounds of testing to perform.
  * @return true if n is probably prime, false if n is composite.
  */
-bool miller_rabin(int n, int k);
+bool miller_rabin(uint64_t n, uint64_t k);
 
 /**
  * @brief Computes the greatest common divisor (GCD) of two integers a and b