/*
         * 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 };
        }
        public BigInteger And(
            BigInteger value)
        {
            if (this.sign == 0 || value.sign == 0)
            {
                return Zero;
            }

            int[] aMag = this.sign > 0
                ? this.magnitude
                : Add(One).magnitude;

            int[] bMag = value.sign > 0
                ? value.magnitude
                : value.Add(One).magnitude;

            bool resultNeg = sign < 0 && value.sign < 0;
            int resultLength = System.Math.Max(aMag.Length, bMag.Length);
            int[] resultMag = new int[resultLength];

            int aStart = resultMag.Length - aMag.Length;
            int bStart = resultMag.Length - bMag.Length;

            for (int i = 0; i < resultMag.Length; ++i)
            {
                int aWord = i >= aStart ? aMag[i - aStart] : 0;
                int bWord = i >= bStart ? bMag[i - bStart] : 0;

                if (this.sign < 0)
                {
                    aWord = ~aWord;
                }

                if (value.sign < 0)
                {
                    bWord = ~bWord;
                }

                resultMag[i] = aWord & bWord;

                if (resultNeg)
                {
                    resultMag[i] = ~resultMag[i];
                }
            }

            BigInteger result = new BigInteger(1, resultMag, true);

            // TODO Optimise this case
            if (resultNeg)
            {
                result = result.Not();
            }

            return result;
        }
        internal static PrivateKey Derivate(this PrivateKey privateKey, byte[] cc, uint nChild, Network network, out byte[] ccChild)
        {
            byte[] l = null;
            if((nChild >> 31) == 0)
            {
                var pubKey = privateKey.GetPublicKey().ToBytes();
                l = Hashes.BIP32Hash(cc, nChild, pubKey[0], pubKey.Skip(1).ToArray());
            }
            else
            {
                l = Hashes.BIP32Hash(cc, nChild, 0, privateKey.ToBytes());
            }
            var ll = l.Take(32).ToArray();
            var lr = l.Skip(32).Take(32).ToArray();

            ccChild = lr;

            var parse256LL = new BigInteger(1, ll);
            var kPar = new BigInteger(1, privateKey.ToBytes());
            var N = ECHelper.CURVE.N;

            if(parse256LL.CompareTo(N) >= 0)
                throw new InvalidOperationException("You won a prize ! this should happen very rarely. Take a screenshot, and roll the dice again.");
            var key = parse256LL.Add(kPar).Mod(N);
            if(key == BigInteger.Zero)
                throw new InvalidOperationException("You won the big prize ! this would happen only 1 in 2^127. Take a screenshot, and roll the dice again.");

            var keyBytes = key.ToByteArrayUnsigned();
            if(keyBytes.Length < 32)
                keyBytes = new byte[32 - keyBytes.Length].Concat(keyBytes).ToArray();

            return new PrivateKey(keyBytes, network);
        }
        private static BigInteger ReduceBarrett(BigInteger x, BigInteger m, BigInteger mr, BigInteger yu)
        {
            int xLen = x.BitLength, mLen = m.BitLength;
            if (xLen < mLen)
                return x;

            if (xLen - mLen > 1)
            {
                int k = m.magnitude.Length;

                BigInteger q1 = x.DivideWords(k - 1);
                BigInteger q2 = q1.Multiply(yu); // TODO Only need partial multiplication here
                BigInteger q3 = q2.DivideWords(k + 1);

                BigInteger r1 = x.RemainderWords(k + 1);
                BigInteger r2 = q3.Multiply(m); // TODO Only need partial multiplication here
                BigInteger r3 = r2.RemainderWords(k + 1);

                x = r1.Subtract(r3);
                if (x.sign < 0)
                {
                    x = x.Add(mr);
                }
            }

            while (x.CompareTo(m) >= 0)
            {
                x = x.Subtract(m);
            }

            return x;
        }