final touches

helper.c

@@ -2,6 +2,8 @@
 #include <stdio.h>
 #include <stdlib.h>
 
+uint32_t rand32() { return (rand() << 16) | (rand() & 0xFFFF) | 1; }
+
 void print_uint128(unsigned __int128 n) {
     if (n == 0) {
         printf("0\n");
@@ -30,12 +32,14 @@ uint64_t rand64() {
     for (int i = 0; i < 4; i++) {
         r = (r << 16) | (rand() & 0xFFFF);
     }
+
+    // Force the bottom bit to 1, this will make all generated primes odd
+    r = r | 1;
     return r;
 }
 
 // Stitch two 64-bit random numbers into a 128-bit number
 unsigned __int128 generate_stitched_128() {
-    // Make sure to seed rand() in your main function with srand(time(NULL))
     uint64_t top_half = rand64();
     uint64_t bottom_half = rand64();
 
@@ -46,10 +50,9 @@ unsigned __int128 generate_stitched_128() {
 }
 
 unsigned __int128 generate_prime_candidate() {
-    // 1. Get the raw random bytes
     unsigned __int128 candidate = generate_stitched_128();
 
-    // 2. Force the bottom bit to 1 (Ensures it is odd)
+    // Force the bottom bit to 1, this will make all generated primes odd
     candidate = candidate | 1;
 
     // 3. Force the top bit to 1 (Ensures it is a full 128-bit number)

main.c

@@ -1,9 +1,12 @@
 #include <inttypes.h>
+#include <math.h>
 #include <pthread.h>
 #include <stdbool.h>
 #include <stdint.h>
 #include <stdio.h>
 #include <stdlib.h>
+#include <sys/types.h>
+#include <time.h>
 
 #include "helper.c"
 
@@ -27,7 +30,7 @@ uint64_t quick_pow(uint64_t *d_binary, uint64_t a, uint64_t n, uint64_t length)
     powed[0] = a;
     for (int i = 1; i <= length; i++) {
         powed[i] = (uint64_t)(((unsigned __int128)powed[i - 1] * powed[i - 1]) % n);
-        printf("powed: %ju, index: %d; ", powed[i], (i));
+        // printf("powed: %ju, index: %d; ", powed[i], (i));
     }
 
     // check where in the binary are ones
@@ -38,7 +41,7 @@ uint64_t quick_pow(uint64_t *d_binary, uint64_t a, uint64_t n, uint64_t length)
         }
     }
 
-    printf("\nbm quick math: %ju; %ju ", multiplied, n);
+    // printf("\nbm quick math: %ju; %ju ", multiplied, n);
 
     free(powed);
 
@@ -46,7 +49,7 @@ uint64_t quick_pow(uint64_t *d_binary, uint64_t a, uint64_t n, uint64_t length)
 }
 
 bool prime_test(uint64_t n, int a) {
-    printf("\n\nprime test: %ju\n", n);
+    // printf("\n\nprime test: %ju\n", n);
     // Miller Rabin prime test
     // choose a base: a, which should be a prime so that (n, a) = 1
     // then do 2 rounds of tests provided the first one did not fail
@@ -56,6 +59,18 @@ bool prime_test(uint64_t n, int a) {
     // S: see above
     // r = {0,... S-1}
 
+    // this should not happen but just in case
+    if (n <= 1) {
+        return false;
+    }
+    if (n == 2) {
+        return true;
+    }
+    if (n % 2 == 0) {
+        return false;
+    }
+    //
+
     uint64_t d = n - 1;
     uint64_t S = 0;
 
@@ -69,8 +84,9 @@ bool prime_test(uint64_t n, int a) {
     // round 1
     // 1: a^d =k 1 mod n
     uint64_t length = 0;
+    // convert exponent to binary to use in quickpow
     uint64_t *d_binary = dec_to_bin(d, &length);
-    uint64_t first_qp_res = quick_pow(d_binary, a, n, length);
+    unsigned __int128 first_qp_res = quick_pow(d_binary, a, n, length);
 
     if (first_qp_res == 1) {
         free(d_binary);
@@ -82,12 +98,10 @@ bool prime_test(uint64_t n, int a) {
     for (int i = 0; i <= r; i++) {
         if (first_qp_res == n - 1) {
             free(d_binary);
-            printf("true\n");
+            // printf("true\n");
             return true;
-        } else if (first_qp_res < n - 2) {
-            printf("first_qp_res became smaller then n!!\n");
-            break;
         } else {
+            //^2 with mod n, for each step since the next is the previous's squared
             first_qp_res = (uint64_t)(((unsigned __int128)first_qp_res * first_qp_res) % n);
         }
     }
@@ -96,56 +110,213 @@ bool prime_test(uint64_t n, int a) {
     return false;
 }
 
+typedef struct {
+    int base;
+    uint32_t prime;
+} prime_test_t;
+
 void *prime_thread_worker(void *arg) {
-    uint64_t *result_ptr = (uint64_t *)arg;
+    prime_test_t *result_ptr = (prime_test_t *)arg;
 
     do {
-        *result_ptr = rand64();
-        printf("\nGenerating a new prime number (%p). Candidate: ", result_ptr);
-        printf("%ju", *result_ptr);
-        printf("\n");
-    } while (!prime_test(*result_ptr, 2));
+        result_ptr->prime = rand32();
+    } while (!prime_test(result_ptr->prime, result_ptr->base));
 
     return NULL;
 }
 
-int main() {
-    // prime_test(111, 5);
-    // prime_test(29, 2);
-    // prime_test(27, 2);
-    // prime_test(17, 2);
-    // prime_test(661, 2);
-    // prime_test(18446744073709551557UL, 2);
-    // prime_test(18446744073709551533UL, 3);
+typedef struct {
+    uint64_t lnko;
+    __int128 x;
+    __int128 y;
+} euklidian_result_t;
+
+euklidian_result_t euklidian_algorigthm_extended(uint64_t a, uint64_t b) {
+    __int128 r = a % b, q = a / b, k = 1, xk = 0, yk = 1, next_r;
+    __int128 prev_r = b, prev_q, prev_xk = 0, prev_yk = 1, prev_prev_xk = 1, prev_prev_yk = 0;
+    euklidian_result_t res = {0, 0, 0};
+
+    while (r != 0) {
+        k++;
+
+        prev_q = q;
+        q = prev_r / r;
+
+        next_r = prev_r % r;
+        prev_r = r;
+        r = next_r;
+
+        xk = prev_xk * prev_q + prev_prev_xk;
+        prev_prev_xk = prev_xk;
+        prev_xk = xk;
+
+        yk = prev_yk * prev_q + prev_prev_yk;
+        prev_prev_yk = prev_yk;
+        prev_yk = yk;
+    }
+
+    __int128 x = k % 2 == 0 ? prev_xk : -prev_xk;
+    __int128 y = k % 2 == 0 ? -prev_yk : prev_yk;
+
+    // the reason this can be casted is that two uint64_t-s cant have a lnko which is bigger than a uint64_t
+    res.lnko = (uint64_t)prev_r;
+    res.x = x;
+    res.y = y;
+
+    return res;
+}
+
+uint64_t kinai_maradek_tetel(uint64_t *m, uint64_t d, prime_test_t *p, prime_test_t *q) {
+    // sum(i: 1,2): Ci * Yi * Mi mod M
+    // M: P*Q, Mp: M/P, Mq: M/Q
+    uint64_t M = (uint64_t)p->prime * q->prime;
+    uint64_t Mp = q->prime;
+    uint64_t Mq = p->prime;
+
+    // C1: c^(d mod P-1) mod P
+    uint64_t temp_exponent = d % (p->prime - 1);
+    uint64_t exponent_bin_length = 0;
+    uint64_t *exponent_as_binary = dec_to_bin(temp_exponent, &exponent_bin_length);
+    uint64_t c1 = quick_pow(exponent_as_binary, *m, p->prime, exponent_bin_length);
+    free(exponent_as_binary);
+
+    // C2: c^(d mod Q-1) mod Q
+    temp_exponent = d % (q->prime - 1);
+    exponent_as_binary = dec_to_bin(temp_exponent, &exponent_bin_length);
+    uint64_t c2 = quick_pow(exponent_as_binary, *m, q->prime, exponent_bin_length);
+    free(exponent_as_binary);
+
+    euklidian_result_t y = euklidian_algorigthm_extended(Mp, Mq); // in the struct the x will mean the y1 and y will mean the y2
+
+    // if either of them is less a negative number shift them into postive range with with hte modulo
+    uint64_t y1_pos;
+    if (y.x < 0) {
+        y1_pos = p->prime - (uint64_t)(-y.x % p->prime);
+    } else {
+        y1_pos = (uint64_t)y.x % p->prime;
+    }
+
+    uint64_t y2_pos;
+    if (y.y < 0) {
+        y2_pos = q->prime - (uint64_t)(-y.y % q->prime);
+    } else {
+        y2_pos = (uint64_t)y.y % q->prime;
+    }
+
+    // Apply the modulo between multiplications to prevent 192-bit overflows!
+    uint64_t s1 = (uint64_t)((((unsigned __int128)c1 * y1_pos) % M * Mp) % M);
+    uint64_t s2 = (uint64_t)((((unsigned __int128)c2 * y2_pos) % M * Mq) % M);
+    return (uint64_t)(((unsigned __int128)s1 + s2) % M);
+}
+
+uint64_t rsa_encrypt(uint64_t *m, prime_test_t *p, prime_test_t *q, uint64_t *out_e, uint64_t *out_d) {
+    uint64_t n = (uint64_t)p->prime * q->prime;
+    printf("n: %ju\n", n);
+
+    uint64_t fi_n = (uint64_t)(p->prime - 1) * (q->prime - 1);
+    printf("n: %ju\n", fi_n);
+
+    // keygen
+    uint64_t e = 65537;
+    do {
+        e = rand32() % fi_n; // should this go back as a condition inside the while loop?
+    } while (e <= 1 || !prime_test(e, p->base)); // the p and q base is used everywhere anyways, i wont pass in another arg
+
+    // calculate the d value, in eae it will be the y value
+    euklidian_result_t calc_d = euklidian_algorigthm_extended(fi_n, e);
+
+    // if either of them is less a negative number shift them into postive range with with hte modulo
+    uint64_t d;
+    if (calc_d.y < 0) {
+        d = fi_n - (uint64_t)(-calc_d.y);
+    } else {
+        d = (uint64_t)calc_d.y;
+    }
+
+    *out_e = e;
+    *out_d = d;
+
+    uint64_t length = 0;
+    // m^e mod n
+    uint64_t *nyenye = dec_to_bin(e, &length);
+    uint64_t c = quick_pow(nyenye, *m, n, length);
+    free(nyenye);
+
+    printf("\nc: ");
+    print_uint128(c);
+    return c;
+}
+
+int main() {
+    int isSignature = 0;
+    printf("Please input 0 for Rsa encryption or 1 for Rsa signature: ");
+    scanf("%d", &isSignature);
+    printf("\n");
+
+    uint64_t m = 0;
+    printf("give input for m: ");
+    scanf("%ju", &m);
+    printf("\n");
+
+    srand(time(NULL));
 
-    uint64_t p = 0;
-    uint64_t q = 0;
     uint64_t base = 2;
     pthread_t thread_p, thread_q;
-
-    // for (int i = 0; i < 10; i++) {
-    //     p = rand64();
-    //     printf("%ju", p);
-    //     prime_test(p, base);
-    // }
+    prime_test_t p = {base, 0};
+    prime_test_t q = {base, 0};
 
     pthread_create(&thread_p, NULL, prime_thread_worker, &p);
     pthread_create(&thread_q, NULL, prime_thread_worker, &q);
 
     pthread_join(thread_p, NULL);
     pthread_join(thread_q, NULL);
-
     printf("\n");
 
-    unsigned __int128 n = p * q;
-    print_uint128(n);
-    printf("\n");
+    printf("p: %u\n", p.prime);
+    printf("q: %u\n", q.prime);
 
-    unsigned __int128 fi_n = (p - 1) * (q - 1);
-    print_uint128(fi_n);
-    printf("\n");
+    uint64_t e = 0;
+    uint64_t d = 0;
 
-    // 2. kulcsgeneralas
+    if (!isSignature) {
+        // rsa encryption
+        uint64_t c = rsa_encrypt(&m, &p, &q, &e, &d);
+        printf("\nkinai maradek tetel:\n");
+        unsigned __int128 S = kinai_maradek_tetel(&c, d, &p, &q);
+        printf("S: ");
+        print_uint128(S);
+        printf("\n");
+    } else if (isSignature == 1) {
+        // rsa signature
+
+        // generate keys
+        rsa_encrypt(&m, &p, &q, &e, &d);
+        printf("\n");
+
+        // c^d -> creates signature
+        uint64_t signature = kinai_maradek_tetel(&m, d, &p, &q);
+        printf("Signature: ");
+        print_uint128(signature);
+
+        // key verifacation
+        // S^e -> verifies the signature
+        uint64_t e_length = 0;
+        uint64_t *e_binary = dec_to_bin(e, &e_length);
+        uint64_t n = (uint64_t)p.prime * q.prime;
+
+        uint64_t verified_message = quick_pow(e_binary, signature, n, e_length);
+        free(e_binary);
+
+        printf("Verified Message: %ju", verified_message);
+
+        if (verified_message == m) {
+            printf("\nSignature correct\n");
+        } else {
+            printf("\nSignature not correct\n");
+        }
+    } else {
+        printf("Why?\n");
+    }
 
     return 0;
 }