private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
BigInteger p, p1, p2, q, q1, q2;
// 1, 2, 3, 4 covered by Guards
// 5
var workingSeed = param.Seed.ToPositiveBigInteger();
// 6
var pResult = PrimeGeneratorHelper.ProvablePrimeConstruction(_sha, param.Modulus / 2, param.BitLens[0], param.BitLens[1], workingSeed, param.PublicE);
if (!pResult.Success)
{
return(new PrimeGeneratorResult($"Bad p gen: {pResult.ErrorMessage}"));
}
p = pResult.Prime;
p1 = pResult.Prime1;
p2 = pResult.Prime2;
workingSeed = pResult.PrimeSeed;
do
{
// 7
var qResult = PrimeGeneratorHelper.ProvablePrimeConstruction(_sha, param.Modulus / 2, param.BitLens[2], param.BitLens[3], workingSeed, param.PublicE);
if (!qResult.Success)
{
return(new PrimeGeneratorResult($"Bad q gen: {qResult.ErrorMessage}"));
}
q = qResult.Prime;
q1 = qResult.Prime1;
q2 = qResult.Prime2;
workingSeed = qResult.PrimeSeed;
// 8
} while (BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100));
var auxValues = new AuxiliaryResult();
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}
private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
// 1, 2, 3, 4 covered by guards
// 5
var workingSeed = param.Seed.ToPositiveBigInteger();
// 6
var ppcResult = PrimeGeneratorHelper.ProvablePrimeConstruction(_sha, param.Modulus / 2, 1, 1, workingSeed, param.PublicE);
if (!ppcResult.Success)
{
return(new PrimeGeneratorResult($"Bad Provable Prime Construction for p: {ppcResult.ErrorMessage}"));
}
var p = ppcResult.Prime;
workingSeed = ppcResult.PrimeSeed;
BigInteger q;
do
{
// 7
ppcResult = PrimeGeneratorHelper.ProvablePrimeConstruction(_sha, param.Modulus / 2, 1, 1, workingSeed, param.PublicE);
if (!ppcResult.Success)
{
return(new PrimeGeneratorResult($"Bad Provable Prime Construction for q: {ppcResult.ErrorMessage}"));
}
q = ppcResult.Prime;
workingSeed = ppcResult.PrimeSeed;
// 8
} while (BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100));
// 9, 10
var auxValues = new AuxiliaryResult();
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}
private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
BigInteger p, p1, p2, q, q1, q2, xp, xq;
// 1, 2, 3, 4 covered by guards
// 5
var p1Result = PrimeGen186_4.ShaweTaylorRandomPrime(param.BitLens[0], param.Seed.ToPositiveBigInteger(), _sha);
if (!p1Result.Success)
{
return(new PrimeGeneratorResult($"Failed to generate p1: {p1Result.ErrorMessage}"));
}
var p2Result = PrimeGen186_4.ShaweTaylorRandomPrime(param.BitLens[1], p1Result.PrimeSeed, _sha);
if (!p2Result.Success)
{
return(new PrimeGeneratorResult($"Failed to generate p2: {p2Result.ErrorMessage}"));
}
p1 = p1Result.Prime;
p2 = p2Result.Prime;
var pResult = PrimeGeneratorHelper.ProbablePrimeFactor(_primeTest, _entropyProvider, _pBound, param.A, p1, p2, param.Modulus, param.PublicE);
if (!pResult.Success)
{
return(new PrimeGeneratorResult($"Failed to generate p: {pResult.ErrorMessage}"));
}
p = pResult.Prime;
xp = pResult.XPrime;
do
{
// 6
var q1Result = PrimeGen186_4.ShaweTaylorRandomPrime(param.BitLens[2], p2Result.PrimeSeed, _sha);
if (!q1Result.Success)
{
return(new PrimeGeneratorResult($"Failed to generate q1: {q1Result.ErrorMessage}"));
}
var q2Result = PrimeGen186_4.ShaweTaylorRandomPrime(param.BitLens[3], q1Result.PrimeSeed, _sha);
if (!q2Result.Success)
{
return(new PrimeGeneratorResult($"Failed to generate q2: {q2Result.ErrorMessage}"));
}
q1 = q1Result.Prime;
q2 = q2Result.Prime;
var qResult = PrimeGeneratorHelper.ProbablePrimeFactor(_primeTest, _entropyProvider, _pBound, param.B, q1, q2, param.Modulus, param.PublicE);
if (!qResult.Success)
{
return(new PrimeGeneratorResult($"Failed to generate q: {qResult.ErrorMessage}"));
}
q = qResult.Prime;
xq = qResult.XPrime;
// 7
} while (BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100) ||
BigInteger.Abs(xp - xq) <= NumberTheory.Pow2(param.Modulus / 2 - 100));
var auxValues = new AuxiliaryResult {
XP = xp, XQ = xq
};
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}
private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
BigInteger p, p1, p2, q, q1, q2, xp, xq, xp1, xp2, xq1, xq2;
// 1, 2, 3 covered by guards
// 4
xp1 = _entropyProvider.GetEntropy(param.BitLens[0]).ToPositiveBigInteger();
if (xp1.IsEven)
{
xp1++;
}
xp2 = _entropyProvider.GetEntropy(param.BitLens[1]).ToPositiveBigInteger();
if (xp2.IsEven)
{
xp2++;
}
p1 = xp1;
while (!PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, p1, true))
{
p1 += 2;
}
p2 = xp2;
while (!PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, p2, true))
{
p2 += 2;
}
var pResult = PrimeGeneratorHelper.ProbablePrimeFactor(_primeTestMode, _entropyProvider, _pBound, param.A, p1, p2, param.Modulus, param.PublicE);
if (!pResult.Success)
{
return(new PrimeGeneratorResult($"Failed to generate p: {pResult.ErrorMessage}"));
}
p = pResult.Prime;
xp = pResult.XPrime;
// 5
do
{
xq1 = _entropyProvider.GetEntropy(param.BitLens[2]).ToPositiveBigInteger();
if (xq1.IsEven)
{
xq1++;
}
xq2 = _entropyProvider.GetEntropy(param.BitLens[3]).ToPositiveBigInteger();
if (xq2.IsEven)
{
xq2++;
}
q1 = xq1;
while (!PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, q1, true))
{
q1 += 2;
}
q2 = xq2;
while (!PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, q2, true))
{
q2 += 2;
}
var qResult = PrimeGeneratorHelper.ProbablePrimeFactor(_primeTestMode, _entropyProvider, _pBound, param.B, q1, q2, param.Modulus, param.PublicE);
if (!qResult.Success)
{
return(new PrimeGeneratorResult($"Failed to generate q: {qResult.ErrorMessage}"));
}
q = qResult.Prime;
xq = qResult.XPrime;
// 6
} while (BigInteger.Abs(xp - xq) <= NumberTheory.Pow2(param.Modulus / 2 - 100) ||
BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100));
var auxValues = new AuxiliaryResult {
XP1 = xp1, XP2 = xp2, XP = xp, XQ1 = xq1, XQ2 = xq2, XQ = xq
};
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}
public PrimeGeneratorResult(PrimePair primes, AuxiliaryResult aux)
{
Primes = primes;
AuxValues = aux;
}
private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
// 1, 2, 3 performed by guards
// 4, 4.1
var i = 0;
BigInteger p = 0;
var pqLowerBound = GetBound(param.Modulus);
do
{
do
{
// 4.2
if (p != 0 && _kat)
{
return(new PrimeGeneratorResult("Given p less than sqrt(2) * 2 ^ (n/2) - 1, need to get a new random number."));
}
p = _entropyProvider.GetEntropy(param.Modulus / 2).ToPositiveBigInteger();
// 4.3
if (_performAShift)
{
p += (param.A - p).PosMod(8);
}
else if (p.IsEven)
{
p++;
}
// 4.4
} while (p < pqLowerBound);
// 4.5
if (NumberTheory.GCD(p - 1, param.PublicE) == 1)
{
if (PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, p, false))
{
break;
}
}
// 4.6, 4.7
i++;
if (i >= _iBoundForP * (param.Modulus / 2))
{
return(new PrimeGeneratorResult("Too many iterations for p"));
}
if (_kat)
{
return(new PrimeGeneratorResult("Given p is not prime"));
}
} while (!_kat);
// 5, 5.1
i = 0;
BigInteger q = 0;
do
{
do
{
// 5.2
if (q != 0 && _kat)
{
return(new PrimeGeneratorResult("Given q less than sqrt(2) * 2 ^ (n/2) - 1, need to get a new random number."));
}
q = _entropyProvider.GetEntropy(param.Modulus / 2).ToPositiveBigInteger();
// 5.3
if (_performBShift)
{
q += (param.B - q).PosMod(8);
}
else if (q.IsEven)
{
q++;
}
// 5.4
// 5.5
} while (BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100) || q < pqLowerBound);
// 5.6
if (NumberTheory.GCD(q - 1, param.PublicE) == 1)
{
if (PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, q, false))
{
break;
}
}
// 5.7, 5.8
i++;
if (i >= _iBoundForQ * (param.Modulus / 2))
{
return(new PrimeGeneratorResult("Too many iterations for q"));
}
if (_kat)
{
return(new PrimeGeneratorResult("Given q is not prime"));
}
} while (!_kat);
var auxValues = new AuxiliaryResult();
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}
public KeyResult(KeyPair key, AuxiliaryResult aux)
{
Key = key;
AuxValues = aux;
}
