Initial data commit

Task/Tonelli-Shanks-algorithm/C-sharp/tonelli-shanks-algorithm.cs

@@ -0,0 +1,116 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+
+namespace TonelliShanks {
+    class Solution {
+        private readonly BigInteger root1, root2;
+        private readonly bool exists;
+
+        public Solution(BigInteger root1, BigInteger root2, bool exists) {
+            this.root1 = root1;
+            this.root2 = root2;
+            this.exists = exists;
+        }
+
+        public BigInteger Root1() {
+            return root1;
+        }
+
+        public BigInteger Root2() {
+            return root2;
+        }
+
+        public bool Exists() {
+            return exists;
+        }
+    }
+
+    class Program {
+        static Solution Ts(BigInteger n, BigInteger p) {
+            if (BigInteger.ModPow(n, (p - 1) / 2, p) != 1) {
+                return new Solution(0, 0, false);
+            }
+
+            BigInteger q = p - 1;
+            BigInteger ss = 0;
+            while ((q & 1) == 0) {
+                ss = ss + 1;
+                q = q >> 1;
+            }
+
+            if (ss == 1) {
+                BigInteger r1 = BigInteger.ModPow(n, (p + 1) / 4, p);
+                return new Solution(r1, p - r1, true);
+            }
+
+            BigInteger z = 2;
+            while (BigInteger.ModPow(z, (p - 1) / 2, p) != p - 1) {
+                z = z + 1;
+            }
+            BigInteger c = BigInteger.ModPow(z, q, p);
+            BigInteger r = BigInteger.ModPow(n, (q + 1) / 2, p);
+            BigInteger t = BigInteger.ModPow(n, q, p);
+            BigInteger m = ss;
+
+            while (true) {
+                if (t == 1) {
+                    return new Solution(r, p - r, true);
+                }
+                BigInteger i = 0;
+                BigInteger zz = t;
+                while (zz != 1 && i < (m - 1)) {
+                    zz = zz * zz % p;
+                    i = i + 1;
+                }
+                BigInteger b = c;
+                BigInteger e = m - i - 1;
+                while (e > 0) {
+                    b = b * b % p;
+                    e = e - 1;
+                }
+                r = r * b % p;
+                c = b * b % p;
+                t = t * c % p;
+                m = i;
+            }
+        }
+
+        static void Main(string[] args) {
+            List<Tuple<long, long>> pairs = new List<Tuple<long, long>>() {
+                new Tuple<long, long>(10, 13),
+                new Tuple<long, long>(56, 101),
+                new Tuple<long, long>(1030, 10009),
+                new Tuple<long, long>(1032, 10009),
+                new Tuple<long, long>(44402, 100049),
+                new Tuple<long, long>(665820697, 1000000009),
+                new Tuple<long, long>(881398088036, 1000000000039),
+            };
+
+            foreach (var pair in pairs) {
+                Solution sol = Ts(pair.Item1, pair.Item2);
+                Console.WriteLine("n = {0}", pair.Item1);
+                Console.WriteLine("p = {0}", pair.Item2);
+                if (sol.Exists()) {
+                    Console.WriteLine("root1 = {0}", sol.Root1());
+                    Console.WriteLine("root2 = {0}", sol.Root2());
+                } else {
+                    Console.WriteLine("No solution exists");
+                }
+                Console.WriteLine();
+            }
+
+            BigInteger bn = BigInteger.Parse("41660815127637347468140745042827704103445750172002");
+            BigInteger bp = BigInteger.Pow(10, 50) + 577;
+            Solution bsol = Ts(bn, bp);
+            Console.WriteLine("n = {0}", bn);
+            Console.WriteLine("p = {0}", bp);
+            if (bsol.Exists()) {
+                Console.WriteLine("root1 = {0}", bsol.Root1());
+                Console.WriteLine("root2 = {0}", bsol.Root2());
+            } else {
+                Console.WriteLine("No solution exists");
+            }
+        }
+    }
+}