private bool MakeAPrime( Integer Result, int SetToIndex, int HowMany )
{
try
{
int Attempts = 0;
while( true )
{
Attempts++;
if( Worker.CancellationPending )
return false;
// Don't hog the server's resources too much.
Thread.Sleep( 1 ); // Give up the time slice. Let other things run.
int HowManyBytes = (SetToIndex * 4) + 4;
byte[] RandBytes = MakeRandomBytes( HowManyBytes );
if( RandBytes == null )
{
Worker.ReportProgress( 0, "Error making random bytes in MakeAPrime()." );
return false;
}
if( !Result.MakeRandomOdd( SetToIndex, RandBytes ))
{
Worker.ReportProgress( 0, "Error making random number in MakeAPrime()." );
return false;
}
// Make sure that it's the size I think it is.
if( Result.GetIndex() < SetToIndex )
throw( new Exception( "Bug. The size of the random prime is not right." ));
uint TestPrime = IntMath.IsDivisibleBySmallPrime( Result );
if( 0 != TestPrime)
continue;
if( !IntMath.IsFermatPrime( Result, HowMany ))
{
Worker.ReportProgress( 0, "Did not pass Fermat test." );
continue;
}
// IsFermatPrime() could take a long time.
if( Worker.CancellationPending )
return false;
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, "Found a probable prime." );
Worker.ReportProgress( 0, "Attempts: " + Attempts.ToString() );
Worker.ReportProgress( 0, " " );
return true; // With Result.
}
}
catch( Exception Except )
{
Worker.ReportProgress( 0, "Error in MakeAPrime()" );
Worker.ReportProgress( 0, Except.Message );
return false;
}
}
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 ); // Give up the time slice. Let other things on the server 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;
IntegerBase TestP = new IntegerBase();
IntegerBaseMath IntBaseMath = new IntegerBaseMath( IntMath );
string TestS = IntMath.ToString10( PrimeP );
IntBaseMath.SetFromString( TestP, TestS );
string TestS2 = IntBaseMath.ToString10( TestP );
if( TestS != TestS2 )
throw( new Exception( "TestS != TestS2 for IntegerBase." ));
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;
// This would never happen since the public key exponent used here
// is one of the small primes in the array in IntegerMath that it
// was checked against. But it does show here in the code that
// they have to be co-prime to each other. And in the future it
// might be found that the public key exponent has to be much larger
// than the one used here.
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.
IntMathNewForP.SetupGeneralBaseArray( PrimeP );
IntMathNewForQ.SetupGeneralBaseArray( PrimeQ );
PrimePMinus1.Copy( PrimeP );
IntMath.SubtractULong( PrimePMinus1, 1 );
PrimeQMinus1.Copy( PrimeQ );
IntMath.SubtractULong( PrimeQMinus1, 1 );
// These checks should be more thorough.
if( Worker.CancellationPending )
return;
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, " " );
// Euler's Theorem:
// https://en.wikipedia.org/wiki/Euler's_theorem
// if x ≡ y (mod φ(n)),
// then a^x ≡ a^y (mod n).
// Euler's Phi function (aka Euler's Totient function) is calculated
// next.
// PhiN is made from the two factors: (P - 1)(Q - 1)
// PhiN is: (P - 1)(Q - 1) = PQ - P - Q + 1
// If I add (P - 1) to PhiN I get:
// PQ - P - Q + 1 + (P - 1) = PQ - Q.
// If I add (Q - 1) to that I get:
// PQ - Q + (Q - 1) = PQ - 1.
// (P - 1)(Q - 1) + (P - 1) + (Q - 1) = PQ - 1
// If (P - 1) and (Q - 1) had a larger GCD then PQ - 1 would have
// that same factor too.
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.IntMathNew.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.IntMathNew.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.Divide( Test1, PrimePMinus1, Quotient, Remainder );
Test1.Copy( Remainder );
if( !Test1.IsEqual( PrivKInverseExponentDP ))
throw( new Exception( "Bug. 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.IntMathNew.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.Divide( Test1, PrimeQMinus1, Quotient, Remainder );
Test1.Copy( Remainder );
if( !Test1.IsEqual( PrivKInverseExponentDQ ))
throw( new Exception( "Bug. 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.IntMathNew.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.IntMathNew.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.IntMathNew.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( "This is a bug. 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 ));
/*
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, " " );
DoCRTTest( PrivKInverseExponent );
Worker.ReportProgress( 0, "Finished CRT test." );
Worker.ReportProgress( 0, " " );
*/
return; // Comment this out to just leave it while( true ) for testing.
}
}
