internal uint ModularPowerSmall( ulong Input, Integer Exponent, uint Modulus )
{
if( Input == 0 )
return 0;
if( Input == Modulus )
{
// It is congruent to zero % Modulus.
return 0;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
return 1;
ulong Result = Input;
if( Input > Modulus )
Result = Input % Modulus;
if( Exponent.IsOne())
return (uint)Result;
ulong XForModPowerU = Result;
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
Result = 1;
while( true )
{
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
Result = Result * XForModPowerU;
Result = Result % Modulus;
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
XForModPowerU = XForModPowerU * XForModPowerU;
XForModPowerU = XForModPowerU % Modulus;
}
return (uint)Result;
}
internal void FindAllFactors( Integer FindFromNotChanged )
{
// ShowStats(); // So far.
OriginalFindFrom.Copy( FindFromNotChanged );
FindFrom.Copy( FindFromNotChanged );
NumbersTested++;
ClearFactorsArray();
Integer OneFactor;
OneFactorRec Rec;
// while( not forever )
for( int Count = 0; Count < 1000; Count++ )
{
if( Worker.CancellationPending )
return;
uint SmallPrime = IntMath.IsDivisibleBySmallPrime( FindFrom );
if( SmallPrime == 0 )
break; // No more small primes.
// Worker.ReportProgress( 0, "Found a small prime factor: " + SmallPrime.ToString() );
AddToStats( SmallPrime );
OneFactor = new Integer();
OneFactor.SetFromULong( SmallPrime );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true;
AddFactorRec( Rec );
if( FindFrom.IsULong())
{
ulong CheckLast = FindFrom.GetAsULong();
if( CheckLast == SmallPrime )
{
Worker.ReportProgress( 0, "It only had small prime factors." );
VerifyFactors();
return; // It had only small prime factors.
}
}
IntMath.Divide( FindFrom, OneFactor, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "Bug in FindAllFactors. Remainder is not zero." ));
FindFrom.Copy( Quotient );
if( FindFrom.IsOne())
throw( new Exception( "Bug in FindAllFactors. This was already checked for 1." ));
}
// Worker.ReportProgress( 0, "No more small primes." );
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
// while( not forever )
for( int Count = 0; Count < 1000; Count++ )
{
if( Worker.CancellationPending )
return;
// If FindFrom is a ulong then this will go up to the square root of
// FindFrom and return zero if it doesn't find it there. So it can't
// go up to the whole value of FindFrom.
uint SmallFactor = NumberIsDivisibleByUInt( FindFrom );
if( SmallFactor == 0 )
break;
// This is necessarily a prime because it was the smallest one found.
AddToStats( SmallFactor );
// Worker.ReportProgress( 0, "Found a small factor: " + SmallFactor.ToString( "N0" ));
OneFactor = new Integer();
OneFactor.SetFromULong( SmallFactor );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true; // The smallest factor. It is necessarily a prime.
AddFactorRec( Rec );
IntMath.Divide( FindFrom, OneFactor, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "Bug in FindAllFactors. Remainder is not zero. Second part." ));
if( Quotient.IsOne())
throw( new Exception( "This can't happen here. It can't go that high." ));
FindFrom.Copy( Quotient );
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
}
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
// If it got this far then it's definitely composite or definitely
// small enough to factor.
Integer P = new Integer();
Integer Q = new Integer();
bool TestedAllTheWay = FindTwoFactorsWithFermat( FindFrom, P, Q, 0 );
if( !P.IsZero())
{
// Q is necessarily prime because it's bigger than the square root.
// But P is not necessarily prime.
// P is the smaller one, so add it first.
if( IsFermatPrimeAdded( P ))
{
Worker.ReportProgress( 0, "P from Fermat method was probably a prime." );
}
else
{
OneFactor = new Integer();
OneFactor.Copy( P );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyNotAPrime = true;
AddFactorRec( Rec );
}
Worker.ReportProgress( 0, "Q is necessarily prime." );
OneFactor = new Integer();
OneFactor.Copy( Q );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true;
AddFactorRec( Rec );
}
else
{
// Didn't find any with Fermat.
OneFactor = new Integer();
OneFactor.Copy( FindFrom );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
if( TestedAllTheWay )
Rec.IsDefinitelyAPrime = true;
else
Rec.IsDefinitelyNotAPrime = true;
AddFactorRec( Rec );
}
Worker.ReportProgress( 0, "That's all it could find." );
VerifyFactors();
}
// This is the standard modular power algorithm that
// you could find in any reference, but its use of
// the new modular reduction algorithm is new.
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
// x^n = (x^2)^((n - 1)/2) if n is odd.
// x^n = (x^2)^(n/2) if n is even.
internal void ModularPower( Integer Result, Integer Exponent, Integer Modulus, bool UsePresetBaseArray )
{
if( Result.IsZero())
return; // With Result still zero.
if( Result.IsEqual( Modulus ))
{
// It is congruent to zero % ModN.
Result.SetToZero();
return;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
{
Result.SetFromULong( 1 );
return;
}
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 );
}
if( Exponent.IsOne())
{
// Result stays the same.
return;
}
if( !UsePresetBaseArray )
SetupGeneralBaseArray( Modulus );
XForModPower.Copy( Result );
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
Result.SetFromULong( 1 );
while( true )
{
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
IntMath.Multiply( Result, XForModPower );
ModularReduction( TempForModPower, Result );
Result.Copy( TempForModPower );
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
IntMath.Multiply( XForModPower, XForModPower );
ModularReduction( TempForModPower, XForModPower );
XForModPower.Copy( TempForModPower );
}
// When ModularReduction() gets called it multiplies a base number
// by a uint sized digit. So that can make the result one digit bigger
// than GeneralBase. Then when they are added up you can get carry
// bits that can make it a little bigger.
int HowBig = Result.GetIndex() - Modulus.GetIndex();
// if( HowBig > 1 )
// throw( new Exception( "This does happen. Diff: " + HowBig.ToString() ));
if( HowBig > 2 )
throw( new Exception( "The never happens. Diff: " + HowBig.ToString() ));
ModularReduction( TempForModPower, Result );
Result.Copy( TempForModPower );
IntMath.Divide( Result, Modulus, Quotient, Remainder );
Result.Copy( Remainder );
if( Quotient.GetIndex() > 1 )
throw( new Exception( "This never happens. The quotient index is never more than 1." ));
}
internal void Divide( Integer ToDivideOriginal,
Integer DivideByOriginal,
Integer Quotient,
Integer Remainder )
{
if( ToDivideOriginal.IsNegative )
throw( new Exception( "Divide() can't be called with negative numbers." ));
if( DivideByOriginal.IsNegative )
throw( new Exception( "Divide() can't be called with negative numbers." ));
// Returns true if it divides exactly with zero remainder.
// This first checks for some basics before trying to divide it:
if( DivideByOriginal.IsZero() )
throw( new Exception( "Divide() dividing by zero." ));
ToDivide.Copy( ToDivideOriginal );
DivideBy.Copy( DivideByOriginal );
if( ToDivide.ParamIsGreater( DivideBy ))
{
Quotient.SetToZero();
Remainder.Copy( ToDivide );
return; // false;
}
if( ToDivide.IsEqual( DivideBy ))
{
Quotient.SetFromULong( 1 );
Remainder.SetToZero();
return; // true;
}
// At this point DivideBy is smaller than ToDivide.
if( ToDivide.IsULong() )
{
ulong ToDivideU = ToDivide.GetAsULong();
ulong DivideByU = DivideBy.GetAsULong();
ulong QuotientU = ToDivideU / DivideByU;
ulong RemainderU = ToDivideU % DivideByU;
Quotient.SetFromULong( QuotientU );
Remainder.SetFromULong( RemainderU );
// if( RemainderU == 0 )
return; // true;
// else
// return false;
}
if( DivideBy.GetIndex() == 0 )
{
ShortDivide( ToDivide, DivideBy, Quotient, Remainder );
return;
}
// return LongDivide1( ToDivide, DivideBy, Quotient, Remainder );
// return LongDivide2( ToDivide, DivideBy, Quotient, Remainder );
LongDivide3( ToDivide, DivideBy, Quotient, Remainder );
}
/*
internal void ModularPowerOld( Integer Result, Integer Exponent, Integer ModN )
{
if( Result.IsZero())
return; // With Result still zero.
if( Result.IsEqual( ModN ))
{
// It is congruent to zero % ModN.
Result.SetToZero();
return;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
{
Result.SetFromULong( 1 );
return;
}
if( ModN.ParamIsGreater( Result ))
{
Divide( Result, ModN, Quotient, Remainder );
Result.Copy( Remainder );
}
if( Exponent.IsEqualToULong( 1 ))
{
// Result stays the same.
return;
}
XForModPower.Copy( Result );
ExponentCopy.Copy( Exponent );
Result.SetFromULong( 1 );
while( !ExponentCopy.IsZero())
{
// If the bit is 1, then do a lot more work here.
if( (ExponentCopy.GetD( 0 ) & 1) == 1 )
{
// This is a multiplication for every _bit_. So a 1024-bit
// modulus means this gets called roughly 512 times.
// The commonly used public exponent is 65537, which has
// only two bits set to 1, the rest are all zeros. But the
// private key exponents are long randomish numbers.
// (See: Hamming Weight.)
Multiply( Result, XForModPower );
SubtractULong( ExponentCopy, 1 );
// Usually it's true that the Result is greater than ModN.
if( ModN.ParamIsGreater( Result ))
{
// Here is where that really long division algorithm gets used a
// lot in a loop. And this Divide() gets called roughly about
// 512 times.
Divide( Result, ModN, Quotient, Remainder );
Result.Copy( Remainder );
}
}
// Square it.
// This is a multiplication for every _bit_. So a 1024-bit
// modulus means this gets called 1024 times.
Multiply( XForModPower, XForModPower );
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ModN.ParamIsGreater( XForModPower ))
{
// And this Divide() gets called about 1024 times.
Divide( XForModPower, ModN, Quotient, Remainder );
XForModPower.Copy( Remainder );
}
}
}
*/
internal void GreatestCommonDivisor( Integer X, Integer Y, Integer Gcd )
{
// This is the basic Euclidean Algorithm.
if( X.IsZero())
throw( new Exception( "Doing GCD with a parameter that is zero." ));
if( Y.IsZero())
throw( new Exception( "Doing GCD with a parameter that is zero." ));
if( X.IsEqual( Y ))
{
Gcd.Copy( X );
return;
}
// Don't change the original numbers that came in as parameters.
if( X.ParamIsGreater( Y ))
{
GcdX.Copy( Y );
GcdY.Copy( X );
}
else
{
GcdX.Copy( X );
GcdY.Copy( Y );
}
while( true )
{
Divide( GcdX, GcdY, Quotient, Remainder );
if( Remainder.IsZero())
{
Gcd.Copy( GcdY ); // It's the smaller one.
// It can't return from this loop until the remainder is zero.
return;
}
GcdX.Copy( GcdY );
GcdY.Copy( Remainder );
}
}
internal void MultiplyULong( Integer Result, ulong ToMul )
{
// Using compile-time checks, this one overflows:
// const ulong Test = ((ulong)0xFFFFFFFF + 1) * ((ulong)0xFFFFFFFF + 1);
// This one doesn't:
// const ulong Test = (ulong)0xFFFFFFFF * ((ulong)0xFFFFFFFF + 1);
if( Result.IsZero())
return; // Then the answer is zero, which it already is.
if( ToMul == 0 )
{
Result.SetToZero();
return;
}
ulong B0 = ToMul & 0xFFFFFFFF;
ulong B1 = ToMul >> 32;
if( B1 == 0 )
{
MultiplyUInt( Result, (uint)B0 );
return;
}
// Since B1 is not zero:
if( (Result.GetIndex() + 1) >= Integer.DigitArraySize )
throw( new Exception( "Overflow in MultiplyULong." ));
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
{
M[Column, 0] = B0 * Result.GetD( Column );
// Column + 1 and Row is 1, so it's just like pen and paper.
M[Column + 1, 1] = B1 * Result.GetD( Column );
}
// Since B1 is not zero, the index is set one higher.
Result.IncrementIndex(); // Might throw an exception if it goes out of range.
M[Result.GetIndex(), 0] = 0; // Otherwise it would be undefined
// when it's added up below.
// Add these up with a carry.
Result.SetD( 0, M[0, 0] & 0xFFFFFFFF );
ulong Carry = M[0, 0] >> 32;
for( int Column = 1; Column <= Result.GetIndex(); Column++ )
{
// This does overflow:
// const ulong Test = ((ulong)0xFFFFFFFF * (ulong)(0xFFFFFFFF))
// + ((ulong)0xFFFFFFFF * (ulong)(0xFFFFFFFF));
// Split the ulongs into right and left sides
// so that they don't overflow.
ulong TotalLeft = 0;
ulong TotalRight = 0;
// There's only the two rows for this.
for( int Row = 0; Row <= 1; Row++ )
{
TotalRight += M[Column, Row] & 0xFFFFFFFF;
TotalLeft += M[Column, Row] >> 32;
}
TotalRight += Carry;
Result.SetD( Column, TotalRight & 0xFFFFFFFF );
Carry = TotalRight >> 32;
Carry += TotalLeft;
}
if( Carry != 0 )
{
Result.IncrementIndex(); // This can throw an exception.
Result.SetD( Result.GetIndex(), Carry );
}
}
internal void Add( Integer Result, Integer ToAdd )
{
if( ToAdd.IsZero())
return;
// The most common form. They are both positive.
if( !Result.IsNegative && !ToAdd.IsNegative )
{
Result.Add( ToAdd );
return;
}
if( !Result.IsNegative && ToAdd.IsNegative )
{
TempAdd1.Copy( ToAdd );
TempAdd1.IsNegative = false;
if( TempAdd1.ParamIsGreater( Result ))
{
Subtract( Result, TempAdd1 );
return;
}
else
{
Subtract( TempAdd1, Result );
Result.Copy( TempAdd1 );
Result.IsNegative = true;
return;
}
}
if( Result.IsNegative && !ToAdd.IsNegative )
{
TempAdd1.Copy( Result );
TempAdd1.IsNegative = false;
TempAdd2.Copy( ToAdd );
if( TempAdd1.ParamIsGreater( TempAdd2 ))
{
Subtract( TempAdd2, TempAdd1 );
Result.Copy( TempAdd2 );
return;
}
else
{
Subtract( TempAdd1, TempAdd2 );
Result.Copy( TempAdd2 );
Result.IsNegative = true;
return;
}
}
if( Result.IsNegative && ToAdd.IsNegative )
{
TempAdd1.Copy( Result );
TempAdd1.IsNegative = false;
TempAdd2.Copy( ToAdd );
TempAdd2.IsNegative = false;
TempAdd1.Add( TempAdd2 );
Result.Copy( TempAdd1 );
Result.IsNegative = true;
return;
}
}
internal bool MultiplicativeInverse( Integer X, Integer Modulus, Integer MultInverse, BackgroundWorker Worker )
{
// 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." ));
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 );
Multiply( TempEuclid2, Quotient );
Subtract( TempEuclid1, TempEuclid2 );
T0.Copy( TempEuclid1 );
TempEuclid1.Copy( U1 );
TempEuclid2.Copy( V1 );
Multiply( TempEuclid2, Quotient );
Subtract( TempEuclid1, TempEuclid2 );
T1.Copy( TempEuclid1 );
TempEuclid1.Copy( U2 );
TempEuclid2.Copy( V2 );
Multiply( TempEuclid2, Quotient );
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 )
{
Add( MultInverse, Modulus );
}
// Worker.ReportProgress( 0, "MultInverse: " + ToString10( MultInverse ));
TestForModInverse1.Copy( MultInverse );
TestForModInverse2.Copy( X );
Multiply( TestForModInverse1, TestForModInverse2 );
Divide( TestForModInverse1, Modulus, Quotient, Remainder );
if( !Remainder.IsOne()) // By the definition of Multiplicative inverse:
throw( new Exception( "Bug. MultInverse is wrong: " + ToString10( Remainder )));
// Worker.ReportProgress( 0, "MultInverse is the right number: " + ToString10( MultInverse ));
return true;
}
// See also: http://en.wikipedia.org/wiki/Karatsuba_algorithm
internal void Multiply( Integer Result, Integer ToMul )
{
// try
// {
if( Result.IsZero())
return;
if( ToMul.IsULong())
{
MultiplyULong( Result, ToMul.GetAsULong());
SetMultiplySign( Result, ToMul );
return;
}
// It could never get here if ToMul is zero because GetIsULong()
// would be true for zero.
// if( ToMul.IsZero())
int TotalIndex = Result.GetIndex() + ToMul.GetIndex();
if( TotalIndex >= Integer.DigitArraySize )
throw( new Exception( "Multiply() overflow." ));
for( int Row = 0; Row <= ToMul.GetIndex(); Row++ )
{
if( ToMul.GetD( Row ) == 0 )
{
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
M[Column + Row, Row] = 0;
}
else
{
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
M[Column + Row, Row] = ToMul.GetD( Row ) * Result.GetD( Column );
}
}
// Add the columns up with a carry.
Result.SetD( 0, M[0, 0] & 0xFFFFFFFF );
ulong Carry = M[0, 0] >> 32;
for( int Column = 1; Column <= TotalIndex; Column++ )
{
ulong TotalLeft = 0;
ulong TotalRight = 0;
for( int Row = 0; Row <= ToMul.GetIndex(); Row++ )
{
if( Row > Column )
break;
if( Column > (Result.GetIndex() + Row) )
continue;
// Split the ulongs into right and left sides
// so that they don't overflow.
TotalRight += M[Column, Row] & 0xFFFFFFFF;
TotalLeft += M[Column, Row] >> 32;
}
TotalRight += Carry;
Result.SetD( Column, TotalRight & 0xFFFFFFFF );
Carry = TotalRight >> 32;
Carry += TotalLeft;
}
Result.SetIndex( TotalIndex );
if( Carry != 0 )
{
Result.IncrementIndex(); // This can throw an exception if it overflowed the index.
Result.SetD( Result.GetIndex(), Carry );
}
SetMultiplySign( Result, ToMul );
}
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 );
}
internal void ModularPower( Integer Result, Integer Exponent, Integer GeneralBase )
{
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
// x^n = (x^2)^((n - 1)/2) if n is odd.
// x^n = (x^2)^(n/2) if n is even.
if( Result.IsZero())
return; // With Result still zero.
if( Result.IsEqual( GeneralBase ))
{
// It is congruent to zero % ModN.
Result.SetToZero();
return;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
{
Result.SetFromULong( 1 );
return;
}
if( GeneralBase.ParamIsGreater( Result ))
{
// throw( new Exception( "This is not supposed to be input for RSA plain text." ));
IntMath.Divide( Result, GeneralBase, Quotient, Remainder );
Result.Copy( Remainder );
}
if( Exponent.IsEqualToULong( 1 ))
{
// Result stays the same.
return;
}
// This could also be called ahead of time if the base (the modulus)
// doesn't change. Like when your public key doesn't change.
SetupGeneralBaseArray( GeneralBase );
XForModPower.Copy( Result );
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
Result.SetFromULong( 1 );
while( true )
{
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
IntMath.Multiply( Result, XForModPower );
// Modular Reduction:
AddByGeneralBaseArrays( TempForModPower, Result );
Result.Copy( TempForModPower );
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
IntMath.Multiply( XForModPower, XForModPower );
// Modular Reduction:
AddByGeneralBaseArrays( TempForModPower, XForModPower );
XForModPower.Copy( TempForModPower );
}
// When AddByGeneralBaseArrays() gets called it multiplies a number
// by a uint sized digit. So that can make the result one digit bigger
// than GeneralBase. Then when they are added up you can get carry
// bits that can make it a little bigger.
// If by chance you got a carry bit on _every_ addition that was done
// in AddByGeneralBaseArrays() then this number could increase in size
// by 1 bit for each addition that was done. It would take 32 bits of
// carrying for HowBig to increase by 1.
// See HowManyToAdd in AddByGeneralBaseArrays() for why this check is done.
int HowBig = Result.GetIndex() - GeneralBase.GetIndex();
if( HowBig > 2 ) // I have not seen this happen yet.
throw( new Exception( "The difference in index size was more than 2. Diff: " + HowBig.ToString() ));
// So this Quotient has only one or two 32-bit digits in it.
// And this Divide() is only called once at the end. Not in the loop.
IntMath.Divide( Result, GeneralBase, Quotient, Remainder );
Result.Copy( Remainder );
}
// Product is along the right side diagonal.
internal void SetProduct( Integer UseBigIntToSet )
{
Integer BigIntToSet = new Integer();
BigIntToSet.Copy( UseBigIntToSet );
// Primes: 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
// 71, 73, 79, 83, 89, 97, 101, 103, 107
if( (BigIntToSet.GetD( 0 ) & 1 ) != 1 )
throw( new Exception( "Product can't be even." ));
int Where = 0;
uint ToSet = 0;
for( int Row = 0; Row < MultArraySize; Row++ )
{
ToSet = MultArray[Row].OneLine[0];
if( (BigIntToSet.GetD( 0 ) & 1 ) == 1 )
ToSet = SetAccumOut( ToSet );
else
ToSet = ClearAccumOut( ToSet );
MultArray[Row].OneLine[0] = ToSet;
Where = Row;
BigIntToSet.ShiftRight( 1 );
if( BigIntToSet.IsZero())
break;
}
ProductBitIndex = Where;
int HowMany = ProductBitIndex + 1;
MForm.ShowStatus( "There were " + HowMany.ToString() + " bits in the product." );
// At the last 1 bit.
ToSet = MultArray[Where].OneLine[0];
ToSet = ClearCarryOut( ToSet );
MultArray[Where].OneLine[0] = ToSet;
// The ProductBits can be:
// Factor1Bits + Factor2Bits
// or it can be:
// Factor1Bits + Factor2Bits + 1
// ProductBits - Factor1Bits = Factor2Bits ( + 1 or not)
int Factor1Bits = GetHighestMult1BitIndex() + 1;
int ProductBits = (Where + 1);
// Factor2Bits might be this or it might be one
// less than this.
int MaximumFactor2Bits = ProductBits - Factor1Bits;
// Factor2BitIndex = Factor2Bits - 1;
// Test if the top bit of Factor2 is in the right place.
// ToSet = MultArray[Factor2BitIndex].OneLine[0];
// ToSet = SetMult( ToSet );
// MultArray[Factor2BitIndex].OneLine[0] = ToSet;
for( int Row = MaximumFactor2Bits + 1; Row < MultArraySize; Row++ )
{
ToSet = MultArray[Row].OneLine[0];
ToSet = ClearMult2( ToSet );
MultArray[Row].OneLine[0] = ToSet;
}
for( int Row = Where + 1; Row < MultArraySize; Row++ )
{
ToSet = MultArray[Row].OneLine[0];
ToSet = ClearMult2( ToSet );
ToSet = ClearMult( ToSet );
ToSet = ClearAccumOut( ToSet );
ToSet = ClearCarryOut( ToSet );
MultArray[Row].OneLine[0] = ToSet;
}
}
// Factor 2 is along the right side diagonal.
internal void SetFactor2( Integer UseBigIntToSet )
{
Integer BigIntToSet = new Integer();
BigIntToSet.Copy( UseBigIntToSet );
if( (BigIntToSet.GetD( 0 ) & 1 ) != 1 )
throw( new Exception( "Factor2 can't be even." ));
uint ToSet = MultArray[0].OneLine[0];
ToSet = SetMult1( ToSet );
ToSet = SetMult2( ToSet );
ToSet = SetMult( ToSet );
ToSet = SetAccumOut( ToSet );
ToSet = ClearCarryOut( ToSet );
MultArray[0].OneLine[0] = ToSet;
// Factor2 has to be odd so Mult2 is set to
// 1 all the way across the top.
SetMult2AtRow( 0 );
BigIntToSet.ShiftRight( 1 );
if( BigIntToSet.IsZero())
throw( new Exception( "Factor2 can't be 1." ));
// 107 = 64 + 32 + 8 + 2 + 1
int Where = 1;
for( int Row = 1; Row < MultArraySize; Row++ )
{
ToSet = MultArray[Row].OneLine[0];
if( (BigIntToSet.GetD( 0 ) & 1 ) == 1 )
ToSet = SetMult2( ToSet );
else
ToSet = ClearMult2( ToSet );
MultArray[Row].OneLine[0] = ToSet;
Where = Row;
BigIntToSet.ShiftRight( 1 );
if( BigIntToSet.IsZero())
break;
}
// At the last 1 bit.
// ToSet = MultArray[Where].OneLine[0];
for( int Row = Where + 1; Row < MultArraySize; Row++ )
{
ToSet = MultArray[Row].OneLine[0];
ToSet = ClearMult2( ToSet );
MultArray[Row].OneLine[0] = ToSet;
}
}
// Factor1 is along the top.
internal void SetFactor1( Integer UseBigIntToSet )
{
Integer BigIntToSet = new Integer();
BigIntToSet.Copy( UseBigIntToSet );
if( (BigIntToSet.GetD( 0 ) & 1 ) != 1 )
throw( new Exception( "Factor1 can't be even." ));
uint ToSet = MultArray[0].OneLine[0];
ToSet = SetMult1( ToSet );
ToSet = SetMult2( ToSet );
ToSet = SetMult( ToSet );
ToSet = SetAccumOut( ToSet );
ToSet = ClearCarryOut( ToSet );
MultArray[0].OneLine[0] = ToSet;
// Factor1 has to be odd so Mult1 is set to
// 1 all the way down the side.
SetMult1AtColumn( 0 );
BigIntToSet.ShiftRight( 1 );
if( BigIntToSet.IsZero())
throw( new Exception( "Factor1 can't be 1." ));
// 107 = 64 + 32 + 8 + 2 + 1
int Where = 1;
for( int Column = 1; Column < MultArraySize; Column++ )
{
ToSet = MultArray[0].OneLine[Column];
if( (BigIntToSet.GetD( 0 ) & 1 ) == 1 )
ToSet = SetMult1( ToSet );
else
ToSet = ClearMult1( ToSet );
MultArray[0].OneLine[Column] = ToSet;
Where = Column;
BigIntToSet.ShiftRight( 1 );
if( BigIntToSet.IsZero())
break;
}
// At the last 1 bit.
// ToSet = MultArray[0].OneLine[Where];
for( int Column = Where + 1; Column < MultArraySize; Column++ )
{
ToSet = MultArray[0].OneLine[Column];
ToSet = ClearMult1( ToSet );
ToSet = ClearMult( ToSet );
ToSet = ClearAccumOut( ToSet );
ToSet = ClearCarryOut( ToSet );
MultArray[0].OneLine[Column] = ToSet;
}
}