internal CRTBaseMath( BackgroundWorker UseWorker, CRTMath UseCRTMath )
{
// Most of these are created ahead of time so that
// they don't have to be created inside a loop.
Worker = UseWorker;
IntMath = new IntegerMath();
CRTMath1 = UseCRTMath;
Quotient = new Integer();
Remainder = new Integer();
CRTAccumulateBase = new ChineseRemainder( IntMath );
CRTAccumulateBasePart = new ChineseRemainder( IntMath );
CRTAccumulateForBaseMultiples = new ChineseRemainder( IntMath );
CRTAccumulatePart = new ChineseRemainder( IntMath );
BaseModArrayModulus = new Integer();
CRTTempForIsEqual = new ChineseRemainder( IntMath );
CRTWorkingTemp = new ChineseRemainder( IntMath );
ExponentCopy = new Integer();
CRTXForModPower = new ChineseRemainder( IntMath );
CRTAccumulate = new ChineseRemainder( IntMath );
CRTCopyForSquare = new ChineseRemainder( IntMath );
FermatExponent = new Integer();
CRTFermatModulus = new ChineseRemainder( IntMath );
FermatModulus = new Integer();
CRTTestFermat = new ChineseRemainder( IntMath );
Worker.ReportProgress( 0, "Setting up numbers array." );
SetupNumbersArray();
Worker.ReportProgress( 0, "Setting up base array." );
SetupBaseArray();
Worker.ReportProgress( 0, "Setting up multiplicative inverses." );
SetMultiplicativeInverses();
}
internal void GetMaximumValues()
{
string RSA2048 = "2519590847565789349402718324004839857142928212620403202777713783604366202070" +
"7595556264018525880784406918290641249515082189298559149176184502808489120072" +
"8449926873928072877767359714183472702618963750149718246911650776133798590957" +
"0009733045974880842840179742910064245869181719511874612151517265463228221686" +
"9987549182422433637259085141865462043576798423387184774447920739934236584823" +
"8242811981638150106748104516603773060562016196762561338441436038339044149526" +
"3443219011465754445417842402092461651572335077870774981712577246796292638635" +
"6373289912154831438167899885040445364023527381951378636564391212010397122822" +
"120720357";
Integer BigRSA = new Integer();
IntMath.SetFromString( BigRSA, RSA2048 );
// Do a basic sanity-check just to make sure the
// RSA number was copied right.
if( 0 != IntMath.IsDivisibleBySmallPrime( BigRSA ))
throw( new Exception( "BigRSA was not copied right." ));
// One factor is smaller than the square root.
// So it's the biggest one that's less than the
// square root.
Integer BiggestFactor = new Integer();
IntMath.SquareRoot( BigRSA, BiggestFactor );
Integer BigBase = MakeBigBase( BiggestFactor );
if( BigBase == null )
{
ShowStatus( "BigBase was null." );
return;
}
}
internal RSACryptoSystem( BackgroundWorker UseWorker, RSACryptoWorkerInfo UseWInfo )
{
Worker = UseWorker;
WorkerInfo = UseWInfo;
StartTime = new ECTime();
StartTime.SetToNow();
RngCsp = new RNGCryptoServiceProvider();
IntMath = new IntegerMath();
IntMathNewForP = new IntegerMathNew( IntMath );
IntMathNewForQ = new IntegerMathNew( IntMath );
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 MultiplyBits( MainForm UseForm )
{
MForm = UseForm;
try
{
IntMath = new IntegerMath();
// MForm.ShowStatus( IntMath.GetStatusString());
InputOutputDictionary = new SortedDictionary<uint, uint>();
Product = new Integer();
TestProduct = new Integer();
Factor1 = new Integer();
Factor2 = new Integer();
Quotient = new Integer();
Remainder = new Integer();
MultArray = new LineRec[MultArraySize];
MultArrayCopyForMult2 = new LineRec[MultArraySize];
for( int Count = 0; Count < MultArraySize; Count++ )
{
MultArray[Count].OneLine = new uint[MultArraySize];
MultArrayCopyForMult2[Count].OneLine = new uint[MultArraySize];
}
SetupFermatLittle( 107 );
}
catch( Exception )
{
MForm.ShowStatus( "Not enough RAM for the MultArray." );
}
}
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 ModularReduction()
{
IntMath = new IntegerMath();
XForModPower = new Integer();
ExponentCopy = new Integer();
Quotient = new Integer();
Remainder = new Integer();
TempForModPower = new Integer();
}
internal FindFactors( BackgroundWorker UseWorker, IntegerMath UseIntMath )
{
Worker = UseWorker;
IntMath = UseIntMath;
Quotient = new Integer();
Remainder = new Integer();
OriginalFindFrom = new Integer();
FindFrom = new Integer();
FactorsArray = new OneFactorRec[8];
SortIndexArray = new int[8];
StatsDictionary = new SortedDictionary<uint, uint>();
}
// internal ExponentVectorNumber( BackgroundWorker UseWorker, IntegerMath UseIntMath )
internal ExponentVectorNumber( IntegerMath UseIntMath )
{
// Worker = UseWorker;
IntMath = UseIntMath;
Quotient = new Integer();
Remainder = new Integer();
ExtraValue = new Integer();
PartAForAdd = new Integer();
PartBForAdd = new Integer();
VectorValuesArray = new VectorValueRec[IncreaseArraySizeBy];
}
// private uint GBaseSmallModulus = 0;
internal IntegerMathNew( IntegerMath UseIntMath )
{
IntMath = UseIntMath;
Quotient = new Integer();
Remainder = new Integer();
XForModPower = new Integer();
ExponentCopy = new Integer();
TempForModPower = new Integer();
TestForModPower = new Integer();
AccumulateBase = new Integer();
TestForModInverse1 = new Integer();
}
internal FactorDictionary( MainForm UseForm )
{
MForm = UseForm;
IntMath = new IntegerMath();
Product = new Integer();
SolutionP = new Integer();
SolutionQ = new Integer();
Quotient = new Integer();
Remainder = new Integer();
MainDictionary = new SortedDictionary<uint, ListRec>();
NumberList = new List<NumberRec>();
}
internal EquationParts( QuadResWorkerInfo UseWInfo, BackgroundWorker UseWorker )
{
WInfo = UseWInfo;
Worker = UseWorker;
IntMath = new IntegerMath();
Quotient = new Integer();
Remainder = new Integer();
Product = new Integer();
SolutionP = new Integer();
SolutionQ = new Integer();
ProductSqrRoot = new Integer();
MaxX = new Integer();
FindFactors1 = new FindFactors( Worker, IntMath );
IntMath.SetFromString( Product, WInfo.PublicKeyModulus );
}
internal QuadResCombinatorics( QuadResWorkerInfo UseWInfo, BackgroundWorker UseWorker )
{
WInfo = UseWInfo;
Worker = UseWorker;
IntMath = new IntegerMath();
Quotient = new Integer();
Remainder = new Integer();
Product = new Integer();
SolutionP = new Integer();
SolutionQ = new Integer();
ToDivideMod32 = new Integer();
LastAccumulateValue = new Integer();
GetValueBasePart = new Integer();
StartTime = new ECTime();
StartTime.SetToNow();
IntMath.SetFromString( Product, WInfo.PublicKeyModulus );
QuadResDigitsArray = new QuadResDigitsRec[DigitsArrayLength];
}
internal void AddDelimString( string ToAdd )
{
// string DelimS = IntMath.ToString10( Y ) + "\t" +
// ExpNumber.ToDelimString();
string[] SplitS = ToAdd.Split( new Char[] { '\t' } );
if( SplitS.Length < 2 )
return;
// MForm.ShowStatus( "Adding: " + ToAdd );
Integer Y = new Integer();
IntMath.SetFromString( Y, SplitS[0] );
ExponentVectorNumber X = new ExponentVectorNumber( IntMath );
X.SetFromDelimString( SplitS[1] );
for( int Count = 0; ; Count++ )
{
VectorValueRec Rec = X.GetValueRecordAt( Count );
if( Rec.Prime == 0 )
break;
// The one X number is being added as a reference in every
// dictionary it belongs to.
NumberRec NRec = new NumberRec();
NRec.Y = Y;
NRec.X = X;
NumberList.Add( NRec );
if( MainDictionary.ContainsKey( Rec.Prime ))
{
MainDictionary[Rec.Prime].OnePrimeList.Add( NRec );
}
else
{
ListRec LRec = new ListRec();
LRec.OnePrimeList = new List<NumberRec>();
LRec.OnePrimeList.Add( NRec );
MainDictionary[Rec.Prime] = LRec;
}
}
}
internal FactorBase( QuadResWorkerInfo UseWInfo, BackgroundWorker UseWorker )
{
WInfo = UseWInfo;
Worker = UseWorker;
IntMath = new IntegerMath();
Quotient = new Integer();
Remainder = new Integer();
Product = new Integer();
ProductSqrRoot = new Integer();
EulerExponent = new Integer();
EulerResult = new Integer();
EulerModulus = new Integer();
OneMainFactor = new Integer();
ExpOneMainFactor = new ExponentVectorNumber( IntMath );
StartTime = new ECTime();
StartTime.SetToNow();
IntMath.SetFromString( Product, WInfo.PublicKeyModulus );
IntMath.SquareRoot( Product, ProductSqrRoot );
}
private void SetupQuadResArray( Integer Product )
{
// I'm doing this differently from finding y^2 = x^2 - N,
// which I think would be faster, unless it complicates it too
// much by having to use large Integers and doing subtraction.
// Here it's looking for when
// P + x^2 = y^2.
// private uint[] QuadResArraySmall;
// private uint[] QuadResArray;
uint SmallBase = 2 * 3 * 5 * 7 * 11 * 13; // 30,030
// 2 3 3 4 6 7
int SmallBaseArraySize = 2 * 3 * 3 * 4 * 6 * 7; // This is not exact.
uint[] QuadResArraySmall = new uint[SmallBaseArraySize];
uint QuadResArraySmallLast = 0;
uint ProductModSmall = (uint)IntMath.GetMod32( Product, SmallBase );
QuadResArraySmallLast = 0;
uint ProdMod4 = (uint)Product.GetD( 0 ) & 3;
for( ulong Count = 0; Count < SmallBase; Count++ )
{
// P is odd.
// if x is even then y is odd.
// if x is odd then y is even.
// If x is even then x^2 is divisible by 4.
// If y is even then y^2 is divisible by 4.
ulong Test = ProductModSmall + (Count * Count); // The Product plus a square.
Test = Test % SmallBase;
if( !IntegerMath.IsSmallQuadResidue( (uint)Test ))
continue;
// What Count was used to make a quad residue?
QuadResArraySmall[QuadResArraySmallLast] = (uint)Count;
QuadResArraySmallLast++;
if( QuadResArraySmallLast >= SmallBaseArraySize )
throw( new Exception( "Went past the small quad res array." ));
}
// Worker.ReportProgress( 0, "Finished setting up small quad res array." );
QuadResBigBase = SmallBase * 17 * 19 * 23; // 223,092,870
// 17 19 23
int QuadResBaseArraySize = SmallBaseArraySize * 9 * 10 * 12; // This is not exact.
QuadResArray = new uint[QuadResBaseArraySize];
uint ProductMod = (uint)IntMath.GetMod32( Product, QuadResBigBase );
int MaxLength = QuadResArray.Length;
QuadResArrayLast = 0;
for( ulong Count23 = 0; Count23 < (17 * 19 * 23); Count23++ )
{
if( Worker.CancellationPending )
return;
ulong BasePart = Count23 * SmallBase;
for( uint Count = 0; Count < QuadResArraySmallLast; Count++ )
{
ulong CountPart = BasePart + QuadResArraySmall[Count];
ulong Test = ProductMod + (CountPart * CountPart); // The Product plus a square.
Test = Test % QuadResBigBase;
if( !IntegerMath.IsQuadResidue17To23( (uint)Test ))
continue;
// What Count was used to make a quad residue?
QuadResArray[QuadResArrayLast] = (uint)CountPart;
QuadResArrayLast++;
if( QuadResArrayLast >= MaxLength )
throw( new Exception( "Went past the quad res array." ));
}
}
Worker.ReportProgress( 0, "Finished setting up main quad res array." );
}
internal void VerifyFactors()
{
Integer TestFactors = new Integer();
TestFactors.SetToOne();
for( int Count = 0; Count < FactorsArrayLast; Count++ )
IntMath.Multiply( TestFactors, FactorsArray[Count].Factor );
if( !TestFactors.IsEqual( OriginalFindFrom ))
throw( new Exception( "VerifyFactors didn't come out right." ));
}
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 void FindAllFactors( Integer FindFromNotChanged )
{
// ShowStats(); // So far.
OriginalFindFrom.Copy( FindFromNotChanged );
FindFrom.Copy( FindFromNotChanged );
NumbersTested++;
ClearFactorsArray();
Integer OneFactor;
OneFactorRec Rec;
// while( not forever )
for( int Count = 0; Count < 1000; Count++ )
{
if( Worker.CancellationPending )
return;
uint SmallPrime = IntMath.IsDivisibleBySmallPrime( FindFrom );
if( SmallPrime == 0 )
break; // No more small primes.
// Worker.ReportProgress( 0, "Found a small prime factor: " + SmallPrime.ToString() );
AddToStats( SmallPrime );
OneFactor = new Integer();
OneFactor.SetFromULong( SmallPrime );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true;
AddFactorRec( Rec );
if( FindFrom.IsULong())
{
ulong CheckLast = FindFrom.GetAsULong();
if( CheckLast == SmallPrime )
{
Worker.ReportProgress( 0, "It only had small prime factors." );
VerifyFactors();
return; // It had only small prime factors.
}
}
IntMath.Divide( FindFrom, OneFactor, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "Bug in FindAllFactors. Remainder is not zero." ));
FindFrom.Copy( Quotient );
if( FindFrom.IsOne())
throw( new Exception( "Bug in FindAllFactors. This was already checked for 1." ));
}
// Worker.ReportProgress( 0, "No more small primes." );
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
// while( not forever )
for( int Count = 0; Count < 1000; Count++ )
{
if( Worker.CancellationPending )
return;
// If FindFrom is a ulong then this will go up to the square root of
// FindFrom and return zero if it doesn't find it there. So it can't
// go up to the whole value of FindFrom.
uint SmallFactor = NumberIsDivisibleByUInt( FindFrom );
if( SmallFactor == 0 )
break;
// This is necessarily a prime because it was the smallest one found.
AddToStats( SmallFactor );
// Worker.ReportProgress( 0, "Found a small factor: " + SmallFactor.ToString( "N0" ));
OneFactor = new Integer();
OneFactor.SetFromULong( SmallFactor );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true; // The smallest factor. It is necessarily a prime.
AddFactorRec( Rec );
IntMath.Divide( FindFrom, OneFactor, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "Bug in FindAllFactors. Remainder is not zero. Second part." ));
if( Quotient.IsOne())
throw( new Exception( "This can't happen here. It can't go that high." ));
FindFrom.Copy( Quotient );
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
}
if( IsFermatPrimeAdded( FindFrom ))
{
VerifyFactors();
return;
}
// If it got this far then it's definitely composite or definitely
// small enough to factor.
Integer P = new Integer();
Integer Q = new Integer();
bool TestedAllTheWay = FindTwoFactorsWithFermat( FindFrom, P, Q, 0 );
if( !P.IsZero())
{
// Q is necessarily prime because it's bigger than the square root.
// But P is not necessarily prime.
// P is the smaller one, so add it first.
if( IsFermatPrimeAdded( P ))
{
Worker.ReportProgress( 0, "P from Fermat method was probably a prime." );
}
else
{
OneFactor = new Integer();
OneFactor.Copy( P );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyNotAPrime = true;
AddFactorRec( Rec );
}
Worker.ReportProgress( 0, "Q is necessarily prime." );
OneFactor = new Integer();
OneFactor.Copy( Q );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true;
AddFactorRec( Rec );
}
else
{
// Didn't find any with Fermat.
OneFactor = new Integer();
OneFactor.Copy( FindFrom );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
if( TestedAllTheWay )
Rec.IsDefinitelyAPrime = true;
else
Rec.IsDefinitelyNotAPrime = true;
AddFactorRec( Rec );
}
Worker.ReportProgress( 0, "That's all it could find." );
VerifyFactors();
}
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.
}
internal bool FindTwoFactorsWithFermat( Integer Product, Integer P, Integer Q, ulong MinimumX )
{
ECTime StartTime = new ECTime();
StartTime.SetToNow();
Integer TestSqrt = new Integer();
Integer TestSquared = new Integer();
Integer SqrRoot = new Integer();
TestSquared.Copy( Product );
IntMath.Multiply( TestSquared, Product );
IntMath.SquareRoot( TestSquared, SqrRoot );
TestSqrt.Copy( SqrRoot );
IntMath.DoSquare( TestSqrt );
// IntMath.Multiply( TestSqrt, SqrRoot );
if( !TestSqrt.IsEqual( TestSquared ))
throw( new Exception( "The square test was bad." ));
// Some primes:
// 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
// 101, 103, 107
P.SetToZero();
Q.SetToZero();
Integer TestX = new Integer();
SetupQuadResArray( Product );
ulong BaseTo37 = QuadResBigBase * 29UL * 31UL * 37UL;
// ulong BaseTo31 = QuadResBigBase * 29UL * 31UL;
ulong ProdModTo37 = IntMath.GetMod64( Product, BaseTo37 );
// ulong ProdModTo31 = IntMath.GetMod64( Product, BaseTo31 );
for( ulong BaseCount = 0; BaseCount < (29 * 31 * 37); BaseCount++ )
{
if( (BaseCount & 0xF) == 0 )
Worker.ReportProgress( 0, "Find with Fermat BaseCount: " + BaseCount.ToString() );
if( Worker.CancellationPending )
return false;
ulong Base = (BaseCount + 1) * QuadResBigBase; // BaseCount times 223,092,870.
if( Base < MinimumX )
continue;
Base = BaseCount * QuadResBigBase; // BaseCount times 223,092,870.
for( uint Count = 0; Count < QuadResArrayLast; Count++ )
{
// The maximum CountPart can be is just under half the size of
// the Product. (Like if Y - X was equal to 1, and Y + X was
// equal to the Product.) If it got anywhere near that big it
// would be inefficient to try and find it this way.
ulong CountPart = Base + QuadResArray[Count];
ulong Test = ProdModTo37 + (CountPart * CountPart);
// ulong Test = ProdModTo31 + (CountPart * CountPart);
Test = Test % BaseTo37;
// Test = Test % BaseTo31;
if( !IntegerMath.IsQuadResidue29( Test ))
continue;
if( !IntegerMath.IsQuadResidue31( Test ))
continue;
if( !IntegerMath.IsQuadResidue37( Test ))
continue;
ulong TestBytes = (CountPart & 0xFFFFF);
TestBytes *= (CountPart & 0xFFFFF);
ulong ProdBytes = Product.GetD( 1 );
ProdBytes <<= 8;
ProdBytes |= Product.GetD( 0 );
uint FirstBytes = (uint)(TestBytes + ProdBytes);
if( !IntegerMath.FirstBytesAreQuadRes( FirstBytes ))
{
// Worker.ReportProgress( 0, "First bytes aren't quad res." );
continue;
}
TestX.SetFromULong( CountPart );
IntMath.MultiplyULong( TestX, CountPart );
TestX.Add( Product );
// uint Mod37 = (uint)IntMath.GetMod32( TestX, 37 );
// if( !IntegerMath.IsQuadResidue37( Mod37 ))
// continue;
// Do more of these tests with 41, 43, 47...
// if( !IntegerMath.IsQuadResidue41( Mod37 ))
// continue;
// Avoid doing this square root at all costs.
if( IntMath.SquareRoot( TestX, SqrRoot ))
{
Worker.ReportProgress( 0, " " );
if( (CountPart & 1) == 0 )
Worker.ReportProgress( 0, "CountPart was even." );
else
Worker.ReportProgress( 0, "CountPart was odd." );
// Found an exact square root.
// P + (CountPart * CountPart) = Y*Y
// P = (Y + CountPart)Y - CountPart)
P.Copy( SqrRoot );
Integer ForSub = new Integer();
ForSub.SetFromULong( CountPart );
IntMath.Subtract( P, ForSub );
// Make Q the bigger one and put them in order.
Q.Copy( SqrRoot );
Q.AddULong( CountPart );
if( P.IsOne() || Q.IsOne())
{
// This happens when testing with small primes.
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, "Went all the way to 1 in FindTwoFactorsWithFermat()." );
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, " " );
P.SetToZero(); // It has no factors.
Q.SetToZero();
return true; // Tested everything, so it's a prime.
}
Worker.ReportProgress( 0, "Found P: " + IntMath.ToString10( P ) );
Worker.ReportProgress( 0, "Found Q: " + IntMath.ToString10( Q ) );
Worker.ReportProgress( 0, "Seconds: " + StartTime.GetSecondsToNow().ToString( "N1" ));
Worker.ReportProgress( 0, " " );
throw( new Exception( "Testing this." ));
// return true; // With P and Q.
}
// else
// Worker.ReportProgress( 0, "It was not an exact square root." );
}
}
// P and Q would still be zero if it never found them.
return false;
}
// This is the standard modular power algorithm that
// you could find in any reference, but its use of
// the new modular reduction algorithm is new.
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
// x^n = (x^2)^((n - 1)/2) if n is odd.
// x^n = (x^2)^(n/2) if n is even.
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.Divide( Result, Modulus, Quotient, Remainder );
Result.Copy( Remainder );
}
if( Exponent.IsOne())
{
// Result stays the same.
return;
}
if( !UsePresetBaseArray )
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.Multiply( Result, XForModPower );
ModularReduction( TempForModPower, Result );
Result.Copy( TempForModPower );
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
IntMath.Multiply( XForModPower, XForModPower );
ModularReduction( 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() ));
if( HowBig > 2 )
throw( new Exception( "The never happens. Diff: " + HowBig.ToString() ));
ModularReduction( TempForModPower, Result );
Result.Copy( TempForModPower );
IntMath.Divide( Result, Modulus, Quotient, Remainder );
Result.Copy( Remainder );
if( Quotient.GetIndex() > 1 )
throw( new Exception( "This never happens. The quotient index is never more than 1." ));
}
internal void SetupGeneralBaseArray( Integer GeneralBase )
{
// The input to the accumulator can be twice the bit length of GeneralBase.
int HowMany = ((GeneralBase.GetIndex() + 1) * 2) + 10; // Plus some extra for carries...
if( GeneralBaseArray == null )
{
GeneralBaseArray = new Integer[HowMany];
}
if( GeneralBaseArray.Length < HowMany )
{
GeneralBaseArray = new Integer[HowMany];
}
Integer Base = new Integer();
Integer BaseValue = 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.
BaseValue.SetFromULong( 1 );
for( int Count = 0; Count < HowMany; Count++ )
{
if( GeneralBaseArray[Count] == null )
GeneralBaseArray[Count] = new Integer();
IntMath.Divide( BaseValue, GeneralBase, Quotient, Remainder );
GeneralBaseArray[Count].Copy( Remainder );
// If this ever happened it would be a bug because
// the point of copying the Remainder in to BaseValue
// is to keep it down to a reasonable size.
// And Base here is one bit bigger than a uint.
if( Base.ParamIsGreater( Quotient ))
throw( new Exception( "Bug. This never happens: Base.ParamIsGreater( Quotient )" ));
// Keep it to mod GeneralBase so Divide() doesn't
// have to do so much work.
BaseValue.Copy( Remainder );
IntMath.Multiply( BaseValue, Base );
}
}
private void DoGeneralConstructorThings()
{
ModifyTime = new ECTime();
MostRecentIntegerValue = new Integer();
BitStreamRecArray = new BitStreamRec[8];
}
internal void MakeBaseNumbers()
{
try
{
MakeYBaseToPrimesArray();
if( Worker.CancellationPending )
return;
Integer YTop = new Integer();
Integer Y = new Integer();
Integer XSquared = new Integer();
Integer Test = new Integer();
YTop.SetToZero();
uint XSquaredBitLength = 1;
ExponentVectorNumber ExpNumber = new ExponentVectorNumber( IntMath );
uint Loops = 0;
uint BSmoothCount = 0;
uint BSmoothTestsCount = 0;
uint IncrementYBy = 0;
while( true )
{
if( Worker.CancellationPending )
return;
Loops++;
if( (Loops & 0xF) == 0 )
{
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, "Loops: " + Loops.ToString( "N0" ));
Worker.ReportProgress( 0, "BSmoothCount: " + BSmoothCount.ToString( "N0" ));
Worker.ReportProgress( 0, "BSmoothTestsCount: " + BSmoothTestsCount.ToString( "N0" ));
if( BSmoothTestsCount != 0 )
{
double TestsRatio = (double)BSmoothCount / (double)BSmoothTestsCount;
Worker.ReportProgress( 0, "TestsRatio: " + TestsRatio.ToString( "N3" ));
}
}
/*
if( (Loops & 0xFFFFF) == 0 )
{
// Use Task Manager to tweak the CPU Utilization if you want
// it be below 100 percent.
Thread.Sleep( 1 );
}
*/
// About 98 percent of the time it is running IncrementBy().
IncrementYBy += IncrementConst;
uint BitLength = IncrementBy();
const uint SomeOptimumBitLength = 2;
if( BitLength < SomeOptimumBitLength )
continue;
// This BitLength has to do with how many small factors you want
// in the number. But it doesn't limit your factor base at all.
// You can still have any size prime in your factor base (up to
// IntegerMath.PrimeArrayLength). Compare the size of
// YBaseToPrimesArrayLast to IntegerMath.PrimeArrayLength.
BSmoothTestsCount++;
YTop.AddULong( IncrementYBy );
IncrementYBy = 0;
Y.Copy( ProductSqrRoot );
Y.Add( YTop );
XSquared.Copy( Y );
IntMath.DoSquare( XSquared );
if( XSquared.ParamIsGreater( Product ))
throw( new Exception( "Bug. XSquared.ParamIsGreater( Product )." ));
IntMath.Subtract( XSquared, Product );
XSquaredBitLength = (uint)(XSquared.GetIndex() * 32);
uint TopDigit = (uint)XSquared.GetD( XSquared.GetIndex());
uint TopLength = GetBitLength( TopDigit );
XSquaredBitLength += TopLength;
if( XSquaredBitLength == 0 )
XSquaredBitLength = 1;
// if( ItIsTheAnswerAlready( XSquared )) It's too unlikely.
// QuadResCombinatorics could run in parallel to check for that,
// and it would be way ahead of this.
GetOneMainFactor();
if( OneMainFactor.IsEqual( XSquared ))
{
MakeFastExpNumber( ExpNumber );
}
else
{
if( OneMainFactor.IsZero())
throw( new Exception( "OneMainFactor.IsZero()." ));
IntMath.Divide( XSquared, OneMainFactor, Quotient, Remainder );
ExpNumber.SetFromTraditionalInteger( Quotient );
ExpNumber.Multiply( ExpOneMainFactor );
ExpNumber.GetTraditionalInteger( Test );
if( !Test.IsEqual( XSquared ))
throw( new Exception( "!Test.IsEqual( XSquared )." ));
}
if( ExpNumber.IsBSmooth())
{
BSmoothCount++;
string DelimS = IntMath.ToString10( Y ) + "\t" +
ExpNumber.ToDelimString();
Worker.ReportProgress( 1, DelimS );
if( (BSmoothCount & 0x3F) == 0 )
{
Worker.ReportProgress( 0, " " );
Worker.ReportProgress( 0, "BitLength: " + BitLength.ToString());
Worker.ReportProgress( 0, "XSquaredBitLength: " + XSquaredBitLength.ToString());
Worker.ReportProgress( 0, ExpNumber.ToString() );
// What should BSmoothLimit be?
// (Since FactorDictionary.cs will reduce the final factor base.)
if( BSmoothCount > BSmoothLimit )
{
Worker.ReportProgress( 0, "Found enough to make the matrix." );
Worker.ReportProgress( 0, "BSmoothCount: " + BSmoothCount.ToString( "N0" ));
Worker.ReportProgress( 0, "BSmoothLimit: " + BSmoothLimit.ToString( "N0" ));
Worker.ReportProgress( 0, "Seconds: " + StartTime.GetSecondsToNow().ToString( "N1" ));
double Seconds = StartTime.GetSecondsToNow();
int Minutes = (int)Seconds / 60;
int Hours = Minutes / 60;
Minutes = Minutes % 60;
Seconds = Seconds % 60;
string ShowS = "Hours: " + Hours.ToString( "N0" ) +
" Minutes: " + Minutes.ToString( "N0" ) +
" Seconds: " + Seconds.ToString( "N0" );
Worker.ReportProgress( 0, ShowS );
return;
}
}
}
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in MakeBaseNumbers():\r\n" + Except.Message ));
}
}
internal uint ModularPowerSmall( ulong Input, Integer Exponent, uint Modulus )
{
if( Input == 0 )
return 0;
if( Input == Modulus )
{
// It is congruent to zero % Modulus.
return 0;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
return 1;
ulong Result = Input;
if( Input > Modulus )
Result = Input % Modulus;
if( Exponent.IsOne())
return (uint)Result;
ulong XForModPowerU = Result;
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
Result = 1;
while( true )
{
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
Result = Result * XForModPowerU;
Result = Result % Modulus;
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
XForModPowerU = XForModPowerU * XForModPowerU;
XForModPowerU = XForModPowerU % Modulus;
}
return (uint)Result;
}
internal void SetFromTraditionalInteger( Integer SetFrom )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
DigitsArray[Count].Value = (int)IntMath.GetMod32( SetFrom, (uint)DigitsArray[Count].Prime );
}
}
// Copyright Eric Chauvin 2015.
private int ModularReduction( Integer Result, Integer ToReduce )
{
try
{
if( GeneralBaseArray == null )
throw( new Exception( "SetupGeneralBaseArray() should have already been called." ));
Result.SetToZero();
int HowManyToAdd = ToReduce.GetIndex() + 1;
if( HowManyToAdd > GeneralBaseArray.Length )
throw( new Exception( "Bug. The Input number should have been reduced first. HowManyToAdd > GeneralBaseArray.Length" ));
int BiggestIndex = 0;
for( int Count = 0; Count < HowManyToAdd; Count++ )
{
// The size of the numbers in GeneralBaseArray are
// all less than the size of GeneralBase.
// This multiplication by a uint is with a number
// that is not bigger than GeneralBase. Compare
// this with the two full Muliply() calls done on
// each digit of the quotient in LongDivide3().
// AccumulateBase is set to a new value here.
int CheckIndex = IntMath.MultiplyUIntFromCopy( AccumulateBase, GeneralBaseArray[Count], ToReduce.GetD( Count ));
if( CheckIndex > BiggestIndex )
BiggestIndex = CheckIndex;
Result.Add( AccumulateBase );
}
return Result.GetIndex();
}
catch( Exception Except )
{
throw( new Exception( "Exception in ModularReduction(): " + Except.Message ));
}
}
internal void GetTraditionalInteger( Integer BigBase,
Integer BasePart,
Integer ToTest,
Integer Accumulate )
{
// This takes several seconds for a large number.
try
{
// The first few numbers for the base:
// 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
// This first one has the prime 2 as its base so it's going to
// be set to either zero or one.
Accumulate.SetFromULong( (uint)DigitsArray[0].Value );
BigBase.SetFromULong( 2 );
// Count starts at 1, so it's the prime 3.
for( int Count = 1; Count < DigitsArraySize; Count++ )
{
for( uint CountPrime = 0; CountPrime < DigitsArray[Count].Prime; CountPrime++ )
{
ToTest.Copy( BigBase );
IntMath.MultiplyUInt( ToTest, CountPrime );
// Notice that the first time through this loop it's zero, so the
// base part isn't added if it's already congruent to the Value.
// So even though it goes all the way up through the DigitsArray,
// this whole thing could add up to a small number like 7.
// Compare this part with how GetMod32() is used in
// SetFromTraditionalInteger(). And also, compare this with how
// IntegerMath.NumberIsDivisibleByUInt() works.
BasePart.Copy( ToTest );
ToTest.Add( Accumulate );
// If it's congruent to the Value mod Prime then it's the right number.
if( (uint)DigitsArray[Count].Value == IntMath.GetMod32( ToTest, (uint)DigitsArray[Count].Prime ))
{
Accumulate.Add( BasePart );
break;
}
}
// The Integers have to be big enough to multiply this base.
IntMath.MultiplyUInt( BigBase, (uint)DigitsArray[Count].Prime );
}
// Returns with Accumulate for the value.
}
catch( Exception Except )
{
throw( new Exception( "Exception in GetTraditionalInteger(): " + Except.Message ));
}
}
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;
}
internal void FindSmallPrimeFactorsOnly( Integer FindFromNotChanged )
{
OriginalFindFrom.Copy( FindFromNotChanged );
FindFrom.Copy( FindFromNotChanged );
ClearFactorsArray();
Integer OneFactor;
OneFactorRec Rec;
// while( not forever )
for( int Count = 0; Count < 1000; Count++ )
{
if( Worker.CancellationPending )
return;
uint SmallPrime = IntMath.IsDivisibleBySmallPrime( FindFrom );
if( SmallPrime == 0 )
break; // No more small primes.
// Worker.ReportProgress( 0, "Found a small prime factor: " + SmallPrime.ToString() );
OneFactor = new Integer();
OneFactor.SetFromULong( SmallPrime );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
Rec.IsDefinitelyAPrime = true;
AddFactorRec( Rec );
if( FindFrom.IsULong())
{
ulong CheckLast = FindFrom.GetAsULong();
if( CheckLast == SmallPrime )
{
// Worker.ReportProgress( 0, "It only had small prime factors." );
VerifyFactors();
return; // It had only small prime factors.
}
}
IntMath.Divide( FindFrom, OneFactor, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "Bug in FindSmallPrimeFactorsOnly(). Remainder is not zero." ));
FindFrom.Copy( Quotient );
if( FindFrom.IsOne())
throw( new Exception( "Bug in FindSmallPrimeFactorsOnly(). This was already checked for 1." ));
}
// Worker.ReportProgress( 0, "One factor was not a small prime." );
OneFactor = new Integer();
OneFactor.Copy( FindFrom );
Rec = new OneFactorRec();
Rec.Factor = OneFactor;
AddFactorRec( Rec );
// Worker.ReportProgress( 0, "No more small primes." );
}
