internal void Add( Integer ToAdd )
{
// There is a separate IntegerMath.Add() that is a wrapper to handle
// negative numbers too.
if( IsNegative )
throw( new Exception( "Integer.Add() is being called when it's negative." ));
if( ToAdd.IsNegative )
throw( new Exception( "Integer.Add() is being called when ToAdd is negative." ));
if( ToAdd.IsULong() )
{
AddULong( ToAdd.GetAsULong() );
return;
}
// Tell the compiler these aren't going to change for the for-loop.
int LocalIndex = Index;
int LocalToAddIndex = ToAdd.Index;
if( LocalIndex < ToAdd.Index )
{
for( int Count = LocalIndex + 1; Count <= LocalToAddIndex; Count++ )
D[Count] = ToAdd.D[Count];
for( int Count = 0; Count <= LocalIndex; Count++ )
D[Count] += ToAdd.D[Count];
Index = ToAdd.Index;
}
else
{
for( int Count = 0; Count <= LocalToAddIndex; Count++ )
D[Count] += ToAdd.D[Count];
}
// After they've been added, reorganize it.
ulong Carry = D[0] >> 32;
D[0] = D[0] & 0xFFFFFFFF;
LocalIndex = Index;
for( int Count = 1; Count <= LocalIndex; Count++ )
{
ulong Total = Carry + D[Count];
D[Count] = Total & 0xFFFFFFFF;
Carry = Total >> 32;
}
if( Carry != 0 )
{
Index++;
if( Index >= DigitArraySize )
throw( new Exception( "Integer.Add() overflow." ));
D[Index] = Carry;
}
}
internal bool FindMultiplicativeInverseSmall( Integer ToFind, Integer KnownNumber, Integer Modulus, BackgroundWorker Worker )
{
// This method is for: KnownNumber * ToFind = 1 mod Modulus
// An example:
// PublicKeyExponent * X = 1 mod PhiN.
// PublicKeyExponent * X = 1 mod (P - 1)(Q - 1).
// This means that
// (PublicKeyExponent * X) = (Y * PhiN) + 1
// X is less than PhiN.
// So Y is less than PublicKExponent.
// Y can't be zero.
// If this equation can be solved then it can be solved modulo
// any number. So it has to be solvable mod PublicKExponent.
// See: Hasse Principle.
// This also depends on the idea that the KnownNumber is prime and
// that there is one unique modular inverse.
// if( !KnownNumber-is-a-prime )
// then it won't work.
if( !KnownNumber.IsULong())
throw( new Exception( "FindMultiplicativeInverseSmall() was called with too big of a KnownNumber." ));
ulong KnownNumberULong = KnownNumber.GetAsULong();
// 65537
if( KnownNumberULong > 1000000 )
throw( new Exception( "KnownNumberULong > 1000000. FindMultiplicativeInverseSmall() was called with too big of an exponent." ));
// (Y * PhiN) + 1 mod PubKExponent has to be zero if Y is a solution.
ulong ModulusModKnown = IntMath.GetMod32( Modulus, KnownNumberULong );
Worker.ReportProgress( 0, "ModulusModExponent: " + ModulusModKnown.ToString( "N0" ));
if( Worker.CancellationPending )
return false;
// Y can't be zero.
// The exponent is a small number like 65537.
for( uint Y = 1; Y < (uint)KnownNumberULong; Y++ )
{
ulong X = (ulong)Y * ModulusModKnown;
X++; // Add 1 to it for (Y * PhiN) + 1.
X = X % KnownNumberULong;
if( X == 0 )
{
if( Worker.CancellationPending )
return false;
// What is PhiN mod 65537?
// That gives me Y.
// The private key exponent is X*65537 + ModPart
// The CipherText raised to that is the PlainText.
// P + zN = C^(X*65537 + ModPart)
// P + zN = C^(X*65537)(C^ModPart)
// P + zN = ((C^65537)^X)(C^ModPart)
Worker.ReportProgress( 0, "Found Y at: " + Y.ToString( "N0" ));
ToFind.Copy( Modulus );
IntMath.MultiplyULong( ToFind, Y );
ToFind.AddULong( 1 );
IntMath.Divide( ToFind, KnownNumber, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "This can't happen. !Remainder.IsZero()" ));
ToFind.Copy( Quotient );
// Worker.ReportProgress( 0, "ToFind: " + ToString10( ToFind ));
break;
}
}
if( Worker.CancellationPending )
return false;
TestForModInverse1.Copy( ToFind );
IntMath.MultiplyULong( TestForModInverse1, KnownNumberULong );
IntMath.Divide( TestForModInverse1, Modulus, Quotient, Remainder );
if( !Remainder.IsOne())
{
// The definition is that it's congruent to 1 mod the modulus,
// so this has to be 1.
// I've only seen this happen once. Were the primes P and Q not
// really primes?
throw( new Exception( "This is a bug. Remainder has to be 1: " + IntMath.ToString10( Remainder ) ));
}
return true;
}
private bool IsFermatPrimeAdded( Integer FindFrom )
{
if( FindFrom.IsULong())
{
// The biggest size that NumberIsDivisibleByUInt() will check to
// see if it has primes for sure.
if( FindFrom.GetAsULong() < (223092870UL * 223092870UL))
return false; // Factor this.
}
int HowManyTimes = 20; // How many primes it will be checked with.
if( !IntMath.IsFermatPrime( FindFrom, HowManyTimes ))
return false;
Integer OneFactor = new Integer();
OneFactor.Copy( FindFrom );
OneFactorRec Rec = new OneFactorRec();
Rec.Factor = OneFactor;
// Neither one of these is set to true here because it's probably
// a prime, but not definitely.
// Rec.IsDefinitelyAPrime = false;
// Rec.IsDefinitelyNotAPrime = false;
AddFactorRec( Rec );
Worker.ReportProgress( 0, "Fermat thinks this one is a prime." );
return true; // It's a Fermat prime and it was added.
}
internal uint NumberIsDivisibleByUInt( Integer ToCheck )
{
if( DivisionArray == null )
SetupDivisionArray(); // Set it up once, when it's needed.
uint Max = 0;
if( ToCheck.IsULong())
{
ulong ForMax = ToCheck.GetAsULong();
// It can't be bigger than the square root.
Max = (uint)IntMath.FindULSqrRoot( ForMax );
}
uint Base = 2 * 3 * 5 * 7 * 11 * 13 * 17;
uint EulerPhi = 2 * 4 * 6 * 10 * 12 * 16;
uint Base19 = Base * 19;
uint Base23 = Base19 * 23;
// The first few base numbers like this:
// 2 2
// 3 6
// 5 30
// 7 210
// 11 2,310
// 13 30,030
// 17 510,510
// 19 9,699,690
// 23 223,092,870
// These loops count up to 223,092,870 - 1.
for( uint Count23 = 0; Count23 < 23; Count23++ )
{
Worker.ReportProgress( 0, "Count23 loop: " + Count23.ToString());
uint Base23Part = (Base19 * Count23);
for( uint Count19 = 0; Count19 < 19; Count19++ )
{
uint Base19Part = Base * Count19;
if( Worker.CancellationPending )
return 0;
for( int Count = 0; Count < EulerPhi; Count++ )
{
if( Worker.CancellationPending )
return 0;
uint Test = Base23Part + Base19Part + DivisionArray[Count];
if( Test == 1 )
continue;
if( (Test % 19) == 0 )
continue;
if( (Test % 23) == 0 )
continue;
if( Max > 0 )
{
if( Test > Max )
return 0;
}
if( 0 == IntMath.GetMod32( ToCheck, Test ))
{
Worker.ReportProgress( 0, "The number is divisible by: " + Test.ToString( "N0" ));
return Test;
}
}
}
}
return 0; // Didn't find a number to divide it.
}
/*
private bool IsQuadResidue( uint Test, int Index )
{
uint TestMod = Test % IntMath.GetPrimeAt( Index );
return QuadResToPrimesArray[Index].QuadRes[TestMod];
}
*/
private uint GetMod32( Integer ToDivideOriginal, uint DivideByU )
{
if( ToDivideOriginal.IsULong())
{
ulong Result = ToDivideOriginal.GetAsULong();
return (uint)(Result % DivideByU);
}
ToDivideMod32.Copy( ToDivideOriginal );
ulong RemainderU = 0;
if( DivideByU <= ToDivideMod32.GetD( ToDivideMod32.GetIndex() ))
{
ulong OneDigit = ToDivideMod32.GetD( ToDivideMod32.GetIndex() );
RemainderU = OneDigit % DivideByU;
ToDivideMod32.SetD( ToDivideMod32.GetIndex(), RemainderU );
}
for( int Count = ToDivideMod32.GetIndex(); Count >= 1; Count-- )
{
ulong TwoDigits = ToDivideMod32.GetD( Count );
TwoDigits <<= 32;
TwoDigits |= ToDivideMod32.GetD( Count - 1 );
RemainderU = TwoDigits % DivideByU;
ToDivideMod32.SetD( Count, 0 );
ToDivideMod32.SetD( Count - 1, RemainderU );
}
return (uint)RemainderU;
}
internal ulong GetMod64( Integer ToDivideOriginal, ulong DivideBy )
{
if( ToDivideOriginal.IsULong())
return ToDivideOriginal.GetAsULong() % DivideBy;
ToDivide.Copy( ToDivideOriginal );
ulong Digit1;
ulong Digit0;
ulong Remainder;
if( ToDivide.GetIndex() == 2 )
{
Digit1 = ToDivide.GetD( 2 );
Digit0 = ToDivide.GetD( 1 ) << 32;
Digit0 |= ToDivide.GetD( 0 );
return GetMod64FromTwoULongs( Digit1, Digit0, DivideBy );
}
if( ToDivide.GetIndex() == 3 )
{
Digit1 = ToDivide.GetD( 3 ) << 32;
Digit1 |= ToDivide.GetD( 2 );
Digit0 = ToDivide.GetD( 1 ) << 32;
Digit0 |= ToDivide.GetD( 0 );
return GetMod64FromTwoULongs( Digit1, Digit0, DivideBy );
}
int Where = ToDivide.GetIndex();
while( true )
{
if( Where <= 3 )
{
if( Where < 2 ) // This can't happen.
throw( new Exception( "Bug: GetMod64(): Where < 2." ));
if( Where == 2 )
{
Digit1 = ToDivide.GetD( 2 );
Digit0 = ToDivide.GetD( 1 ) << 32;
Digit0 |= ToDivide.GetD( 0 );
return GetMod64FromTwoULongs( Digit1, Digit0, DivideBy );
}
if( Where == 3 )
{
Digit1 = ToDivide.GetD( 3 ) << 32;
Digit1 |= ToDivide.GetD( 2 );
Digit0 = ToDivide.GetD( 1 ) << 32;
Digit0 |= ToDivide.GetD( 0 );
return GetMod64FromTwoULongs( Digit1, Digit0, DivideBy );
}
}
else
{
// The index is bigger than 3.
// This part would get called at least once.
Digit1 = ToDivide.GetD( Where ) << 32;
Digit1 |= ToDivide.GetD( Where - 1 );
Digit0 = ToDivide.GetD( Where - 2 ) << 32;
Digit0 |= ToDivide.GetD( Where - 3 );
Remainder = GetMod64FromTwoULongs( Digit1, Digit0, DivideBy );
ToDivide.SetD( Where, 0 );
ToDivide.SetD( Where - 1, 0 );
ToDivide.SetD( Where - 2, Remainder >> 32 );
ToDivide.SetD( Where - 3, Remainder & 0xFFFFFFFF );
}
Where -= 2;
}
}
// This is a variation on ShortDivide() to get the remainder only.
internal ulong GetMod32( Integer ToDivideOriginal, ulong DivideByU )
{
if( (DivideByU >> 32) != 0 )
throw( new Exception( "GetMod32: (DivideByU >> 32) != 0." ));
// If this is _equal_ to a small prime it would return zero.
if( ToDivideOriginal.IsULong())
{
ulong Result = ToDivideOriginal.GetAsULong();
return Result % DivideByU;
}
ToDivide.Copy( ToDivideOriginal );
ulong RemainderU = 0;
if( DivideByU <= ToDivide.GetD( ToDivide.GetIndex() ))
{
ulong OneDigit = ToDivide.GetD( ToDivide.GetIndex() );
RemainderU = OneDigit % DivideByU;
ToDivide.SetD( ToDivide.GetIndex(), RemainderU );
}
for( int Count = ToDivide.GetIndex(); Count >= 1; Count-- )
{
ulong TwoDigits = ToDivide.GetD( Count );
TwoDigits <<= 32;
TwoDigits |= ToDivide.GetD( Count - 1 );
RemainderU = TwoDigits % DivideByU;
ToDivide.SetD( Count, 0 );
ToDivide.SetD( Count - 1, RemainderU );
}
return RemainderU;
}
internal string ToString10( Integer From )
{
if( From.IsULong())
{
ulong N = From.GetAsULong();
if( From.IsNegative )
return "-" + N.ToString( "N0" );
else
return N.ToString( "N0" );
}
string Result = "";
ToDivide.Copy( From );
int CommaCount = 0;
while( !ToDivide.IsZero())
{
uint Digit = (uint)ShortDivideRem( ToDivide, 10, Quotient );
ToDivide.Copy( Quotient );
if( ((CommaCount % 3) == 0) && (CommaCount != 0) )
Result = Digit.ToString() + "," + Result; // Or use a StringBuilder.
else
Result = Digit.ToString() + Result;
CommaCount++;
}
if( From.IsNegative )
return "-" + Result;
else
return Result;
}
// Finding the square root of a number is similar to division since
// it is a search algorithm. The TestSqrtBits method shown next is
// very much like TestDivideBits(). It works the same as
// FindULSqrRoot(), but on a bigger scale.
/*
private void TestSqrtBits( int TestIndex, Integer Square, Integer SqrRoot )
{
Integer Test1 = new Integer();
uint BitTest = 0x80000000;
for( int BitCount = 31; BitCount >= 0; BitCount-- )
{
Test1.Copy( SqrRoot );
Test1.D[TestIndex] |= BitTest;
Test1.Square();
if( !Square.ParamIsGreater( Test1 ) )
SqrRoot.D[TestIndex] |= BitTest; // Use the bit.
BitTest >>= 1;
}
}
*/
// In the SquareRoot() method SqrRoot.Index is half of Square.Index.
// Compare this to the Square() method where the Carry might or
// might not increment the index to an odd number. (So if the Index
// was 5 its square root would have an Index of 5 / 2 = 2.)
// The SquareRoot1() method uses FindULSqrRoot() either to find the
// whole answer, if it's a small number, or it uses it to find the
// top part. Then from there it goes on to a bit by bit search
// with TestSqrtBits().
public bool SquareRoot( Integer Square, Integer SqrRoot )
{
ulong ToMatch;
if( Square.IsULong() )
{
ToMatch = Square.GetAsULong();
SqrRoot.SetD( 0, FindULSqrRoot( ToMatch ));
SqrRoot.SetIndex( 0 );
if( (SqrRoot.GetD(0 ) * SqrRoot.GetD( 0 )) == ToMatch )
return true;
else
return false;
}
int TestIndex = Square.GetIndex() >> 1; // LgSquare.Index / 2;
SqrRoot.SetDigitAndClear( TestIndex, 1 );
// if( (TestIndex * 2) > (LgSquare.Index - 1) )
if( (TestIndex << 1) > (Square.GetIndex() - 1) )
{
ToMatch = Square.GetD( Square.GetIndex());
}
else
{
// LgSquare.Index is at least 2 here.
ToMatch = Square.GetD( Square.GetIndex()) << 32;
ToMatch |= Square.GetD( Square.GetIndex() - 1 );
}
SqrRoot.SetD( TestIndex, FindULSqrRoot( ToMatch ));
TestIndex--;
while( true )
{
// TestSqrtBits( TestIndex, LgSquare, LgSqrRoot );
SearchSqrtXPart( TestIndex, Square, SqrRoot );
if( TestIndex == 0 )
break;
TestIndex--;
}
// Avoid squaring the whole thing to see if it's an exact square root:
if( ((SqrRoot.GetD( 0 ) * SqrRoot.GetD( 0 )) & 0xFFFFFFFF) != Square.GetD( 0 ))
return false;
TestForSquareRoot.Copy( SqrRoot );
DoSquare( TestForSquareRoot );
if( Square.IsEqual( TestForSquareRoot ))
return true;
else
return false;
}
internal void SubtractULong( Integer Result, ulong ToSub )
{
if( Result.IsULong())
{
ulong ResultU = Result.GetAsULong();
if( ToSub > ResultU )
throw( new Exception( "SubULong() (IsULong() and (ToSub > Result)." ));
ResultU = ResultU - ToSub;
Result.SetD( 0, ResultU & 0xFFFFFFFF );
Result.SetD( 1, ResultU >> 32 );
if( Result.GetD( 1 ) == 0 )
Result.SetIndex( 0 );
else
Result.SetIndex( 1 );
return;
}
// If it got this far then Index is at least 2.
SignedD[0] = (long)Result.GetD( 0 ) - (long)(ToSub & 0xFFFFFFFF);
SignedD[1] = (long)Result.GetD( 1 ) - (long)(ToSub >> 32);
if( (SignedD[0] >= 0) && (SignedD[1] >= 0) )
{
// No need to reorganize it.
Result.SetD( 0, (ulong)SignedD[0] );
Result.SetD( 1, (ulong)SignedD[1] );
return;
}
for( int Count = 2; Count <= Result.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count );
for( int Count = 0; Count < Result.GetIndex(); Count++ )
{
if( SignedD[Count] < 0 )
{
SignedD[Count] += (long)0xFFFFFFFF + 1;
SignedD[Count + 1]--;
}
}
if( SignedD[Result.GetIndex()] < 0 )
throw( new Exception( "SubULong() SignedD[Index] < 0." ));
for( int Count = 0; Count <= Result.GetIndex(); Count++ )
Result.SetD( Count, (ulong)SignedD[Count] );
for( int Count = Result.GetIndex(); Count >= 0; Count-- )
{
if( Result.GetD( Count ) != 0 )
{
Result.SetIndex( Count );
return;
}
}
// If this was zero it wouldn't find a nonzero
// digit to set the Index to and it would end up down here.
Result.SetIndex( 0 );
}
internal void SubtractPositive( Integer Result, Integer ToSub )
{
if( ToSub.IsULong() )
{
SubtractULong( Result, ToSub.GetAsULong());
return;
}
if( ToSub.GetIndex() > Result.GetIndex() )
throw( new Exception( "In Subtract() ToSub.Index > Index." ));
for( int Count = 0; Count <= ToSub.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count ) - (long)ToSub.GetD( Count );
for( int Count = ToSub.GetIndex() + 1; Count <= Result.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count );
for( int Count = 0; Count < Result.GetIndex(); Count++ )
{
if( SignedD[Count] < 0 )
{
SignedD[Count] += (long)0xFFFFFFFF + 1;
SignedD[Count + 1]--;
}
}
if( SignedD[Result.GetIndex()] < 0 )
throw( new Exception( "Subtract() SignedD[Index] < 0." ));
for( int Count = 0; Count <= Result.GetIndex(); Count++ )
Result.SetD( Count, (ulong)SignedD[Count] );
for( int Count = Result.GetIndex(); Count >= 0; Count-- )
{
if( Result.GetD( Count ) != 0 )
{
Result.SetIndex( Count );
return;
}
}
// If it never found a non-zero digit it would get down to here.
Result.SetIndex( 0 );
}
// 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;
}
// 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 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.
}
}