internal static Digits NewPrime(int pBitN, Random generator)
{
if (pBitN < Digit.BitN)
{
throw new ArgumentException();
}
int pDigitN = (pBitN + (Digit.BitN - 1)) / Digit.BitN;
Digits p = new Digits(pDigitN);
while (true)
{
for (
int iteration = 0;
iteration < _IterationsAllowed;
iteration++
)
{
Digits.Random(p, pDigitN, generator);
p[pDigitN - 1] >>= Digit.BitN * pDigitN - pBitN;
p[0] |= 1;
Digits.SetBit(p, pBitN - 1, 1);
Digits.SetBit(p, pBitN - 2, 1);
if (DivisibleBySomeLowPrime(p, pDigitN))
{
continue;
}
Modulus modulus = new Modulus(p, pDigitN, true);
Digits minus1 = new Digits(pDigitN);
Modular
.Neg(modulus._one, minus1, modulus._mod, modulus._digitN);
Digits exp = new Digits(pDigitN);
Digits.Shift(p, -1, exp, pDigitN);
Digits @base = new Digits(pDigitN);
for (int i = 1; i <= _RabinTestN; i++)
{
if (i == 1)
{
Modular.Add(modulus._one
, modulus._one
, @base
, modulus._mod
, modulus._digitN);
}
else
{
Modular.NonZeroRandom(
p, @base, pDigitN, generator);
}
Digits result = new Digits(pDigitN);
modulus._Exp(@base, exp, pDigitN, result);
if (Digits.Compare(result, minus1, pDigitN) == 0)
{
return(p);
}
if (
Digits.Compare(result, modulus._one, pDigitN) != 0
)
{
break;
}
}
}
Debug.Assert(false, "too many iterations");
}
}
public Key(int bitN, Random generator)
{
_modBitN = bitN;
// The public exponent is 2^16 + 1
_eBitN = 17;
_eBytes = new byte[] { 1, 0, 1 };
int p1BitN = (bitN + 1) / 2
, p1ByteN = (p1BitN + 7) / 8
, p1DigitN = (p1BitN + (Digit.BitN - 1)) / Digit.BitN
, p2BitN = bitN / 2
, p2ByteN = (p2BitN + 7) / 8
, p2DigitN = (p2BitN + (Digit.BitN - 1)) / Digit.BitN
, longerDigitN = p1DigitN > p2DigitN ? p1DigitN : p2DigitN;
Digits d1 = new Digits(p1DigitN), d2 = new Digits(p2DigitN);
_modDigits = new Digits(_modDigitN);
_eDigits = new Digits(1);
Digits gcd = new Digits(longerDigitN)
, temp = new Digits(longerDigitN);
Digits.BytesToDigits(_eBytes, 0, _eDigits, _eBitN);
int[] pBitN = new int[] { p1BitN, p2BitN };
int nPrimeFound = 0;
Digits p1 = null, p2 = null;
while (nPrimeFound != 2)
{
int pNowBitN = pBitN[nPrimeFound]
, pNowDigitN
= (pNowBitN + (Digit.BitN - 1)) / Digit.BitN;
Digits pNow = Prime.NewPrime(pNowBitN, generator);
if (nPrimeFound == 0)
{
p1 = pNow;
}
else
{
p2 = pNow;
}
Digits.Sub(pNow, 1, temp, pNowDigitN);
int lgcd;
Digits.ExtendedGcd(_eDigits
, _eDigitN
, temp
, pNowDigitN
, nPrimeFound == 0 ? d1 : d2
, null
, gcd
, out lgcd);
if (Digits.Compare(gcd, 1, lgcd) != 0)
{
Debug.Assert(false, "untested code");
continue;
}
if (
nPrimeFound == 1 &&
Digits.Compare(p1, p1DigitN, p2, p2DigitN) == 0
)
{
Debug.Assert(false, "untested code");
continue;
}
nPrimeFound++;
}
Digits.Mul(p1, p1DigitN, p2, p2DigitN, _modDigits);
int modBitN = Digits.SigBitN(_modDigits, _modDigitN);
Debug.Assert(modBitN == p1BitN + p2BitN && modBitN == _modBitN
, "internal error");
_primeBitN = new int[2] {
p1BitN, p2BitN
};
_modBytes = new byte[_modByteN];
_primeBytes
= new byte[2][] { new byte[p1ByteN], new byte[p2ByteN] };
_dBytes
= new byte[2][] { new byte[p1ByteN], new byte[p2ByteN] };
Digits.DigitsToBytes(_modDigits, _modBytes, 0, _modBitN);
for (int ip = 0; ip != 2; ip++)
{
Digits.DigitsToBytes(
ip == 0 ? p1 : p2, _primeBytes[ip], 0, pBitN[ip]);
Digits.DigitsToBytes(
ip == 0 ? d1 : d2, _dBytes[ip], 0, pBitN[ip]);
}
int moduliCreated = 0;
Digits.BytesToDigits(_eBytes, 0, _eDigits, _eBitN);
_modulus = new Modulus(_modDigits, _modDigitN, true);
_privateModulus = new Modulus[2];
_dDigits = new Digits[2];
_chineseDigits = new Digits[2];
for (int ip = 0; ip != 2; ip++)
{
Digits temp2 = new Digits(_modDigitN);
_dDigits[ip] = new Digits(p1DigitN);
_chineseDigits[ip] = new Digits(p1DigitN);
Digits.BytesToDigits(
_primeBytes[ip], 0, temp2, _primeBitN[ip]);
_privateModulus[ip]
= new
Modulus(temp2
, (_primeBitN[ip] + (Digit.BitN - 1)) / Digit.BitN
, true);
moduliCreated++;
Digits.BytesToDigits(
_dBytes[ip], 0, _dDigits[ip], _primeBitN[ip]);
}
int lgcd2 = 0;
Digits gcd2 = new Digits(_modDigitN);
Digits.ExtendedGcd(_privateModulus[0]._mod
, p1DigitN
, _privateModulus[1]._mod
, p2DigitN
, _chineseDigits[1]
, _chineseDigits[0]
, gcd2
, out lgcd2);
if (Digits.Compare(gcd2, 1, lgcd2) != 0)
{
throw new ArgumentException();
}
}