/// <summary> /// Constructs a new parse tree for an integer literal. /// </summary> /// <param name="literal">The literal value.</param> /// <param name="integerBase">The integer base of the literal.</param> /// <param name="typeCharacter">The type character on the literal.</param> /// <param name="span">The location of the parse tree.</param> public IntegerLiteralExpression(long literal, IntegerBase integerBase, TypeCharacter typeCharacter, Span span) : base(literal, typeCharacter, TreeType.IntegerLiteralExpression, span) { if (!Enum.IsDefined(typeof(IntegerBase), integerBase)) { throw new ArgumentOutOfRangeException("integerBase"); } _IntegerBase = integerBase; }
/// <summary> /// Constructs a new integer literal. /// </summary> /// <param name="literal">The literal value.</param> /// <param name="integerBase">The integer base of the literal.</param> /// <param name="typeCharacter">The type character of the literal.</param> /// <param name="span">The location of the literal.</param> public IntegerLiteralToken(long literal, IntegerBase integerBase, TypeCharacter typeCharacter, Span span) : base(TokenType.IntegerLiteral, literal, span) { if (!Enum.IsDefined(typeof(IntegerBase), integerBase)) { throw new ArgumentOutOfRangeException("integerBase"); } if (typeCharacter != TypeCharacter.None && typeCharacter != TypeCharacter.IntegerSymbol && typeCharacter != TypeCharacter.IntegerChar && typeCharacter != TypeCharacter.ShortChar && typeCharacter != TypeCharacter.LongSymbol && typeCharacter != TypeCharacter.LongChar) { throw new ArgumentOutOfRangeException("typeCharacter"); } _IntegerBase = integerBase; _TypeCharacter = typeCharacter; }
public static LimitedIntegerToken Parse(string value, IntegerBase numBase, IntegerBitWidth bitWidth, bool isSigned, bool isNeg, string rawToken, SourcePosition position, IConfiguration configuration) { BigInteger val; switch (numBase) { case IntegerBase.Binary: val = value.Replace("b", "").Replace("B", "").BigIntegerFromBinary(); break; case IntegerBase.Octal: val = value.Replace("o", "").Replace("O", "").BigIntegerFromOctal(); break; case IntegerBase.Decimal: val = BigInteger.Parse(value, NumberStyles.Integer); break; case IntegerBase.Hexadecimal: val = BigInteger.Parse(value.Replace("0x", "00").Replace("0X", "00"), NumberStyles.HexNumber); break; default: throw new ParseException($"Unhandled integer base {numBase}."); } return(new LimitedIntegerToken(val, bitWidth, isSigned, isNeg, $"{(isNeg ? "-" : "")}{rawToken}", position, configuration)); }
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. } }