C# ModInverse Function

C# ModInverse Function

To calculate the modular multiplicative inverse of a number in C#, you can use the Extended Euclidean Algorithm. The modular multiplicative inverse of a number a under modulo m is the number x such that (a * x) % m is equal to 1.

Here's an implementation of the modular inverse function in C#:

using System; public class Program { public static void Main() { int a = 5; int m = 17; int inverse = ModInverse(a, m); Console.WriteLine($"Modular inverse of {a} under {m} is: {inverse}"); } public static int ModInverse(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, process same as Euclid's algo m = a % m; a = t; t = y; // Update x and y y = x - q * y; x = t; } // Make x positive if (x < 0) x += m0; return x; } }

In this example, we want to find the modular inverse of a = 5 under modulo m = 17. The ModInverse function calculates the modular inverse using the Extended Euclidean Algorithm and returns the result.

The output will be:

Modular inverse of 5 under 17 is: 7

The modular inverse of 5 under modulo 17 is 7 because (5 * 7) % 17 = 1.

Examples

  1. "C# Modular Inverse Algorithm"

    • Description: Learn about algorithms for calculating modular inverses and how to implement them in C#.
    • Code:
      public static int ModInverse(int a, int m) { for (int x = 1; x < m; x++) { if ((a * x) % m == 1) return x; } throw new ArithmeticException("Inverse does not exist"); }

  2. "C# Extended Euclidean Algorithm ModInverse"

    • Description: Explore the Extended Euclidean Algorithm for computing the modular inverse and its implementation in C#.
    • Code:
      public static int ModInverse(int a, int m) { int m0 = m, t, q; int x0 = 0, x1 = 1; if (m == 1) return 0; while (a > 1) { q = a / m; t = m; m = a % m; a = t; t = x0; x0 = x1 - q * x0; x1 = t; } if (x1 < 0) x1 += m0; return x1; }

  3. "C# Modular Inverse Fermat's Little Theorem"

    • Description: Understand how Fermat's Little Theorem can be used for modular inverse calculation and implement it in C#.
    • Code:
      public static int ModInverse(int a, int m) { return Power(a, m - 2, m); } public static int Power(int x, int y, int p) { int result = 1; x = x % p; while (y > 0) { if (y % 2 == 1) result = (result * x) % p; y = y >> 1; x = (x * x) % p; } return result; }

  4. "C# Modular Inverse Binary Exponentiation"

    • Description: Learn about the binary exponentiation method for modular inverse and its C# implementation.
    • Code:
      public static int ModInverse(int a, int m) { return Power(a, m - 2, m); } public static int Power(int x, int y, int p) { int result = 1; x = x % p; while (y > 0) { if (y % 2 == 1) result = (result * x) % p; y = y >> 1; x = (x * x) % p; } return result; }

  5. "C# BigInteger ModInverse"

    • Description: Explore using the BigInteger class for modular inverse calculations in C#.
    • Code:
      using System.Numerics; public static BigInteger ModInverse(BigInteger a, BigInteger m) { return BigInteger.ModPow(a, -1, m); }

  6. "C# Modular Arithmetic ModInverse"

    • Description: Understand the principles of modular arithmetic and how to apply them to compute modular inverses in C#.
    • Code:
      public static int ModInverse(int a, int m) { a = a % m; for (int x = 1; x < m; x++) { if ((a * x) % m == 1) return x; } throw new ArithmeticException("Inverse does not exist"); }

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