Initial data commit

Task/Tonelli-Shanks-algorithm/C/tonelli-shanks-algorithm-1.c

@@ -0,0 +1,102 @@
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdio.h>
+
+uint64_t modpow(uint64_t a, uint64_t b, uint64_t n) {
+    uint64_t x = 1, y = a;
+    while (b > 0) {
+        if (b % 2 == 1) {
+            x = (x * y) % n; // multiplying with base
+        }
+        y = (y * y) % n; // squaring the base
+        b /= 2;
+    }
+    return x % n;
+}
+
+struct Solution {
+    uint64_t root1, root2;
+    bool exists;
+};
+
+struct Solution makeSolution(uint64_t root1, uint64_t root2, bool exists) {
+    struct Solution sol;
+    sol.root1 = root1;
+    sol.root2 = root2;
+    sol.exists = exists;
+    return sol;
+}
+
+struct Solution ts(uint64_t n, uint64_t p) {
+    uint64_t q = p - 1;
+    uint64_t ss = 0;
+    uint64_t z = 2;
+    uint64_t c, r, t, m;
+
+    if (modpow(n, (p - 1) / 2, p) != 1) {
+        return makeSolution(0, 0, false);
+    }
+
+    while ((q & 1) == 0) {
+        ss += 1;
+        q >>= 1;
+    }
+
+    if (ss == 1) {
+        uint64_t r1 = modpow(n, (p + 1) / 4, p);
+        return makeSolution(r1, p - r1, true);
+    }
+
+    while (modpow(z, (p - 1) / 2, p) != p - 1) {
+        z++;
+    }
+
+    c = modpow(z, q, p);
+    r = modpow(n, (q + 1) / 2, p);
+    t = modpow(n, q, p);
+    m = ss;
+
+    while (true) {
+        uint64_t i = 0, zz = t;
+        uint64_t b = c, e;
+        if (t == 1) {
+            return makeSolution(r, p - r, true);
+        }
+        while (zz != 1 && i < (m - 1)) {
+            zz = zz * zz % p;
+            i++;
+        }
+        e = m - i - 1;
+        while (e > 0) {
+            b = b * b % p;
+            e--;
+        }
+        r = r * b % p;
+        c = b * b % p;
+        t = t * c % p;
+        m = i;
+    }
+}
+
+void test(uint64_t n, uint64_t p) {
+    struct Solution sol = ts(n, p);
+    printf("n = %llu\n", n);
+    printf("p = %llu\n", p);
+    if (sol.exists) {
+        printf("root1 = %llu\n", sol.root1);
+        printf("root2 = %llu\n", sol.root2);
+    } else {
+        printf("No solution exists\n");
+    }
+    printf("\n");
+}
+
+int main() {
+    test(10, 13);
+    test(56, 101);
+    test(1030, 10009);
+    test(1032, 10009);
+    test(44402, 100049);
+
+    return 0;
+}