avt.DynamicFlashRotator.Net.RegCore.Cryptography.BigInteger.BarrettReduction C# (CSharp) Method

        private BigInteger BarrettReduction(BigInteger x, BigInteger n, BigInteger constant)
        {
            int k = n.dataLength,
                kPlusOne = k + 1,
                kMinusOne = k - 1;

            BigInteger q1 = new BigInteger();

            // q1 = x / b^(k-1)
            for (int i = kMinusOne, j = 0; i < x.dataLength; i++, j++)
                q1.data[j] = x.data[i];
            q1.dataLength = x.dataLength - kMinusOne;
            if (q1.dataLength <= 0)
                q1.dataLength = 1;


            BigInteger q2 = q1 * constant;
            BigInteger q3 = new BigInteger();

            // q3 = q2 / b^(k+1)
            for (int i = kPlusOne, j = 0; i < q2.dataLength; i++, j++)
                q3.data[j] = q2.data[i];
            q3.dataLength = q2.dataLength - kPlusOne;
            if (q3.dataLength <= 0)
                q3.dataLength = 1;


            // r1 = x mod b^(k+1)
            // i.e. keep the lowest (k+1) words
            BigInteger r1 = new BigInteger();
            int lengthToCopy = (x.dataLength > kPlusOne) ? kPlusOne : x.dataLength;
            for (int i = 0; i < lengthToCopy; i++)
                r1.data[i] = x.data[i];
            r1.dataLength = lengthToCopy;


            // r2 = (q3 * n) mod b^(k+1)
            // partial multiplication of q3 and n

            BigInteger r2 = new BigInteger();
            for (int i = 0; i < q3.dataLength; i++) {
                if (q3.data[i] == 0) continue;

                ulong mcarry = 0;
                int t = i;
                for (int j = 0; j < n.dataLength && t < kPlusOne; j++, t++) {
                    // t = i + j
                    ulong val = ((ulong)q3.data[i] * (ulong)n.data[j]) +
                                 (ulong)r2.data[t] + mcarry;

                    r2.data[t] = (uint)(val & 0xFFFFFFFF);
                    mcarry = (val >> 32);
                }

                if (t < kPlusOne)
                    r2.data[t] = (uint)mcarry;
            }
            r2.dataLength = kPlusOne;
            while (r2.dataLength > 1 && r2.data[r2.dataLength - 1] == 0)
                r2.dataLength--;

            r1 -= r2;
            if ((r1.data[maxLength - 1] & 0x80000000) != 0)        // negative
                {
                BigInteger val = new BigInteger();
                val.data[kPlusOne] = 0x00000001;
                val.dataLength = kPlusOne + 1;
                r1 += val;
            }

            while (r1 >= n)
                r1 -= n;

            return r1;
        }

        //***********************************************************************
        // Performs the calculation of the kth term in the Lucas Sequence.
        // For details of the algorithm, see reference [9].
        //
        // k must be odd.  i.e LSB == 1
        //***********************************************************************

        private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q,
                                                        BigInteger k, BigInteger n,
                                                        BigInteger constant, int s)
        {
            BigInteger[] result = new BigInteger[3];

            if ((k.data[0] & 0x00000001) == 0)
                throw (new ArgumentException("Argument k must be odd."));

            int numbits = k.bitCount();
            uint mask = (uint)0x1 << ((numbits & 0x1F) - 1);

            // v = v0, v1 = v1, u1 = u1, Q_k = Q^0

            BigInteger v = 2 % n, Q_k = 1 % n,
                       v1 = P % n, u1 = Q_k;
            bool flag = true;

            for (int i = k.dataLength - 1; i >= 0; i--)     // iterate on the binary expansion of k
                {
                //Console.WriteLine("round");
                while (mask != 0) {
                    if (i == 0 && mask == 0x00000001)        // last bit
                        break;

                    if ((k.data[i] & mask) != 0)             // bit is set
                                {
                        // index doubling with addition

                        u1 = (u1 * v1) % n;

                        v = ((v * v1) - (P * Q_k)) % n;
                        v1 = n.BarrettReduction(v1 * v1, n, constant);
                        v1 = (v1 - ((Q_k * Q) << 1)) % n;

                        if (flag)
                            flag = false;
                        else
                            Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

                        Q_k = (Q_k * Q) % n;
                    } else {
                        // index doubling
                        u1 = ((u1 * v) - Q_k) % n;

                        v1 = ((v * v1) - (P * Q_k)) % n;
                        v = n.BarrettReduction(v * v, n, constant);
                        v = (v - (Q_k << 1)) % n;

                        if (flag) {
                            Q_k = Q % n;
                            flag = false;
                        } else
                            Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
                    }

                    mask >>= 1;
                }
                mask = 0x80000000;
            }

            // at this point u1 = u(n+1) and v = v(n)
            // since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1)

            u1 = ((u1 * v) - Q_k) % n;
            v = ((v * v1) - (P * Q_k)) % n;
            if (flag)
                flag = false;
            else
                Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

            Q_k = (Q_k * Q) % n;


            for (int i = 0; i < s; i++) {
                // index doubling
                u1 = (u1 * v) % n;
                v = ((v * v) - (Q_k << 1)) % n;

                if (flag) {
                    Q_k = Q % n;
                    flag = false;
                } else
                    Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
            }

            result[0] = u1;
            result[1] = v;
            result[2] = Q_k;

            return result;
        }