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)
{
IntMath.Divider.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 Subtract(Integer Result, Integer ToSub)
{
// This checks that the sign is equal too.
if (Result.IsEqual(ToSub))
{
Result.SetToZero();
return;
}
// ParamIsGreater() handles positive and negative values, so if the
// parameter is more toward the positive side then it's true. It's greater.
// The most common form. They are both positive.
if (!Result.IsNegative && !ToSub.IsNegative)
{
if (ToSub.ParamIsGreater(Result))
{
SubtractPositive(Result, ToSub);
return;
}
// ToSub is bigger.
TempSub1.Copy(Result);
TempSub2.Copy(ToSub);
SubtractPositive(TempSub2, TempSub1);
Result.Copy(TempSub2);
Result.IsNegative = true;
return;
}
if (Result.IsNegative && !ToSub.IsNegative)
{
TempSub1.Copy(Result);
TempSub1.IsNegative = false;
TempSub1.Add(ToSub);
Result.Copy(TempSub1);
Result.IsNegative = true;
return;
}
if (!Result.IsNegative && ToSub.IsNegative)
{
TempSub1.Copy(ToSub);
TempSub1.IsNegative = false;
Result.Add(TempSub1);
return;
}
if (Result.IsNegative && ToSub.IsNegative)
{
TempSub1.Copy(Result);
TempSub1.IsNegative = false;
TempSub2.Copy(ToSub);
TempSub2.IsNegative = false;
// -12 - -7 = -12 + 7 = -5
// Comparing the positive numbers here.
if (TempSub2.ParamIsGreater(TempSub1))
{
SubtractPositive(TempSub1, TempSub2);
Result.Copy(TempSub1);
Result.IsNegative = true;
return;
}
// -7 - -12 = -7 + 12 = 5
SubtractPositive(TempSub2, TempSub1);
Result.Copy(TempSub2);
Result.IsNegative = false;
return;
}
}
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 void MakeRSAKeys()
{
int ShowBits = (PrimeIndex + 1) * 32;
// int TestLoops = 0;
Worker.ReportProgress(0, "Making RSA keys.");
Worker.ReportProgress(0, "Bits size is: " + ShowBits.ToString());
// ulong Loops = 0;
while (true)
{
if (Worker.CancellationPending)
{
return;
}
Thread.Sleep(1); // Let other things run.
// Make two prime factors.
// Normally you'd only make new primes when you pay the Certificate
// Authority for a new certificate.
if (!MakeAPrime(PrimeP, PrimeIndex, 20))
{
return;
}
if (Worker.CancellationPending)
{
return;
}
if (!MakeAPrime(PrimeQ, PrimeIndex, 20))
{
return;
}
if (Worker.CancellationPending)
{
return;
}
// This is extremely unlikely.
Integer Gcd = new Integer();
IntMath.GreatestCommonDivisor(PrimeP, PrimeQ, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "They had a GCD: " + IntMath.ToString10(Gcd));
continue;
}
if (Worker.CancellationPending)
{
return;
}
IntMath.GreatestCommonDivisor(PrimeP, PubKeyExponent, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "They had a GCD with PubKeyExponent: " + IntMath.ToString10(Gcd));
continue;
}
if (Worker.CancellationPending)
{
return;
}
IntMath.GreatestCommonDivisor(PrimeQ, PubKeyExponent, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "2) They had a GCD with PubKeyExponent: " + IntMath.ToString10(Gcd));
continue;
}
// For Modular Reduction. This only has to be done
// once, when P and Q are made.
IntMathForP.ModReduction.SetupGeneralBaseArray(PrimeP);
IntMathForQ.ModReduction.SetupGeneralBaseArray(PrimeQ);
PrimePMinus1.Copy(PrimeP);
IntMath.SubtractULong(PrimePMinus1, 1);
PrimeQMinus1.Copy(PrimeQ);
IntMath.SubtractULong(PrimeQMinus1, 1);
if (Worker.CancellationPending)
{
return;
}
// These checks should be more thorough to
// make sure the primes P and Q are numbers
// that can be used in a secure way.
Worker.ReportProgress(0, "The Index of Prime P is: " + PrimeP.GetIndex().ToString());
Worker.ReportProgress(0, "Prime P:");
Worker.ReportProgress(0, IntMath.ToString10(PrimeP));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Prime Q:");
Worker.ReportProgress(0, IntMath.ToString10(PrimeQ));
Worker.ReportProgress(0, " ");
PubKeyN.Copy(PrimeP);
IntMath.Multiply(PubKeyN, PrimeQ);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PubKeyN:");
Worker.ReportProgress(0, IntMath.ToString10(PubKeyN));
Worker.ReportProgress(0, " ");
// Test Division:
Integer QuotientTest = new Integer();
Integer RemainderTest = new Integer();
IntMath.Divider.Divide(PubKeyN, PrimeP, QuotientTest, RemainderTest);
if (!RemainderTest.IsZero())
{
throw(new Exception("RemainderTest should be zero after divide by PrimeP."));
}
IntMath.Multiply(QuotientTest, PrimeP);
if (!QuotientTest.IsEqual(PubKeyN))
{
throw(new Exception("QuotientTest didn't come out right."));
}
// Euler's Theorem:
// https://en.wikipedia.org/wiki/Euler's_theorem
// ==========
// Work on the Least Common Multiple thing for
// P - 1 and Q - 1.
// =====
IntMath.GreatestCommonDivisor(PrimePMinus1, PrimeQMinus1, Gcd);
Worker.ReportProgress(0, "GCD of PrimePMinus1, PrimeQMinus1 is: " + IntMath.ToString10(Gcd));
if (!Gcd.IsULong())
{
Worker.ReportProgress(0, "This GCD number is too big: " + IntMath.ToString10(Gcd));
continue;
}
else
{
ulong TooBig = Gcd.GetAsULong();
// How big of a GCD is too big?
// ==============
if (TooBig > 1234567)
{
// (P - 1)(Q - 1) + (P - 1) + (Q - 1) = PQ - 1
Worker.ReportProgress(0, "This GCD number is bigger than 1234567: " + IntMath.ToString10(Gcd));
continue;
}
}
Integer Temp1 = new Integer();
PhiN.Copy(PrimePMinus1);
Temp1.Copy(PrimeQMinus1);
IntMath.Multiply(PhiN, Temp1);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PhiN:");
Worker.ReportProgress(0, IntMath.ToString10(PhiN));
Worker.ReportProgress(0, " ");
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 there are commonly used letters/symbols to represent
// the numbers used. So the number e is the public exponent.
// The number e that is used here is called PubKeyExponentUint = 65537.
// In the RFC the private key d is the multiplicative inverse of
// e mod PhiN. Which is mod (P - 1)(Q - 1). It's called
// PrivKInverseExponent here.
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponent, PubKeyExponent, PhiN, Worker))
{
return;
}
if (PrivKInverseExponent.IsZero())
{
continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponent: " + IntMath.ToString10(PrivKInverseExponent));
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 it defines a number dP which is the multiplicative
// inverse, mod (P - 1) of e. That dP is named PrivKInverseExponentDP here.
Worker.ReportProgress(0, " ");
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponentDP, PubKeyExponent, PrimePMinus1, Worker))
{
return;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponentDP: " + IntMath.ToString10(PrivKInverseExponentDP));
if (PrivKInverseExponentDP.IsZero())
{
continue;
}
// PrivKInverseExponentDP is PrivKInverseExponent mod PrimePMinus1.
Integer Test1 = new Integer();
Test1.Copy(PrivKInverseExponent);
IntMath.Divider.Divide(Test1, PrimePMinus1, Quotient, Remainder);
Test1.Copy(Remainder);
if (!Test1.IsEqual(PrivKInverseExponentDP))
{
throw(new Exception("This does not match the definition of PrivKInverseExponentDP."));
}
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 it defines a number dQ which is the multiplicative
// inverse, mod (Q - 1) of e. That dQ is named PrivKInverseExponentDQ here.
Worker.ReportProgress(0, " ");
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponentDQ, PubKeyExponent, PrimeQMinus1, Worker))
{
return;
}
if (PrivKInverseExponentDQ.IsZero())
{
continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponentDQ: " + IntMath.ToString10(PrivKInverseExponentDQ));
if (Worker.CancellationPending)
{
return;
}
Test1.Copy(PrivKInverseExponent);
IntMath.Divider.Divide(Test1, PrimeQMinus1, Quotient, Remainder);
Test1.Copy(Remainder);
if (!Test1.IsEqual(PrivKInverseExponentDQ))
{
throw(new Exception("This does not match the definition of PrivKInverseExponentDQ."));
}
// Make a random number to test encryption/decryption.
Integer ToEncrypt = new Integer();
int HowManyBytes = PrimeIndex * 4;
byte[] RandBytes = MakeRandomBytes(HowManyBytes);
if (RandBytes == null)
{
Worker.ReportProgress(0, "Error making random bytes in MakeRSAKeys().");
return;
}
if (!ToEncrypt.MakeRandomOdd(PrimeIndex - 1, RandBytes))
{
Worker.ReportProgress(0, "Error making random number ToEncrypt.");
return;
}
Integer PlainTextNumber = new Integer();
PlainTextNumber.Copy(ToEncrypt);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Before encrypting number: " + IntMath.ToString10(ToEncrypt));
Worker.ReportProgress(0, " ");
IntMath.ModReduction.ModularPower(ToEncrypt, PubKeyExponent, PubKeyN, false);
if (Worker.CancellationPending)
{
return;
}
// Worker.ReportProgress( 0, IntMath.GetStatusString() );
Integer CipherTextNumber = new Integer();
CipherTextNumber.Copy(ToEncrypt);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Encrypted number: " + IntMath.ToString10(CipherTextNumber));
Worker.ReportProgress(0, " ");
ECTime DecryptTime = new ECTime();
DecryptTime.SetToNow();
IntMath.ModReduction.ModularPower(ToEncrypt, PrivKInverseExponent, PubKeyN, false);
Worker.ReportProgress(0, "Decrypted number: " + IntMath.ToString10(ToEncrypt));
if (!PlainTextNumber.IsEqual(ToEncrypt))
{
throw(new Exception("PlainTextNumber not equal to unencrypted value."));
// Because P or Q wasn't really a prime?
// Worker.ReportProgress( 0, "PlainTextNumber not equal to unencrypted value." );
// continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Decrypt time seconds: " + DecryptTime.GetSecondsToNow().ToString("N2"));
Worker.ReportProgress(0, " ");
if (Worker.CancellationPending)
{
return;
}
// Test the standard optimized way of decrypting:
if (!ToEncrypt.MakeRandomOdd(PrimeIndex - 1, RandBytes))
{
Worker.ReportProgress(0, "Error making random number in MakeRSAKeys().");
return;
}
PlainTextNumber.Copy(ToEncrypt);
IntMath.ModReduction.ModularPower(ToEncrypt, PubKeyExponent, PubKeyN, false);
if (Worker.CancellationPending)
{
return;
}
CipherTextNumber.Copy(ToEncrypt);
// QInv is the multiplicative inverse of PrimeQ mod PrimeP.
if (!IntMath.MultiplicativeInverse(PrimeQ, PrimeP, QInv, Worker))
{
throw(new Exception("MultiplicativeInverse() returned false."));
}
if (QInv.IsNegative)
{
throw(new Exception("QInv is negative."));
}
Worker.ReportProgress(0, "QInv is: " + IntMath.ToString10(QInv));
DecryptWithQInverse(CipherTextNumber,
ToEncrypt, // Decrypt it to this.
PlainTextNumber, // Test it against this.
PubKeyN,
PrivKInverseExponentDP,
PrivKInverseExponentDQ,
PrimeP,
PrimeQ,
Worker);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Found the values:");
Worker.ReportProgress(0, "Seconds: " + StartTime.GetSecondsToNow().ToString("N0"));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "Prime1: " + IntMath.ToString10(PrimeP));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "Prime2: " + IntMath.ToString10(PrimeQ));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "PubKeyN: " + IntMath.ToString10(PubKeyN));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "PrivKInverseExponent: " + IntMath.ToString10(PrivKInverseExponent));
// return; // Comment this out to just leave it while( true ) for testing.
}
}
private void LongDivide3(Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder)
{
//////////////////
Integer Test2 = new Integer();
/////////////////
int TestIndex = ToDivide.GetIndex() - DivideBy.GetIndex();
if (TestIndex < 0)
{
throw(new Exception("TestIndex < 0 in Divide3."));
}
if (TestIndex != 0)
{
// Is 1 too high?
TestForDivide1.SetDigitAndClear(TestIndex, 1);
IntMath.MultiplyTopOne(TestForDivide1, DivideBy);
if (ToDivide.ParamIsGreater(TestForDivide1))
{
TestIndex--;
}
}
// Keep a copy of the originals.
ToDivideKeep.Copy(ToDivide);
DivideByKeep.Copy(DivideBy);
ulong TestBits = DivideBy.GetD(DivideBy.GetIndex());
int ShiftBy = FindShiftBy(TestBits);
ToDivide.ShiftLeft(ShiftBy); // Multiply the numerator and the denominator
DivideBy.ShiftLeft(ShiftBy); // by the same amount.
ulong MaxValue;
if ((ToDivide.GetIndex() - 1) > (DivideBy.GetIndex() + TestIndex))
{
MaxValue = ToDivide.GetD(ToDivide.GetIndex());
}
else
{
MaxValue = ToDivide.GetD(ToDivide.GetIndex()) << 32;
MaxValue |= ToDivide.GetD(ToDivide.GetIndex() - 1);
}
ulong Denom = DivideBy.GetD(DivideBy.GetIndex());
if (Denom != 0)
{
MaxValue = MaxValue / Denom;
}
else
{
MaxValue = 0xFFFFFFFF;
}
if (MaxValue > 0xFFFFFFFF)
{
MaxValue = 0xFFFFFFFF;
}
if (MaxValue == 0)
{
throw(new Exception("MaxValue is zero at the top in LongDivide3()."));
}
Quotient.SetDigitAndClear(TestIndex, 1);
Quotient.SetD(TestIndex, 0);
TestForDivide1.Copy(Quotient);
TestForDivide1.SetD(TestIndex, MaxValue);
IntMath.MultiplyTop(TestForDivide1, DivideBy);
/////////////
Test2.Copy(Quotient);
Test2.SetD(TestIndex, MaxValue);
IntMath.Multiply(Test2, DivideBy);
if (!Test2.IsEqual(TestForDivide1))
{
throw(new Exception("In Divide3() !IsEqual( Test2, TestForDivide1 )"));
}
///////////
if (TestForDivide1.ParamIsGreaterOrEq(ToDivide))
{
// ToMatchExactCount++;
// Most of the time (roughly 5 out of every 6
// times) this MaxValue estimate is exactly
// right:
Quotient.SetD(TestIndex, MaxValue);
}
else
{
// MaxValue can't be zero here. If it was it
// would already be low enough before it got
// here.
MaxValue--;
if (MaxValue == 0)
{
throw(new Exception("After decrement: MaxValue is zero in LongDivide3()."));
}
TestForDivide1.Copy(Quotient);
TestForDivide1.SetD(TestIndex, MaxValue);
IntMath.MultiplyTop(TestForDivide1, DivideBy);
if (TestForDivide1.ParamIsGreaterOrEq(ToDivide))
{
// ToMatchDecCount++;
Quotient.SetD(TestIndex, MaxValue);
}
else
{
// TestDivideBits is done as a last resort,
// but it's rare. But it does at least limit
// it to a worst case scenario of trying 32
// bits, rather than 4 billion or so
// decrements.
TestDivideBits(MaxValue,
true,
TestIndex,
ToDivide,
DivideBy,
Quotient,
Remainder);
}
// TestGap = MaxValue - LgQuotient.D[TestIndex];
// if( TestGap > HighestToMatchGap )
// HighestToMatchGap = TestGap;
// HighestToMatchGap: 4,294,967,293
// uint size: 4,294,967,295 uint
}
// If it's done.
if (TestIndex == 0)
{
TestForDivide1.Copy(Quotient);
IntMath.Multiply(TestForDivide1, DivideByKeep);
Remainder.Copy(ToDivideKeep);
IntMath.Subtract(Remainder, TestForDivide1);
if (DivideByKeep.ParamIsGreater(Remainder))
{
throw(new Exception("Remainder > DivideBy in LongDivide3()."));
}
return;
}
// Now do the rest of the digits.
TestIndex--;
while (true)
{
TestForDivide1.Copy(Quotient);
// First Multiply() for each digit.
IntMath.Multiply(TestForDivide1, DivideBy);
if (ToDivide.ParamIsGreater(TestForDivide1))
{
throw(new Exception("Problem here in LongDivide3()."));
}
Remainder.Copy(ToDivide);
IntMath.Subtract(Remainder, TestForDivide1);
MaxValue = Remainder.GetD(Remainder.GetIndex()) << 32;
int CheckIndex = Remainder.GetIndex() - 1;
if (CheckIndex > 0)
{
MaxValue |= Remainder.GetD(CheckIndex);
}
Denom = DivideBy.GetD(DivideBy.GetIndex());
if (Denom != 0)
{
MaxValue = MaxValue / Denom;
}
else
{
MaxValue = 0xFFFFFFFF;
}
if (MaxValue > 0xFFFFFFFF)
{
MaxValue = 0xFFFFFFFF;
}
TestForDivide1.Copy(Quotient);
TestForDivide1.SetD(TestIndex, MaxValue);
// There's a minimum of two full Multiply() operations per digit.
IntMath.Multiply(TestForDivide1, DivideBy);
if (TestForDivide1.ParamIsGreaterOrEq(ToDivide))
{
// Most of the time this MaxValue estimate is exactly right:
// ToMatchExactCount++;
Quotient.SetD(TestIndex, MaxValue);
}
else
{
MaxValue--;
TestForDivide1.Copy(Quotient);
TestForDivide1.SetD(TestIndex, MaxValue);
IntMath.Multiply(TestForDivide1, DivideBy);
if (TestForDivide1.ParamIsGreaterOrEq(ToDivide))
{
// ToMatchDecCount++;
Quotient.SetD(TestIndex, MaxValue);
}
else
{
TestDivideBits(MaxValue,
false,
TestIndex,
ToDivide,
DivideBy,
Quotient,
Remainder);
// TestGap = MaxValue - LgQuotient.D[TestIndex];
// if( TestGap > HighestToMatchGap )
// HighestToMatchGap = TestGap;
}
}
if (TestIndex == 0)
{
break;
}
TestIndex--;
}
TestForDivide1.Copy(Quotient);
IntMath.Multiply(TestForDivide1, DivideByKeep);
Remainder.Copy(ToDivideKeep);
IntMath.Subtract(Remainder, TestForDivide1);
if (DivideByKeep.ParamIsGreater(Remainder))
{
throw(new Exception("Remainder > DivideBy in LongDivide3()."));
}
}
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 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."));
}
}