| public RabinMillerTest ( int confidence ) : bool | ||
| confidence | int | |
| return | bool | |
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger integer;
BigInteger integer2;
int num3;
int bitLength = size - 1;
int num2 = size >> 2;
if (size <= 0x20)
{
while (true)
{
integer2 = new BigInteger(bitLength, 2, random);
integer = integer2.ShiftLeft(1).Add(BigInteger.One);
if (integer.IsProbablePrime(certainty, true) && ((certainty <= 2) || integer2.IsProbablePrime(certainty, true)))
{
goto Label_01B9;
}
}
}
Label_006F:
integer2 = new BigInteger(bitLength, 0, random);
Label_0078:
num3 = 0;
while (num3 < primeLists.Length)
{
int intValue = integer2.Remainder(BigPrimeProducts[num3]).IntValue;
if (num3 == 0)
{
int num5 = intValue % 3;
if (num5 != 2)
{
int num6 = (2 * num5) + 2;
integer2 = integer2.Add(BigInteger.ValueOf((long)num6));
intValue = (intValue + num6) % primeProducts[num3];
}
}
foreach (int num8 in primeLists[num3])
{
int num9 = intValue % num8;
if ((num9 == 0) || (num9 == (num8 >> 1)))
{
integer2 = integer2.Add(Six);
goto Label_0078;
}
}
num3++;
}
if ((integer2.BitLength != bitLength) || !integer2.RabinMillerTest(2, random, true))
{
goto Label_006F;
}
integer = integer2.ShiftLeft(1).Add(BigInteger.One);
if ((!integer.RabinMillerTest(certainty, random, true) || ((certainty > 2) && !integer2.RabinMillerTest(certainty - 2, random, true))) || (WNafUtilities.GetNafWeight(integer) < num2))
{
goto Label_006F;
}
Label_01B9:
return(new BigInteger[] { integer, integer2 });
}
private static BigInteger GetRandomNumber()
{
while (true)
{
Random random = new Random();
var number = new BigInteger(1024, random);
if (number.RabinMillerTest(10, random))
{
return(number);
}
}
}
public static bool IsProbablePrime(this BigInteger thisVal, int confidence)
{
// test for divisibility by the smaller primes
for (var p = 0; p < SmallPrimes.Length; p++)
{
BigInteger divisor = SmallPrimes[p];
if (divisor >= thisVal)
{
break;
}
BigInteger resultNum = thisVal % divisor;
if (resultNum == BigInteger.Zero)
{
return(false);
}
}
return(thisVal.RabinMillerTest(confidence));
}
public static bool IsProbablePrime(this BigInteger thisVal, int confidence)
{
// test for divisibility by primes < 2000
for (int p = 0; p < primesBelow2000.Length; p++)
{
BigInteger divisor = primesBelow2000[p];
if (divisor >= thisVal)
{
break;
}
BigInteger resultNum = thisVal % divisor;
if (resultNum == BigInteger.Zero)
{
return(false);
}
}
return(thisVal.RabinMillerTest(confidence));
}
public static bool IsProbablePrime(this BigInteger bi, int confidence = 1024, Random rand = null)
{
rand ??= new Random();
if (bi == 0 || bi.IsEven)
{
return(false);
}
if (bi < 0)
{
bi = -bi;
}
// test for divisibility by primes < 2000
if (_primesBelow2000.TakeWhile(divisor => divisor < bi).Any(divisor => bi % divisor == 0))
{
return(false);
}
return(bi.RabinMillerTest(confidence, rand));
}
public static void Main(string[] args)
{
// Known problem -> these two pseudoprimes passes my implementation of
// primality test but failed in JDK's isProbablePrime test.
byte[] pseudoPrime1 = { (byte)0x00,
(byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
(byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
(byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
(byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
(byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
(byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
(byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
(byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
(byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
(byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
(byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
};
byte[] pseudoPrime2 = { (byte)0x00,
(byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7,
(byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E,
(byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3,
(byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93,
(byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF,
(byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20,
(byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8,
(byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F,
(byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C,
(byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80,
(byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB,
};
Console.WriteLine("List of primes < 2000\n---------------------");
int limit = 100, count = 0;
for(int i = 0; i < 2000; i++)
{
if(i >= limit)
{
Console.WriteLine();
limit += 100;
}
BigInteger p = new BigInteger(-i);
if(p.isProbablePrime())
{
Console.Write(i + ", ");
count++;
}
}
Console.WriteLine("\nCount = " + count);
BigInteger bi1 = new BigInteger(pseudoPrime1);
Console.WriteLine("\n\nPrimality testing for\n" + bi1.ToString() + "\n");
Console.WriteLine("SolovayStrassenTest(5) = " + bi1.SolovayStrassenTest(5));
Console.WriteLine("RabinMillerTest(5) = " + bi1.RabinMillerTest(5));
Console.WriteLine("FermatLittleTest(5) = " + bi1.FermatLittleTest(5));
Console.WriteLine("isProbablePrime() = " + bi1.isProbablePrime());
Console.Write("\nGenerating 512-bits random pseudoprime. . .");
Random rand = new Random();
BigInteger prime = BigInteger.genPseudoPrime(512, 5, rand);
Console.WriteLine("\n" + prime);
//int dwStart = System.Environment.TickCount;
//BigInteger.MulDivTest(100000);
//BigInteger.RSATest(10);
//BigInteger.RSATest2(10);
//Console.WriteLine(System.Environment.TickCount - dwStart);
}
/*
* Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
*
* (see: Handbook of Applied Cryptography 4.86)
*/
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger p, q;
int qLength = size - 1;
int minWeight = size >> 2;
if (size <= 32)
{
for (;;)
{
q = new BigInteger(qLength, 2, random);
p = q.ShiftLeft(1).Add(BigInteger.One);
if (!p.IsProbablePrime(certainty, true))
{
continue;
}
if (certainty > 2 && !q.IsProbablePrime(certainty, true))
{
continue;
}
break;
}
}
else
{
// Note: Modified from Java version for speed
for (;;)
{
q = new BigInteger(qLength, 0, random);
retry:
for (int i = 0; i < primeLists.Length; ++i)
{
int test = q.Remainder(BigPrimeProducts[i]).IntValue;
if (i == 0)
{
int rem3 = test % 3;
if (rem3 != 2)
{
int diff = 2 * rem3 + 2;
q = q.Add(BigInteger.ValueOf(diff));
test = (test + diff) % primeProducts[i];
}
}
int[] primeList = primeLists[i];
for (int j = 0; j < primeList.Length; ++j)
{
int prime = primeList[j];
int qRem = test % prime;
if (qRem == 0 || qRem == (prime >> 1))
{
q = q.Add(Six);
goto retry;
}
}
}
if (q.BitLength != qLength)
{
continue;
}
if (!q.RabinMillerTest(2, random, true))
{
continue;
}
p = q.ShiftLeft(1).Add(BigInteger.One);
if (!p.RabinMillerTest(certainty, random, true))
{
continue;
}
if (certainty > 2 && !q.RabinMillerTest(certainty - 2, random, true))
{
continue;
}
/*
* Require a minimum weight of the NAF representation, since low-weight primes may be
* weak against a version of the number-field-sieve for the discrete-logarithm-problem.
*
* See "The number field sieve for integers of low weight", Oliver Schirokauer.
*/
if (WNafUtilities.GetNafWeight(p) < minWeight)
{
continue;
}
break;
}
}
return(new BigInteger[] { p, q });
}
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
int num = size - 1;
int num2 = size >> 2;
BigInteger bigInteger;
BigInteger bigInteger2;
if (size <= 32)
{
while (true)
{
bigInteger = new BigInteger(num, 2, random);
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
if (bigInteger2.IsProbablePrime(certainty))
{
if (certainty <= 2 || bigInteger.IsProbablePrime(certainty - 2))
{
break;
}
}
}
}
else
{
while (true)
{
bigInteger = new BigInteger(num, 0, random);
while (true)
{
IL_51:
for (int i = 0; i < DHParametersHelper.primeLists.Length; i++)
{
int num3 = bigInteger.Remainder(DHParametersHelper.BigPrimeProducts[i]).IntValue;
if (i == 0)
{
int num4 = num3 % 3;
if (num4 != 2)
{
int num5 = 2 * num4 + 2;
bigInteger = bigInteger.Add(BigInteger.ValueOf((long)num5));
num3 = (num3 + num5) % DHParametersHelper.primeProducts[i];
}
}
int[] array = DHParametersHelper.primeLists[i];
for (int j = 0; j < array.Length; j++)
{
int num6 = array[j];
int num7 = num3 % num6;
if (num7 == 0 || num7 == num6 >> 1)
{
bigInteger = bigInteger.Add(DHParametersHelper.Six);
goto IL_51;
}
}
}
break;
}
if (bigInteger.BitLength == num && bigInteger.RabinMillerTest(2, random))
{
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
if (bigInteger2.RabinMillerTest(certainty, random) && (certainty <= 2 || bigInteger.RabinMillerTest(certainty - 2, random)) && WNafUtilities.GetNafWeight(bigInteger2) >= num2)
{
break;
}
}
}
}
return(new BigInteger[]
{
bigInteger2,
bigInteger
});
}
/*
* Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
*
* (see: Handbook of Applied Cryptography 4.86)
*/
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger p, q;
int qLength = size - 1;
if (size <= 32)
{
for (;;)
{
q = new BigInteger(qLength, 2, random);
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.IsProbablePrime(certainty) &&
(certainty <= 2 || q.IsProbablePrime(certainty)))
{
break;
}
}
}
else
{
// Note: Modified from Java version for speed
for (;;)
{
q = new BigInteger(qLength, 0, random);
retry:
for (int i = 0; i < primeLists.Length; ++i)
{
int test = q.Remainder(PrimeProducts[i]).IntValue;
if (i == 0)
{
int rem3 = test % 3;
if (rem3 != 2)
{
int diff = 2 * rem3 + 2;
q = q.Add(BigInteger.ValueOf(diff));
test = (test + diff) % primeProducts[i];
}
}
int[] primeList = primeLists[i];
for (int j = 0; j < primeList.Length; ++j)
{
int prime = primeList[j];
int qRem = test % prime;
if (qRem == 0 || qRem == (prime >> 1))
{
q = q.Add(Six);
goto retry;
}
}
}
if (q.BitLength != qLength)
{
continue;
}
if (!q.RabinMillerTest(2, random))
{
continue;
}
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.RabinMillerTest(certainty, random) &&
(certainty <= 2 || q.RabinMillerTest(certainty - 2, random)))
{
break;
}
}
}
return(new BigInteger[] { p, q });
}
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
int num = size - 1;
int num2 = size >> 2;
BigInteger bigInteger;
BigInteger bigInteger2;
if (size <= 32)
{
do
{
bigInteger = new BigInteger(num, 2, (Random)(object)random);
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
}while (!bigInteger2.IsProbablePrime(certainty, randomlySelected: true) || (certainty > 2 && !bigInteger.IsProbablePrime(certainty, randomlySelected: true)));
}
else
{
while (true)
{
bigInteger = new BigInteger(num, 0, (Random)(object)random);
while (true)
{
for (int i = 0; i < primeLists.Length; i++)
{
int num3 = bigInteger.Remainder(BigPrimeProducts[i]).IntValue;
if (i == 0)
{
int num4 = num3 % 3;
if (num4 != 2)
{
int num5 = 2 * num4 + 2;
bigInteger = bigInteger.Add(BigInteger.ValueOf(num5));
num3 = (num3 + num5) % primeProducts[i];
}
}
int[] array = primeLists[i];
foreach (int num6 in array)
{
int num7 = num3 % num6;
if (num7 == 0 || num7 == num6 >> 1)
{
goto IL_00cd;
}
}
}
break;
IL_00cd:
bigInteger = bigInteger.Add(Six);
}
if (bigInteger.BitLength == num && bigInteger.RabinMillerTest(2, (Random)(object)random, randomlySelected: true))
{
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
if (bigInteger2.RabinMillerTest(certainty, (Random)(object)random, randomlySelected: true) && (certainty <= 2 || bigInteger.RabinMillerTest(certainty - 2, (Random)(object)random, randomlySelected: true)) && WNafUtilities.GetNafWeight(bigInteger2) >= num2)
{
break;
}
}
}
}
return(new BigInteger[2] {
bigInteger2, bigInteger
});
}
/*
* Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
*
* (see: Handbook of Applied Cryptography 4.86)
*/
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger p, q;
int qLength = size - 1;
if (size <= 32)
{
for (;;)
{
q = new BigInteger(qLength, 2, random);
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.IsProbablePrime(certainty)
&& (certainty <= 2 || q.IsProbablePrime(certainty)))
break;
}
}
else
{
// Note: Modified from Java version for speed
for (;;)
{
q = new BigInteger(qLength, 0, random);
retry:
for (int i = 0; i < primeLists.Length; ++i)
{
int test = q.Remainder(PrimeProducts[i]).IntValue;
if (i == 0)
{
int rem3 = test % 3;
if (rem3 != 2)
{
int diff = 2 * rem3 + 2;
q = q.Add(BigInteger.ValueOf(diff));
test = (test + diff) % primeProducts[i];
}
}
int[] primeList = primeLists[i];
for (int j = 0; j < primeList.Length; ++j)
{
int prime = primeList[j];
int qRem = test % prime;
if (qRem == 0 || qRem == (prime >> 1))
{
q = q.Add(Six);
goto retry;
}
}
}
if (q.BitLength != qLength)
continue;
if (!q.RabinMillerTest(2, random))
continue;
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.RabinMillerTest(certainty, random)
&& (certainty <= 2 || q.RabinMillerTest(certainty - 2, random)))
break;
}
}
return new BigInteger[] { p, q };
}
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
int num = size - 1;
int num2 = size >> 2;
BigInteger bigInteger;
BigInteger bigInteger2;
if (size > 32)
{
while (true)
{
bigInteger = new BigInteger(num, 0, random);
while (true)
{
for (int i = 0; i < primeLists.Length; i++)
{
int num3 = bigInteger.Remainder(BigPrimeProducts[i]).IntValue;
if (i == 0)
{
int num4 = num3 % 3;
if (num4 != 2)
{
int num5 = 2 * num4 + 2;
bigInteger = bigInteger.Add(BigInteger.ValueOf(num5));
num3 = (num3 + num5) % primeProducts[i];
}
}
int[] array = primeLists[i];
int num6 = 0;
while (num6 < array.Length)
{
int num7 = array[num6];
int num8 = num3 % num7;
if (num8 != 0 && num8 != num7 >> 1)
{
num6++;
continue;
}
goto IL_0103;
}
}
break;
IL_0103:
bigInteger = bigInteger.Add(Six);
}
if (bigInteger.BitLength == num && bigInteger.RabinMillerTest(2, random))
{
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
if (bigInteger2.RabinMillerTest(certainty, random) && (certainty <= 2 || bigInteger.RabinMillerTest(certainty - 2, random)) && WNafUtilities.GetNafWeight(bigInteger2) >= num2)
{
break;
}
}
}
}
else
{
do
{
bigInteger = new BigInteger(num, 2, random);
bigInteger2 = bigInteger.ShiftLeft(1).Add(BigInteger.One);
}while (!bigInteger2.IsProbablePrime(certainty) || (certainty > 2 && !bigInteger.IsProbablePrime(certainty - 2)));
}
return(new BigInteger[2]
{
bigInteger2,
bigInteger
});
}
