ModularMultiplicativeInverse.cs

usingSystem;
usingSystem.Numerics;

namespaceAlgorithms.ModularArithmetic;

/// <summary>
/// Modular multiplicative inverse: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse.
/// </summary>
publicstaticclassModularMultiplicativeInverse
{
/// <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>
publicstaticlongCompute(longa,longn)
{
vareeaResult=ExtendedEuclideanAlgorithm.Compute(a,n);

// Check if there is an inverse:
if(eeaResult.Gcd!=1)
{
thrownewArithmeticException($"{a} is not invertible in Z/{n}Z.");
}

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

returninverseOfA;
}

/// <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>
publicstaticBigIntegerCompute(BigIntegera,BigIntegern)
{
vareeaResult=ExtendedEuclideanAlgorithm.Compute(a,n);

// Check if there is an inverse:
if(eeaResult.Gcd!=1)
{
thrownewArithmeticException($"{a} is not invertible in Z/{n}Z.");
}

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

returninverseOfA;
}
}