Modular Multiplicative Inverse

K
```using System;
using System.Numerics;

namespace Algorithms.ModularArithmetic
{
/// <summary>
/// Modular multiplicative inverse: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse.
/// </summary>
public static class ModularMultiplicativeInverse
{
/// <summary>
///     Computes the modular multiplicative inverse of a in Z/nZ, if there is any (i.e. if a and n are coprime).
/// </summary>
/// <param name="a">The number a, of which to compute the multiplicative inverse.</param>
/// <param name="n">The modulus n.</param>
/// <returns>The multiplicative inverse of a in Z/nZ, a value in the interval [0, n).</returns>
/// <exception cref="ArithmeticException">If there exists no multiplicative inverse of a in Z/nZ.</exception>
public static long Compute(long a, long n)
{
var eeaResult = ExtendedEuclideanAlgorithm.Compute(a, n);

// Check if there is an inverse:
if (eeaResult.gcd != 1)
{
throw new ArithmeticException(\$"{a} is not invertible in Z/{n}Z.");
}

// Make sure, inverseOfA (i.e. the bezout coefficient of a) is in the interval [0, n).
var inverseOfA = eeaResult.bezoutA;
if (inverseOfA < 0)
{
inverseOfA += n;
}

return inverseOfA;
}

/// <summary>
///     Computes the modular multiplicative inverse of a in Z/nZ, if there is any (i.e. if a and n are coprime).
/// </summary>
/// <param name="a">The number a, of which to compute the multiplicative inverse.</param>
/// <param name="n">The modulus n.</param>
/// <returns>The multiplicative inverse of a in Z/nZ, a value in the interval [0, n).</returns>
/// <exception cref="ArithmeticException">If there exists no multiplicative inverse of a in Z/nZ.</exception>
public static BigInteger Compute(BigInteger a, BigInteger n)
{
var eeaResult = ExtendedEuclideanAlgorithm.Compute(a, n);

// Check if there is an inverse:
if (eeaResult.gcd != 1)
{
throw new ArithmeticException(\$"{a} is not invertible in Z/{n}Z.");
}

// Make sure, inverseOfA (i.e. the bezout coefficient of a) is in the interval [0, n).
var inverseOfA = eeaResult.bezoutA;
if (inverseOfA < 0)
{
inverseOfA += n;
}

return inverseOfA;
}
}
}
```