private bool LongDivide1(Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder)
{
uint Digit = 0;
Integer Test1 = new Integer();
int TestIndex = ToDivide.GetIndex() - DivideBy.GetIndex();
if (TestIndex != 0)
{
// Is 1 too high?
Test1.SetDigitAndClear(TestIndex, 1);
IntMath.MultiplyTopOne(Test1, DivideBy);
if (ToDivide.ParamIsGreater(Test1))
{
TestIndex--;
}
}
Quotient.SetDigitAndClear(TestIndex, 1);
Quotient.SetD(TestIndex, 0);
uint BitTest = 0x80000000;
while (true)
{
// For-loop to test each bit:
for (int BitCount = 31; BitCount >= 0; BitCount--)
{
Test1.Copy(Quotient);
Digit = (uint)Test1.GetD(TestIndex) | BitTest;
Test1.SetD(TestIndex, Digit);
IntMath.Multiply(Test1, DivideBy);
if (Test1.ParamIsGreaterOrEq(ToDivide))
{
Digit = (uint)Quotient.GetD(TestIndex) | BitTest;
// I want to keep this bit because it
// passed the test.
Quotient.SetD(TestIndex, Digit);
}
BitTest >>= 1;
}
if (TestIndex == 0)
{
break;
}
TestIndex--;
BitTest = 0x80000000;
}
Test1.Copy(Quotient);
IntMath.Multiply(Test1, DivideBy);
if (Test1.IsEqual(ToDivide))
{
Remainder.SetToZero();
return(true); // Divides exactly.
}
Remainder.Copy(ToDivide);
IntMath.Subtract(Remainder, Test1);
// Does not divide it exactly.
return(false);
}
internal bool DecryptWithQInverse(Integer EncryptedNumber,
Integer DecryptedNumber,
Integer TestDecryptedNumber,
Integer PubKeyN,
Integer PrivKInverseExponentDP,
Integer PrivKInverseExponentDQ,
Integer PrimeP,
Integer PrimeQ,
BackgroundWorker Worker)
{
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Top of DecryptWithQInverse().");
// QInv and the dP and dQ numbers are normally already set up before
// you start your listening socket.
ECTime DecryptTime = new ECTime();
DecryptTime.SetToNow();
// See section 5.1.2 of RFC 2437 for these steps:
// http://tools.ietf.org/html/rfc2437
// 2.2 Let m_1 = c^dP mod p.
// 2.3 Let m_2 = c^dQ mod q.
// 2.4 Let h = qInv ( m_1 - m_2 ) mod p.
// 2.5 Let m = m_2 + hq.
Worker.ReportProgress(0, "EncryptedNumber: " + IntMath.ToString10(EncryptedNumber));
// 2.2 Let m_1 = c^dP mod p.
TestForDecrypt.Copy(EncryptedNumber);
IntMathForP.ModReduction.ModularPower(TestForDecrypt, PrivKInverseExponentDP, PrimeP, true);
if (Worker.CancellationPending)
{
return(false);
}
M1ForInverse.Copy(TestForDecrypt);
// 2.3 Let m_2 = c^dQ mod q.
TestForDecrypt.Copy(EncryptedNumber);
IntMathForQ.ModReduction.ModularPower(TestForDecrypt, PrivKInverseExponentDQ, PrimeQ, true);
if (Worker.CancellationPending)
{
return(false);
}
M2ForInverse.Copy(TestForDecrypt);
// 2.4 Let h = qInv ( m_1 - m_2 ) mod p.
// How many is optimal to avoid the division?
int HowManyIsOptimal = (PrimeP.GetIndex() * 3);
for (int Count = 0; Count < HowManyIsOptimal; Count++)
{
if (M1ForInverse.ParamIsGreater(M2ForInverse))
{
M1ForInverse.Add(PrimeP);
}
else
{
break;
}
}
if (M1ForInverse.ParamIsGreater(M2ForInverse))
{
M1M2SizeDiff.Copy(M2ForInverse);
IntMath.Subtract(M1M2SizeDiff, M1ForInverse);
// Unfortunately this long Divide() has to be done.
IntMath.Divider.Divide(M1M2SizeDiff, PrimeP, Quotient, Remainder);
Quotient.AddULong(1);
Worker.ReportProgress(0, "The Quotient for M1M2SizeDiff is: " + IntMath.ToString10(Quotient));
IntMath.Multiply(Quotient, PrimeP);
M1ForInverse.Add(Quotient);
}
M1MinusM2.Copy(M1ForInverse);
IntMath.Subtract(M1MinusM2, M2ForInverse);
if (M1MinusM2.IsNegative)
{
throw(new Exception("M1MinusM2.IsNegative is true."));
}
if (QInv.IsNegative)
{
throw(new Exception("QInv.IsNegative is true."));
}
HForQInv.Copy(M1MinusM2);
IntMath.Multiply(HForQInv, QInv);
if (HForQInv.IsNegative)
{
throw(new Exception("HForQInv.IsNegative is true."));
}
if (PrimeP.ParamIsGreater(HForQInv))
{
IntMath.Divider.Divide(HForQInv, PrimeP, Quotient, Remainder);
HForQInv.Copy(Remainder);
}
// 2.5 Let m = m_2 + hq.
DecryptedNumber.Copy(HForQInv);
IntMath.Multiply(DecryptedNumber, PrimeQ);
DecryptedNumber.Add(M2ForInverse);
if (!TestDecryptedNumber.IsEqual(DecryptedNumber))
{
throw(new Exception("!TestDecryptedNumber.IsEqual( DecryptedNumber )."));
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "DecryptedNumber: " + IntMath.ToString10(DecryptedNumber));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "TestDecryptedNumber: " + IntMath.ToString10(TestDecryptedNumber));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Decrypt with QInv time seconds: " + DecryptTime.GetSecondsToNow().ToString("N2"));
Worker.ReportProgress(0, " ");
return(true);
}
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);
}