private bool LucasStrongTestHelper(BigInteger thisVal) { long D = 5, sign = -1, dCount = 0; bool done = false; while (!done) { int Jresult = Jacobi(D, thisVal); if (Jresult == -1) done = true; else { if (Jresult == 0 && Math.Abs(D) < thisVal) return false; if (dCount == 20) { BigInteger root = thisVal.Sqrt(); if (root * root == thisVal) return false; } D = (Math.Abs(D) + 2) * sign; sign = -sign; } dCount++; } long Q = (1 - D) >> 2; BigInteger p_add1 = thisVal + 1; int s = 0; for (int index = 0; index < p_add1.DataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_add1._data[index] & mask) != 0) { index = p_add1.DataLength; break; } mask <<= 1; s++; } } BigInteger t = p_add1 >> s; BigInteger constant = new BigInteger(); int nLen = thisVal.DataLength << 1; constant._data[nLen] = 0x00000001; constant.DataLength = nLen + 1; constant = constant / thisVal; BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0); bool isPrime = false; if ((lucas[0].DataLength == 1 && lucas[0]._data[0] == 0) || (lucas[1].DataLength == 1 && lucas[1]._data[0] == 0)) { isPrime = true; } for (int i = 1; i < s; i++) { if (!isPrime) { lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant); lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal; lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal; if ((lucas[1].DataLength == 1 && lucas[1]._data[0] == 0)) isPrime = true; } lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); } if (isPrime) { BigInteger g = thisVal.Gcd(Q); if (g.DataLength == 1 && g._data[0] == 1) { if ((lucas[2]._data[MAX_LENGTH - 1] & 0x80000000) != 0) lucas[2] += thisVal; BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal; if ((temp._data[MAX_LENGTH - 1] & 0x80000000) != 0) temp += thisVal; if (lucas[2] != temp) isPrime = false; } } return isPrime; }
/// <summary> /// Probabilistic prime test based on Rabin-Miller's test. /// </summary> /// <param name="confidence">The amount of times/iterations to check the primality of the current instance.</param> /// <returns>true if the current instance is a strong pseudo-prime to randomly chosen bases, otherwise false if not prime.</returns> public bool RabinMillerTest(int confidence) { BigInteger thisVal; if ((_data[MAX_LENGTH - 1] & 0x80000000) != 0) thisVal = -this; else thisVal = this; if (thisVal.DataLength == 1) { if (thisVal._data[0] == 0 || thisVal._data[0] == 1) return false; else if (thisVal._data[0] == 2 || thisVal._data[0] == 3) return true; } if ((thisVal._data[0] & 0x1) == 0) return false; BigInteger p_sub1 = thisVal - (new BigInteger(1)); int s = 0; for (int index = 0; index < p_sub1.DataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_sub1._data[index] & mask) != 0) { index = p_sub1.DataLength; break; } mask <<= 1; s++; } } BigInteger t = p_sub1 >> s; int bits = thisVal.BitCount(); BigInteger a = new BigInteger(); Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done) { int testBits = 0; while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.GenRandomBits(testBits, rand); int byteLen = a.DataLength; if (byteLen > 1 || (byteLen == 1 && a._data[0] != 1)) done = true; } BigInteger gcdTest = a.Gcd(thisVal); if (gcdTest.DataLength == 1 && gcdTest._data[0] != 1) return false; BigInteger b = a.ModPow(t, thisVal); bool result = false; if (b.DataLength == 1 && b._data[0] == 1) result = true; for (int j = 0; result == false && j < s; j++) { if (b == p_sub1) { result = true; break; } b = (b * b) % thisVal; } if (result == false) return false; } return true; }