internal bool MultiplicativeInverse(Integer X, Integer Modulus, Integer MultInverse)
{
// This is the extended Euclidean Algorithm.
// A*X + B*Y = Gcd
// A*X + B*Y = 1 If there's a multiplicative inverse.
// A*X = 1 - B*Y so A is the multiplicative inverse of X mod Y.
if (X.IsZero())
{
throw(new Exception("Doing Multiplicative Inverse with a parameter that is zero."));
}
if (Modulus.IsZero())
{
throw(new Exception("Doing Multiplicative Inverse with a parameter that is zero."));
}
// This happens sometimes:
// if( Modulus.ParamIsGreaterOrEq( X ))
// throw( new Exception( "Modulus.ParamIsGreaterOrEq( X ) for Euclid." ));
// Worker.ReportProgress( 0, " " );
// Worker.ReportProgress( 0, " " );
// Worker.ReportProgress( 0, "Top of mod inverse." );
// U is the old part to keep.
U0.SetToZero();
U1.SetToOne();
U2.Copy(Modulus); // Don't change the original numbers that came in as parameters.
// V is the new part.
V0.SetToOne();
V1.SetToZero();
V2.Copy(X);
T0.SetToZero();
T1.SetToZero();
T2.SetToZero();
Quotient.SetToZero();
// while( not forever if there's a problem )
for (int Count = 0; Count < 10000; Count++)
{
if (U2.IsNegative)
{
throw(new Exception("U2 was negative."));
}
if (V2.IsNegative)
{
throw(new Exception("V2 was negative."));
}
IntMath.Divider.Divide(U2, V2, Quotient, Remainder);
if (Remainder.IsZero())
{
// Worker.ReportProgress( 0, "Remainder is zero. No multiplicative-inverse." );
return(false);
}
TempEuclid1.Copy(U0);
TempEuclid2.Copy(V0);
IntMath.Multiplier.Multiply(TempEuclid2, Quotient);
IntMath.Subtract(TempEuclid1, TempEuclid2);
T0.Copy(TempEuclid1);
TempEuclid1.Copy(U1);
TempEuclid2.Copy(V1);
IntMath.Multiplier.Multiply(TempEuclid2, Quotient);
IntMath.Subtract(TempEuclid1, TempEuclid2);
T1.Copy(TempEuclid1);
TempEuclid1.Copy(U2);
TempEuclid2.Copy(V2);
IntMath.Multiplier.Multiply(TempEuclid2, Quotient);
IntMath.Subtract(TempEuclid1, TempEuclid2);
T2.Copy(TempEuclid1);
U0.Copy(V0);
U1.Copy(V1);
U2.Copy(V2);
V0.Copy(T0);
V1.Copy(T1);
V2.Copy(T2);
if (Remainder.IsOne())
{
// Worker.ReportProgress( 0, " " );
// Worker.ReportProgress( 0, "Remainder is 1. There is a multiplicative-inverse." );
break;
}
}
MultInverse.Copy(T0);
if (MultInverse.IsNegative)
{
IntMath.Add(MultInverse, Modulus);
}
// Worker.ReportProgress( 0, "MultInverse: " + ToString10( MultInverse ));
TestForModInverse1.Copy(MultInverse);
TestForModInverse2.Copy(X);
IntMath.Multiplier.Multiply(TestForModInverse1, TestForModInverse2);
IntMath.Divider.Divide(TestForModInverse1, Modulus, Quotient, Remainder);
if (!Remainder.IsOne()) // By the definition of Multiplicative inverse:
{
throw(new Exception("MultInverse is wrong: " + IntMath.ToString10(Remainder)));
}
// Worker.ReportProgress( 0, "MultInverse is the right number: " + ToString10( MultInverse ));
return(true);
}
