// Copyright Eric Chauvin.
internal void ModularReduction( ChineseRemainder CRTInput,
ChineseRemainder CRTAccumulate )
{
try
{
if( NumbersArray == null )
throw( new Exception( "Bug: The NumbersArray should have been set up already." ));
if( CRTBaseModArray == null )
throw( new Exception( "Bug: The BaseModArray should have been set up already." ));
// This first one has the prime 2 as its base so it's going to
// be set to either zero or one.
if( CRTInput.GetDigitAt( 0 ) == 1 )
{
CRTAccumulate.SetToOne();
}
else
{
CRTAccumulate.SetToZero();
}
CRTBase CRTBaseInput = new CRTBase( IntMath );
int HowManyToAdd = SetFromCRTNumber( CRTBaseInput, CRTInput );
// Integer Test = new Integer();
// ChineseRemainder CRTTest = new ChineseRemainder( IntMath );
// GetTraditionalInteger( CRTBaseInput, Test );
// CRTTest.SetFromTraditionalInteger( Test );
// if( !CRTTest.IsEqual( CRTInput ))
// throw( new Exception( "CRTTest for CRTInput isn't right." ));
// Count starts at 1, so it's the prime 3.
for( int Count = 1; Count <= HowManyToAdd; Count++ )
{
// BaseMultiple is a number that is not bigger
// than the prime at this point. (The prime at:
// IntMath.GetPrimeAt( Count ).)
uint BaseMultiple = (uint)CRTBaseInput.GetDigitAt( Count );
// It uses the CRTBaseModArray here:
CRTWorkingTemp.Copy( CRTBaseModArray[Count] );
CRTWorkingTemp.Multiply( NumbersArray[BaseMultiple] );
CRTAccumulate.Add( CRTWorkingTemp );
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in ModularReduction(): " + Except.Message ));
}
}
internal void ModularPower( ChineseRemainder CRTResult,
Integer Exponent,
ChineseRemainder CRTModulus,
bool UsePresetBaseArray )
{
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
if( Worker.CancellationPending )
return;
if( CRTResult.IsZero())
return; // With CRTResult still zero.
if( CRTResult.IsEqual( CRTModulus ))
{
// It is congruent to zero % ModN.
CRTResult.SetToZero();
return;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
{
CRTResult.SetToOne();
return;
}
Integer Result = new Integer();
CRTMath1.GetTraditionalInteger( Result, CRTResult );
Integer Modulus = new Integer();
CRTMath1.GetTraditionalInteger( Modulus, CRTModulus );
if( Modulus.ParamIsGreater( Result ))
{
// throw( new Exception( "This is not supposed to be input for RSA plain text." ));
IntMath.Divide( Result, Modulus, Quotient, Remainder );
Result.Copy( Remainder );
CRTResult.SetFromTraditionalInteger( Remainder );
}
if( Exponent.IsEqualToULong( 1 ))
{
// Result stays the same.
return;
}
if( !UsePresetBaseArray )
SetupBaseModArray( Modulus );
if( CRTBaseModArray == null )
throw( new Exception( "SetupBaseModArray() should have already been done here." ));
CRTXForModPower.Copy( CRTResult );
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
CRTResult.SetToOne();
int LoopsTest = 0;
while( true )
{
LoopsTest++;
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
CRTResult.Multiply( CRTXForModPower );
ModularReduction( CRTResult, CRTAccumulate );
CRTResult.Copy( CRTAccumulate );
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
CRTCopyForSquare.Copy( CRTXForModPower );
CRTXForModPower.Multiply( CRTCopyForSquare );
ModularReduction( CRTXForModPower, CRTAccumulate );
CRTXForModPower.Copy( CRTAccumulate );
}
ModularReduction( CRTResult, CRTAccumulate );
CRTResult.Copy( CRTAccumulate );
// Division is never used in the loop above.
// This is a very small Quotient.
// See SetupBaseMultiples() for a description of how to calculate
// the maximum size of this quotient.
CRTMath1.GetTraditionalInteger( Result, CRTResult );
IntMath.Divide( Result, Modulus, Quotient, Remainder );
// Is the Quotient bigger than a 32 bit integer?
if( Quotient.GetIndex() > 0 )
throw( new Exception( "I haven't ever seen this happen. Quotient.GetIndex() > 0. It is: " + Quotient.GetIndex().ToString() ));
QuotientForTest = Quotient.GetAsULong();
if( QuotientForTest > 2097867 )
throw( new Exception( "This can never happen unless I increase ChineseRemainder.DigitsArraySize." ));
Result.Copy( Remainder );
CRTResult.SetFromTraditionalInteger( Remainder );
}