_Exp(Digits @base, Digits exp, int expDigitN, Digits answer)
{
int expBitNUsed = Digits.SigBitN(exp, expDigitN);
ushort[] widthCutoffs = new ushort[] { 6, 24, 80, 240, 672 };
Digits basepower = answer;
int bucketWidth = 1;
while (
bucketWidth < 5 && widthCutoffs[bucketWidth - 1] < expBitNUsed
)
{
bucketWidth++;
}
Modular.ValidateData(@base, _mod, _digitN);
UInt32 bucketMask = (1U << bucketWidth) - 1;
UInt32 maxBucket = bucketMask;
Digits bucketData = new Digits((int)(_digitN * maxBucket));
Temps2000 temps = new Temps2000();
temps._modulus = this;
temps._bucket[0] = null;
Modular.Add(_one, _one, bucketData, _mod, _digitN);
bool base2 = Digits.Compare(@base, bucketData, _digitN) == 0;
if (base2 && expBitNUsed != 0)
{
int shiftMax
= Digit.BitN * _digitN > 1024 ? 1024 : Digit.BitN * _digitN;
int highExponBitN = 0;
bool bighBitNProcessed = false;
Digits temp = bucketData;
for (int i = expBitNUsed; i-- != 0;)
{
Digit expBit = Digits.GetBit(exp, i);
if (bighBitNProcessed)
{
_Mul(temp, temp, temp);
if (expBit != 0)
{
Modular.Add(temp, temp, temp, _mod, _digitN);
}
}
else
{
highExponBitN = (int)(2 * highExponBitN + expBit);
if (i == 0 || 2 * highExponBitN >= shiftMax)
{
bighBitNProcessed = true;
_Shift(_one, highExponBitN, temp);
}
}
}
temps._bucket[1] = temp;
Debug.Assert(bighBitNProcessed, "internal error");
}
else
{
UInt32 ibucket;
for (ibucket = 1; ibucket <= maxBucket; ibucket++)
{
Digits bloc = bucketData
+ (int)(_digitN
* (ibucket
- 1
+ ((ibucket & 1) == 0 ? maxBucket : 0))
/ 2);
temps._bucket[ibucket] = bloc;
temps._bucketBusy[ibucket] = false;
bloc._Set(_one, _digitN);
}
basepower._Set(@base, _digitN);
Digit carried = 0;
int ndoubling = 0;
for (int i = 0; i != expBitNUsed; i++)
{
Digit bitNow = Digits.GetBit(exp, i);
Debug.Assert(carried >> bucketWidth + 2 == 0
, "internal error");
if (bitNow != 0)
{
while (ndoubling >= bucketWidth + 1)
{
if ((carried & 1) != 0)
{
ibucket = carried & bucketMask;
carried -= ibucket;
temps._modulus
._BucketMul(ibucket, basepower, temps);
}
temps._modulus._BasePowerSquaring(basepower);
carried /= 2;
ndoubling--;
}
carried |= 1U << ndoubling;
}
ndoubling++;
}
while (carried != 0)
{
bool squareNow = false;
if (carried <= maxBucket)
{
ibucket = carried;
}
else if ((carried & 1) == 0)
{
squareNow = true;
}
else if (carried <= 3 * maxBucket)
{
ibucket = maxBucket;
}
else
{
Debug.Assert(false, "untested code");
ibucket = carried & bucketMask;
}
if (squareNow)
{
carried /= 2;
temps._modulus._BasePowerSquaring(basepower);
}
else
{
carried -= ibucket;
temps._modulus._BucketMul(ibucket, basepower, temps);
}
}
for (ibucket = maxBucket; ibucket >= 2; ibucket--)
{
if (temps._bucketBusy[ibucket])
{
bool found = false;
UInt32 jbucket, jbucketMax, kbucket;
Digits bloci;
if ((ibucket & 1) == 0)
{
jbucketMax = ibucket / 2;
}
else
{
jbucketMax = 1;
}
for (
jbucket = ibucket >> 1;
jbucket != ibucket && !found;
jbucket++
)
{
if (temps._bucketBusy[jbucket])
{
jbucketMax = jbucket;
found = temps._bucketBusy[ibucket - jbucket];
}
}
jbucket = jbucketMax;
kbucket = ibucket - jbucket;
bloci = temps._bucket[ibucket];
temps._modulus._BucketMul(jbucket, bloci, temps);
temps._modulus._BucketMul(kbucket, bloci, temps);
}
}
}
answer._Set(temps._bucket[1], _digitN);
}
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();
}
}
