/// <summary>Choose a random prime value for use with RSA</summary>
        /// <param name="bitlength">the bit-length of the returned prime</param>
        /// <param name="e">the RSA public exponent</param>
        /// <returns>a prime p, with (p-1) relatively prime to e</returns>
        protected virtual BigInteger ChooseRandomPrime(int bitlength, BigInteger e)
        {
            for (;;)
            {
                BigInteger p = new BigInteger(bitlength, 1, param.Random);

                if (p.Mod(e).Equals(BigInteger.One))
                    continue;

                if (!p.IsProbablePrime(param.Certainty))
                    continue;

                if (!e.Gcd(p.Subtract(BigInteger.One)).Equals(BigInteger.One))
                    continue;

                return p;
            }
        }
        /*
         * 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))
                        continue;

                    if (certainty > 2 && !q.IsProbablePrime(certainty - 2))
                        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))
                        continue;

                    p = q.ShiftLeft(1).Add(BigInteger.One);

                    if (!p.RabinMillerTest(certainty, random))
                        continue;

                    if (certainty > 2 && !q.RabinMillerTest(certainty - 2, random))
                        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 };
        }