internal RSACryptoSystem(BackgroundWorker UseWorker, RSACryptoWorkerInfo UseWInfo)
{
Worker = UseWorker;
WorkerInfo = UseWInfo;
StartTime = new ECTime();
StartTime.SetToNow();
RngCsp = new RNGCryptoServiceProvider();
IntMath = new IntegerMath(null);
IntMathForP = new IntegerMath(null);
IntMathForQ = new IntegerMath(null);
// Worker.ReportProgress( 0, IntMath.GetStatusString() );
Quotient = new Integer();
Remainder = new Integer();
PrimeP = new Integer();
PrimeQ = new Integer();
PrimePMinus1 = new Integer();
PrimeQMinus1 = new Integer();
PubKeyN = new Integer();
PubKeyExponent = new Integer();
PrivKInverseExponent = new Integer();
PrivKInverseExponentDP = new Integer();
PrivKInverseExponentDQ = new Integer();
QInv = new Integer();
PhiN = new Integer();
TestForDecrypt = new Integer();
M1ForInverse = new Integer();
M2ForInverse = new Integer();
HForQInv = new Integer();
M1MinusM2 = new Integer();
M1M2SizeDiff = new Integer();
PubKeyExponent.SetFromULong(PubKeyExponentUint);
}
internal void SetFromString(Integer Result, string InString)
{
if (InString == null)
{
throw(new Exception("InString was null in SetFromString()."));
}
if (InString.Length < 1)
{
Result.SetToZero();
return;
}
Base10Number Base10N = new Base10Number();
Integer Tens = new Integer();
Integer OnePart = new Integer();
// This might throw an exception if the string is bad.
Base10N.SetFromString(InString);
Result.SetFromULong(Base10N.GetD(0));
Tens.SetFromULong(10);
for (int Count = 1; Count <= Base10N.GetIndex(); Count++)
{
OnePart.SetFromULong(Base10N.GetD(Count));
Multiplier.Multiply(OnePart, Tens);
Result.Add(OnePart);
Multiplier.MultiplyULong(Tens, 10);
}
}
internal bool IsFermatPrimeForOneValue(Integer ToTest, ulong Base)
{
// Assume ToTest is not a small number. (Not the size of a small prime.)
// Normally it would be something like a 1024 bit number or bigger,
// but I assume it's at least bigger than a 32 bit number.
// Assume this has already been checked to see if it's divisible
// by a small prime.
// A has to be coprime to P and it is here because ToTest is not
// divisible by a small prime.
// Fermat's little theorem:
// A ^ (P - 1) is congruent to 1 mod P if P is a prime.
// Or: A^P - A is congrunt to A mod P.
// If you multiply A by itself P times then divide it by P,
// the remainder is A. (A^P / P)
// 5^3 = 125. 125 - 5 = 120. A multiple of 5.
// 2^7 = 128. 128 - 2 = 7 * 18 (a multiple of 7.)
Fermat1.Copy(ToTest);
IntMath.SubtractULong(Fermat1, 1);
TestFermat.SetFromULong(Base);
// ModularPower( Result, Exponent, Modulus, UsePresetBaseArray )
ModularPower(TestFermat, Fermat1, ToTest, false);
// if( !TestFermat.IsEqual( Fermat2 ))
// throw( new Exception( "!TestFermat.IsEqual( Fermat2 )." ));
if (TestFermat.IsOne())
{
return(true); // It passed the test. It _might_ be a prime.
}
else
{
return(false); // It is _definitely_ a composite number.
}
}
internal void SetupGeneralBaseArray(Integer GeneralBase)
{
// The word 'Base' comes from the base of a number
// system. Like normal decimal numbers have base
// 10, binary numbers have base 2, etc.
CurrentModReductionBase.Copy(GeneralBase);
// The input to the accumulator can be twice the
// bit length of GeneralBase.
int HowManyDigits = ((GeneralBase.GetIndex() + 1) * 2) + 10; // Plus some extra for carries...
GeneralBaseArray = new Integer[HowManyDigits];
// int HowManyPrimes = 100;
// Row, Column
// SmallBasesArray = new uint[HowManyDigits, HowManyPrimes];
Integer Base = new Integer();
Base.SetFromULong(256); // 0x100
IntMath.MultiplyUInt(Base, 256); // 0x10000
IntMath.MultiplyUInt(Base, 256); // 0x1000000
IntMath.MultiplyUInt(Base, 256); // 0x100000000 is the base of this number system.
// 0x1 0000 0000
Integer BaseValue = new Integer();
BaseValue.SetFromULong(1);
for (int Column = 0; Column < HowManyDigits; Column++)
{
if (GeneralBaseArray[Column] == null)
{
GeneralBaseArray[Column] = new Integer();
}
IntMath.Divider.Divide(BaseValue, GeneralBase, Quotient, Remainder);
GeneralBaseArray[Column].Copy(Remainder);
/*
* for( int Row = 0; Row < HowManyPrimes; Row++ )
* {
* This base value mod this prime?
*
* SmallBasesArray[Row, Column] = what?
* }
*/
// Done at the bottom for the next round of the
// loop.
BaseValue.Copy(Remainder);
IntMath.Multiply(BaseValue, Base);
}
}
// This is a variation on ShortDivide that returns
// the remainder.
// Also, DivideBy is a ulong.
internal ulong ShortDivideRem(Integer ToDivideOriginal,
ulong DivideByU,
Integer Quotient)
{
if (ToDivideOriginal.IsULong())
{
ulong ToDiv = ToDivideOriginal.GetAsULong();
ulong Q = ToDiv / DivideByU;
Quotient.SetFromULong(Q);
return(ToDiv % DivideByU);
}
ToDivide.Copy(ToDivideOriginal);
Quotient.Copy(ToDivide);
ulong RemainderU = 0;
if (DivideByU > Quotient.GetD(Quotient.GetIndex()))
{
Quotient.SetD(Quotient.GetIndex(), 0);
}
else
{
ulong OneDigit = Quotient.GetD(Quotient.GetIndex());
Quotient.SetD(Quotient.GetIndex(), OneDigit / DivideByU);
RemainderU = OneDigit % DivideByU;
ToDivide.SetD(ToDivide.GetIndex(), RemainderU);
}
for (int Count = Quotient.GetIndex(); Count >= 1; Count--)
{
ulong TwoDigits = ToDivide.GetD(Count);
TwoDigits <<= 32;
TwoDigits |= ToDivide.GetD(Count - 1);
Quotient.SetD(Count - 1, TwoDigits / DivideByU);
RemainderU = TwoDigits % DivideByU;
ToDivide.SetD(Count, 0);
ToDivide.SetD(Count - 1, RemainderU);
}
for (int Count = Quotient.GetIndex(); Count >= 0; Count--)
{
if (Quotient.GetD(Count) != 0)
{
Quotient.SetIndex(Count);
break;
}
}
return(RemainderU);
}
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;
}
Integer ToDivideTest2 = new Integer();
Integer DivideByTest2 = new Integer();
Integer QuotientTest2 = new Integer();
Integer RemainderTest2 = new Integer();
Integer ToDivideTest3 = new Integer();
Integer DivideByTest3 = new Integer();
Integer QuotientTest3 = new Integer();
Integer RemainderTest3 = new Integer();
ToDivideTest2.Copy(ToDivide);
ToDivideTest3.Copy(ToDivide);
DivideByTest2.Copy(DivideBy);
DivideByTest3.Copy(DivideBy);
LongDivide1(ToDivideTest2, DivideByTest2, QuotientTest2, RemainderTest2);
LongDivide2(ToDivideTest3, DivideByTest3, QuotientTest3, RemainderTest3);
LongDivide3(ToDivide, DivideBy, Quotient, Remainder);
if (!Quotient.IsEqual(QuotientTest2))
{
throw(new Exception("!Quotient.IsEqual( QuotientTest2 )"));
}
if (!Quotient.IsEqual(QuotientTest3))
{
throw(new Exception("!Quotient.IsEqual( QuotientTest3 )"));
}
if (!Remainder.IsEqual(RemainderTest2))
{
throw(new Exception("!Remainder.IsEqual( RemainderTest2 )"));
}
if (!Remainder.IsEqual(RemainderTest3))
{
throw(new Exception("!Remainder.IsEqual( RemainderTest3 )"));
}
}
// This is the standard modular power algorithm that
// you could find in any reference, but its use of
// my modular reduction algorithm in it is new (in 2015).
// (I mean as opposed to using some other modular reduction
// algorithm.)
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
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.Divider.Divide(Result, Modulus, Quotient, Remainder);
Result.Copy(Remainder);
}
if (Exponent.IsOne())
{
// Result stays the same.
return;
}
if (!UsePresetBaseArray)
{
IntMath.ModReduction.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.Multiplier.Multiply(Result, XForModPower);
// if( Result.ParamIsGreater( CurrentModReductionBase ))
// TestForModReduction2.Copy( Result );
IntMath.ModReduction.Reduce(TempForModPower, Result);
// ModularReduction2( TestForModReduction2ForModPower, TestForModReduction2 );
// if( !TestForModReduction2ForModPower.IsEqual( TempForModPower ))
// {
// throw( new Exception( "Mod Reduction 2 is not right." ));
// }
Result.Copy(TempForModPower);
}
ExponentCopy.ShiftRight(1); // Divide by 2.
if (ExponentCopy.IsZero())
{
break;
}
// Square it.
IntMath.Multiplier.Multiply(XForModPower, XForModPower);
// if( XForModPower.ParamIsGreater( CurrentModReductionBase ))
IntMath.ModReduction.Reduce(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() ));
// Do a proof for how big this can be.
if (HowBig > 2)
{
throw(new Exception("This never happens. Diff: " + HowBig.ToString()));
}
IntMath.ModReduction.Reduce(TempForModPower, Result);
Result.Copy(TempForModPower);
// Notice that this Divide() is done once. Not
// a thousand or two thousand times.
/*
* Integer ResultTest = new Integer();
* Integer ModulusTest = new Integer();
* Integer QuotientTest = new Integer();
* Integer RemainderTest = new Integer();
*
* ResultTest.Copy( Result );
* ModulusTest.Copy( Modulus );
* IntMath.Divider.DivideForSmallQuotient( ResultTest,
* ModulusTest,
* QuotientTest,
* RemainderTest );
*
*/
IntMath.Divider.Divide(Result, Modulus, Quotient, Remainder);
// if( !RemainderTest.IsEqual( Remainder ))
// throw( new Exception( "DivideForSmallQuotient() !RemainderTest.IsEqual( Remainder )." ));
// if( !QuotientTest.IsEqual( Quotient ))
// throw( new Exception( "DivideForSmallQuotient() !QuotientTest.IsEqual( Quotient )." ));
Result.Copy(Remainder);
if (Quotient.GetIndex() > 1)
{
throw(new Exception("This never happens. The quotient index is never more than 1."));
}
}