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 }); }