/Microsoft.Cryptography.Samples.RSAManaged/FlexInt.cs

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using System;

using System.Security.Cryptography;



namespace Microsoft.Cryptography

{



    internal class FlexInt

    {



        #region Data Storage



        /// <summary>

        /// The Length of this FlexInt

        /// </summary>

        uint length = 1;



        /// <summary>

        /// The data for this FlexInt

        /// </summary>

        uint[] data;



        #endregion



        #region Constants



        /// <summary>

        /// Default length of a FlexInt in bytes

        /// </summary>

        const uint DEFAULT_LEN = 20;



        /// <summary>

        ///		Table of primes below 2000. The values were generated using Mathematica 4.1.

        /// </summary>

        public static readonly uint[] smallPrimes = {

			2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,

			73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,

			157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,

			239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,

			331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,

			421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,

			509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,

			613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,

			709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,

			821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,

			919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,



			1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,

			1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181,

			1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,

			1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,

			1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471,

			1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,

			1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,

			1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,

			1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867,

			1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973,

			1979, 1987, 1993, 1997, 1999, 

		

			2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,

			2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207,

			2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,

			2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389,

			2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,

			2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,

			2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707,

			2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797,

			2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,

			2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,

			

			3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109,

			3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,

			3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329,

			3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449,

			3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,

			3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,

			3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,

			3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,

			3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943,

			3947, 3967, 3989,

			

			4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091,

			4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,

			4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,

			4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,

			4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523,

			4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,

			4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,

			4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,

			4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987,

			4993, 4999,

			

			5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101,

			5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 

			5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,

			5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,

			5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563,

			5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669,

			5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,

			5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869,

			5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987

		};



        public enum Sign : int

        {

            Negative = -1,

            Zero = 0,

            Positive = 1

        };



        #region Exception Messages

        private const string ERR_VALUEISNEGATIVE = "This operation would return a negative value.";

        #endregion



        #endregion



        #region Constructors



        public FlexInt()

        {

            data = new uint[DEFAULT_LEN];

            this.length = DEFAULT_LEN;

        }



        public FlexInt(Sign sign, uint len)

        {

            this.data = new uint[len];

            this.length = len;

        }



        public FlexInt(FlexInt bi)

        {

            this.data = (uint[])bi.data.Clone();

            this.length = bi.length;

        }



        public FlexInt(FlexInt bi, uint len)

        {



            this.data = new uint[len];



            for (uint i = 0; i < bi.length; i++)

                this.data[i] = bi.data[i];



            this.length = bi.length;

        }



        #endregion



        #region Conversions

        public FlexInt(byte[] inData)

        {

            length = (uint)inData.Length >> 2;

            int leftOver = inData.Length & 0x3;



            // length not multiples of 4

            if (leftOver != 0) length++;



            data = new uint[length];



            for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++)

            {

                data[j] = (uint)(

                    (inData[i - 3] << (3 * 8)) |

                    (inData[i - 2] << (2 * 8)) |

                    (inData[i - 1] << (1 * 8)) |

                    (inData[i])

                    );

            }



            switch (leftOver)

            {

                case 1: data[length - 1] = (uint)inData[0]; break;

                case 2: data[length - 1] = (uint)((inData[0] << 8) | inData[1]); break;

                case 3: data[length - 1] = (uint)((inData[0] << 16) | (inData[1] << 8) | inData[2]); break;

            }



            this.Normalize();

        }



        public FlexInt(uint[] inData)

        {

            length = (uint)inData.Length;



            data = new uint[length];



            for (int i = (int)length - 1, j = 0; i >= 0; i--, j++)

                data[j] = inData[i];



            this.Normalize();

        }



        public FlexInt(uint ui)

        {

            data = new uint[] { ui };

        }



        public FlexInt(ulong ul)

        {

            data = new uint[2] { (uint)ul, (uint)(ul >> 32) };

            length = 2;



            this.Normalize();

        }



        public static implicit operator FlexInt(uint value)

        {

            return (new FlexInt(value));

        }



        public static implicit operator FlexInt(int value)

        {

            if (value < 0) throw new ArgumentOutOfRangeException("value");

            return (new FlexInt((uint)value));

        }



        public static implicit operator FlexInt(ulong value)

        {

            return (new FlexInt(value));

        }



        /* This is the FlexInt.Parse method I use. This method works

        because FlexInt.ToString returns the input I gave to Parse. */

        public static FlexInt Parse(string number)

        {

            if (number == null)

                throw new ArgumentNullException("number");



            int i = 0, len = number.Length;

            char c;

            bool digits_seen = false;

            FlexInt val = new FlexInt(0);

            if (number[i] == '+')

            {

                i++;

            }

            else if (number[i] == '-')

            {

                throw new FormatException(ERR_VALUEISNEGATIVE);

            }



            for (; i < len; i++)

            {

                c = number[i];

                if (c == '\0')

                {

                    i = len;

                    continue;

                }

                if (c >= '0' && c <= '9')

                {

                    val = val * 10 + (c - '0');

                    digits_seen = true;

                }

                else

                {

                    if (Char.IsWhiteSpace(c))

                    {

                        for (i++; i < len; i++)

                        {

                            if (!Char.IsWhiteSpace(number[i]))

                                throw new FormatException();

                        }

                        break;

                    }

                    else

                        throw new FormatException();

                }

            }

            if (!digits_seen)

                throw new FormatException();

            return val;

        }



        #endregion



        #region Operators



        public static FlexInt operator +(FlexInt bi1, FlexInt bi2)

        {

            if (bi1 == 0)

                return new FlexInt(bi2);

            else if (bi2 == 0)

                return new FlexInt(bi1);

            else

                return PrimitivesHelper.AddSameSign(bi1, bi2);

        }



        public static FlexInt operator -(FlexInt bi1, FlexInt bi2)

        {

            if (bi2 == 0)

                return new FlexInt(bi1);



            if (bi1 == 0)

                throw new ArithmeticException(ERR_VALUEISNEGATIVE);



            switch (PrimitivesHelper.Compare(bi1, bi2))

            {



                case Sign.Zero:

                    return 0;



                case Sign.Positive:

                    return PrimitivesHelper.Subtract(bi1, bi2);



                case Sign.Negative:

                    throw new ArithmeticException(ERR_VALUEISNEGATIVE);

                default:

                    throw new Exception();

            }

        }



        public static int operator %(FlexInt bi, int i)

        {

            if (i > 0)

                return (int)PrimitivesHelper.DwordMod(bi, (uint)i);

            else

                return -(int)PrimitivesHelper.DwordMod(bi, (uint)-i);

        }



        public static uint operator %(FlexInt bi, uint ui)

        {

            return PrimitivesHelper.DwordMod(bi, (uint)ui);

        }



        public static FlexInt operator %(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.multiByteDivide(bi1, bi2)[1];

        }



        public static FlexInt operator /(FlexInt bi, int i)

        {

            if (i > 0)

                return PrimitivesHelper.DwordDiv(bi, (uint)i);



            throw new ArithmeticException(ERR_VALUEISNEGATIVE);

        }



        public static FlexInt operator /(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.multiByteDivide(bi1, bi2)[0];

        }



        public static FlexInt operator *(FlexInt bi1, FlexInt bi2)

        {

            if (bi1 == 0 || bi2 == 0) return 0;



            //

            // Validate pointers

            //

            if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException("bi1 out of range");

            if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException("bi2 out of range");



            FlexInt ret = new FlexInt(Sign.Positive, bi1.length + bi2.length);



            PrimitivesHelper.Multiply(bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);



            ret.Normalize();

            return ret;

        }



        public static FlexInt operator <<(FlexInt bi1, int shiftVal)

        {

            return PrimitivesHelper.LeftShift(bi1, shiftVal);

        }



        public static FlexInt operator >>(FlexInt bi1, int shiftVal)

        {

            return PrimitivesHelper.RightShift(bi1, shiftVal);

        }



        #endregion



        #region Friendly names for operators



        // with names suggested by FxCop 1.30



        public static FlexInt Add(FlexInt bi1, FlexInt bi2)

        {

            return (bi1 + bi2);

        }



        public static FlexInt Subtract(FlexInt bi1, FlexInt bi2)

        {

            return (bi1 - bi2);

        }



        public static FlexInt Modulus(FlexInt bi1, FlexInt bi2)

        {

            return (bi1 % bi2);

        }



        public static FlexInt Divid(FlexInt bi1, FlexInt bi2)

        {

            return (bi1 / bi2);

        }



        public static FlexInt Multiply(FlexInt bi1, FlexInt bi2)

        {

            return (bi1 * bi2);

        }



        #endregion



        #region Bitwise



        public int BitCount()

        {

            this.Normalize();



            uint value = data[length - 1];

            uint mask = 0x80000000;

            uint bits = 32;



            while (bits > 0 && (value & mask) == 0)

            {

                bits--;

                mask >>= 1;

            }

            bits += ((length - 1) << 5);



            return (int)bits;

        }



        /// <summary>

        /// Tests if the specified bit is 1.

        /// </summary>

        /// <param name="bitNum">The bit to test. The least significant bit is 0.</param>

        /// <returns>True if bitNum is set to 1, else false.</returns>

        public bool TestBit(uint bitNum)

        {

            uint bytePos = bitNum >> 5;             // divide by 32

            byte bitPos = (byte)(bitNum & 0x1F);    // get the lowest 5 bits



            uint mask = (uint)1 << bitPos;

            return ((this.data[bytePos] & mask) != 0);

        }



        public bool TestBit(int bitNum)

        {

            if (bitNum < 0) throw new IndexOutOfRangeException("bitNum out of range");



            uint bytePos = (uint)bitNum >> 5;             // divide by 32

            byte bitPos = (byte)(bitNum & 0x1F);    // get the lowest 5 bits



            uint mask = (uint)1 << bitPos;

            return ((this.data[bytePos] | mask) == this.data[bytePos]);

        }



        public void SetBit(uint bitNum)

        {

            SetBit(bitNum, true);

        }



        public void ClearBit(uint bitNum)

        {

            SetBit(bitNum, false);

        }



        public void SetBit(uint bitNum, bool value)

        {

            uint bytePos = bitNum >> 5;             // divide by 32



            if (bytePos < this.length)

            {

                uint mask = (uint)1 << (int)(bitNum & 0x1F);

                if (value)

                    this.data[bytePos] |= mask;

                else

                    this.data[bytePos] &= ~mask;

            }

        }



        public int LowestSetBit()

        {

            if (this == 0) return -1;

            int i = 0;

            while (!TestBit(i)) i++;

            return i;

        }



        public byte[] GetBytes()

        {

            if (this == 0) return new byte[1];



            int numBits = BitCount();

            int numBytes = numBits >> 3;

            if ((numBits & 0x7) != 0)

                numBytes++;



            byte[] result = new byte[numBytes];



            int numBytesInWord = numBytes & 0x3;

            if (numBytesInWord == 0) numBytesInWord = 4;



            int pos = 0;

            for (int i = (int)length - 1; i >= 0; i--)

            {

                uint val = data[i];

                for (int j = numBytesInWord - 1; j >= 0; j--)

                {

                    result[pos + j] = (byte)(val & 0xFF);

                    val >>= 8;

                }

                pos += numBytesInWord;

                numBytesInWord = 4;

            }

            return result;

        }



        #endregion



        #region Compare



        public static bool operator ==(FlexInt bi1, FlexInt bi2)

        {

            // we need to compare with null

            if ((bi1 as object) == (bi2 as object))

                return true;

            if (null == bi1 || null == bi2)

                return false;

            return PrimitivesHelper.Compare(bi1, bi2) == 0;

        }



        public static bool operator !=(FlexInt bi1, FlexInt bi2)

        {

            // we need to compare with null

            if ((bi1 as object) == (bi2 as object))

                return false;

            if (null == bi1 || null == bi2)

                return true;

            return PrimitivesHelper.Compare(bi1, bi2) != 0;

        }



        public static bool operator >(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.Compare(bi1, bi2) > 0;

        }



        public static bool operator <(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.Compare(bi1, bi2) < 0;

        }



        public static bool operator >=(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.Compare(bi1, bi2) >= 0;

        }



        public static bool operator <=(FlexInt bi1, FlexInt bi2)

        {

            return PrimitivesHelper.Compare(bi1, bi2) <= 0;

        }



        public Sign Compare(FlexInt bi)

        {

            return PrimitivesHelper.Compare(this, bi);

        }



        #endregion



        #region Formatting



        public string ToString(uint radix)

        {

            return ToString(radix, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");

        }



        public string ToString(uint radix, string characterSet)

        {

            if (characterSet.Length < radix)

                throw new ArgumentException("characterSet length is less than radix!", "characterSet");

            if (radix == 1)

                throw new ArgumentException("Radix '1' is not supported. Radix must be greater or equal '2'", "radix");



            if (this == 0) return "0";

            if (this == 1) return "1";



            string result = "";



            FlexInt a = new FlexInt(this);



            while (a != 0)

            {

                uint rem = PrimitivesHelper.SingleByteDivideInPlace(a, radix);

                result = characterSet[(int)rem] + result;

            }



            return result;

        }



        #endregion



        #region Misc



        /// <summary>

        ///     Normalizes this by setting the length to the actual number of

        ///     uints used in data and by setting the sign to Sign.Zero if the

        ///     value of this is 0.

        /// </summary>

        private void Normalize()

        {

            // Normalize length

            while (length > 0 && data[length - 1] == 0) length--;



            // Check for zero

            if (length == 0)

                length++;

        }



        public void Clear()

        {

            for (int i = 0; i < length; i++)

                data[i] = 0x00;

        }



        #endregion



        #region Object Impl



        public override int GetHashCode()

        {

            uint val = 0;



            for (uint i = 0; i < this.length; i++)

                val ^= this.data[i];



            return (int)val;

        }



        public override string ToString()

        {

            return ToString(10);

        }



        public override bool Equals(object o)

        {

            if (o == null) return false;

            if (o is int) return (int)o >= 0 && this == (uint)o;



            return PrimitivesHelper.Compare(this, (FlexInt)o) == 0;

        }



        #endregion



        #region Number Theory



        public FlexInt ModPow(FlexInt exp, FlexInt n)

        {

            ModulusHelper mr = new ModulusHelper(n);

            return mr.Pow(this, exp);

        }



        #endregion



        public class ModulusHelper

        {

            FlexInt mod, constant;



            public ModulusHelper(FlexInt modulus)

            {

                this.mod = modulus;



                // calculate constant = b^ (2k) / m

                uint i = mod.length << 1;



                constant = new FlexInt(Sign.Positive, i + 1);

                constant.data[i] = 0x00000001;



                constant = constant / mod;

            }



            public void BarrettReduction(FlexInt x)

            {

                FlexInt n = mod;

                uint k = n.length,

                    kPlusOne = k + 1,

                    kMinusOne = k - 1;



                // x < mod, so nothing to do.

                if (x.length < k) return;



                FlexInt q3;



                //

                // Validate pointers

                //

                if (x.data.Length < x.length) throw new IndexOutOfRangeException("x out of range");



                // q1 = x / b^ (k-1)

                // q2 = q1 * constant

                // q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne



                // TODO: We should the method in HAC p 604 to do this (14.45)

                q3 = new FlexInt(Sign.Positive, x.length - kMinusOne + constant.length);

                PrimitivesHelper.Multiply(x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);



                // r1 = x mod b^ (k+1)

                // i.e. keep the lowest (k+1) words



                uint lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;



                x.length = lengthToCopy;

                x.Normalize();



                // r2 = (q3 * n) mod b^ (k+1)

                // partial multiplication of q3 and n



                FlexInt r2 = new FlexInt(Sign.Positive, kPlusOne);

                PrimitivesHelper.MultiplyMod2p32pmod(q3.data, (int)kPlusOne, (int)q3.length - (int)kPlusOne, n.data, 0, (int)n.length, r2.data, 0, (int)kPlusOne);



                r2.Normalize();



                if (r2 <= x)

                {

                    PrimitivesHelper.MinusEq(x, r2);

                }

                else

                {

                    FlexInt val = new FlexInt(Sign.Positive, kPlusOne + 1);

                    val.data[kPlusOne] = 0x00000001;



                    PrimitivesHelper.MinusEq(val, r2);

                    PrimitivesHelper.PlusEq(x, val);

                }



                while (x >= n)

                    PrimitivesHelper.MinusEq(x, n);

            }



            public FlexInt Multiply(FlexInt a, FlexInt b)

            {

                if (a == 0 || b == 0) return 0;



                if (a.length >= mod.length << 1)

                    a %= mod;



                if (b.length >= mod.length << 1)

                    b %= mod;



                if (a.length >= mod.length)

                    BarrettReduction(a);



                if (b.length >= mod.length)

                    BarrettReduction(b);



                FlexInt ret = new FlexInt(a * b);

                BarrettReduction(ret);



                return ret;

            }



            public FlexInt Difference(FlexInt a, FlexInt b)

            {

                Sign cmp = PrimitivesHelper.Compare(a, b);

                FlexInt diff;



                switch (cmp)

                {

                    case Sign.Zero:

                        return 0;

                    case Sign.Positive:

                        diff = a - b; break;

                    case Sign.Negative:

                        diff = b - a; break;

                    default:

                        throw new Exception();

                }



                if (diff >= mod)

                {

                    if (diff.length >= mod.length << 1)

                        diff %= mod;

                    else

                        BarrettReduction(diff);

                }

                if (cmp == Sign.Negative)

                    diff = mod - diff;

                return diff;

            }



            public FlexInt Pow(FlexInt b, FlexInt exp)

            {

                if ((mod.data[0] & 1) == 1) return OddPow(b, exp);

                else return EvenPow(b, exp);

            }



            public FlexInt EvenPow(FlexInt b, FlexInt exp)

            {

                FlexInt resultNum = new FlexInt((FlexInt)1, mod.length << 1);

                FlexInt tempNum = new FlexInt(b % mod, mod.length << 1);  // ensures (tempNum * tempNum) < b^ (2k)



                uint totalBits = (uint)exp.BitCount();



                uint[] wkspace = new uint[mod.length << 1];



                // perform squaring and multiply exponentiation

                for (uint pos = 0; pos < totalBits; pos++)

                {

                    if (exp.TestBit(pos))

                    {



                        Array.Clear(wkspace, 0, wkspace.Length);

                        PrimitivesHelper.Multiply(resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);

                        resultNum.length += tempNum.length;

                        uint[] t = wkspace;

                        wkspace = resultNum.data;

                        resultNum.data = t;



                        BarrettReduction(resultNum);

                    }



                    PrimitivesHelper.SquarePositive(tempNum, ref wkspace);

                    BarrettReduction(tempNum);



                    if (tempNum == 1)

                    {

                        return resultNum;

                    }

                }



                return resultNum;

            }



            private FlexInt OddPow(FlexInt b, FlexInt exp)

            {

                FlexInt resultNum = new FlexInt(Montgomery.ToMont(1, mod), mod.length << 1);

                FlexInt tempNum = new FlexInt(Montgomery.ToMont(b, mod), mod.length << 1);  // ensures (tempNum * tempNum) < b^ (2k)

                uint mPrime = Montgomery.Inverse(mod.data[0]);

                uint totalBits = (uint)exp.BitCount();



                uint[] wkspace = new uint[mod.length << 1];



                // perform squaring and multiply exponentiation

                for (uint pos = 0; pos < totalBits; pos++)

                {

                    if (exp.TestBit(pos))

                    {



                        Array.Clear(wkspace, 0, wkspace.Length);

                        PrimitivesHelper.Multiply(resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);

                        resultNum.length += tempNum.length;

                        uint[] t = wkspace;

                        wkspace = resultNum.data;

                        resultNum.data = t;



                        Montgomery.Reduce(resultNum, mod, mPrime);

                    }



                    PrimitivesHelper.SquarePositive(tempNum, ref wkspace);

                    Montgomery.Reduce(tempNum, mod, mPrime);

                }



                Montgomery.Reduce(resultNum, mod, mPrime);

                return resultNum;

            }



            #region Pow Small Base



            public FlexInt Pow(uint b, FlexInt exp)

            {

                if ((mod.data[0] & 1) == 1)

                    return OddPow(b, exp);

                else

                    return EvenPow(b, exp);

            }



            private unsafe FlexInt OddPow(uint b, FlexInt exp)

            {

                exp.Normalize();

                uint[] wkspace = new uint[mod.length << 1 + 1];



                FlexInt resultNum = Montgomery.ToMont((FlexInt)b, this.mod);

                resultNum = new FlexInt(resultNum, mod.length << 1 + 1);



                uint mPrime = Montgomery.Inverse(mod.data[0]);



                uint pos = (uint)exp.BitCount() - 2;



                //

                // We know that the first itr will make the val b

                //



                do

                {

                    //

                    // r = r ^ 2 % m

                    //

                    PrimitivesHelper.SquarePositive(resultNum, ref wkspace);

                    resultNum = Montgomery.Reduce(resultNum, mod, mPrime);



                    if (exp.TestBit(pos))

                    {



                        //

                        // r = r * b % m

                        //



                        fixed (uint* u = resultNum.data)

                        {



                            uint i = 0;

                            ulong mc = 0;



                            do

                            {

                                mc += (ulong)u[i] * (ulong)b;

                                u[i] = (uint)mc;

                                mc >>= 32;

                            } while (++i < resultNum.length);



                            if (resultNum.length < mod.length)

                            {

                                if (mc != 0)

                                {

                                    u[i] = (uint)mc;

                                    resultNum.length++;

                                    while (resultNum >= mod)

                                        PrimitivesHelper.MinusEq(resultNum, mod);

                                }

                            }

                            else if (mc != 0)

                            {



                                //

                                // First, we estimate the quotient by dividing

                                // the first part of each of the numbers. Then

                                // we correct this, if necessary, with a subtraction.

                                //



                                uint cc = (uint)mc;



                                // We would rather have this estimate overshoot,

                                // so we add one to the divisor

                                uint divEstimate;

                                if (mod.data[mod.length - 1] < UInt32.MaxValue)

                                {

                                    divEstimate = (uint)((((ulong)cc << 32) | (ulong)u[i - 1]) /

                                        (mod.data[mod.length - 1] + 1));

                                }

                                else

                                {

                                    // guess but don't divide by 0

                                    divEstimate = (uint)((((ulong)cc << 32) | (ulong)u[i - 1]) /

                                        (mod.data[mod.length - 1]));

                                }



                                uint t;



                                i = 0;

                                mc = 0;

                                do

                                {

                                    mc += (ulong)mod.data[i] * (ulong)divEstimate;

                                    t = u[i];

                                    u[i] -= (uint)mc;

                                    mc >>= 32;

                                    if (u[i] > t) mc++;

                                    i++;

                                } while (i < resultNum.length);

                                cc -= (uint)mc;



                                if (cc != 0)

                                {



                                    uint sc = 0, j = 0;

                                    uint[] s = mod.data;

                                    do

                                    {

                                        uint a = s[j];

                                        if (((a += sc) < sc) | ((u[j] -= a) > ~a)) sc = 1;

                                        else sc = 0;

                                        j++;

                                    } while (j < resultNum.length);

                                    cc -= sc;

                                }

                                while (resultNum >= mod)

                                    PrimitivesHelper.MinusEq(resultNum, mod);

                            }

                            else

                            {

                                while (resultNum >= mod)

                                    PrimitivesHelper.MinusEq(resultNum, mod);

                            }

                        }

                    }

                } while (pos-- > 0);



                resultNum = Montgomery.Reduce(resultNum, mod, mPrime);

                return resultNum;



            }



            private unsafe FlexInt EvenPow(uint b, FlexInt exp)

            {

                exp.Normalize();

                uint[] wkspace = new uint[mod.length << 1 + 1];

                FlexInt resultNum = new FlexInt((FlexInt)b, mod.length << 1 + 1);



                uint pos = (uint)exp.BitCount() - 2;



                //

                // We know that the first itr will make the val b

                //



                do

                {

                    //

                    // r = r ^ 2 % m

                    //

                    PrimitivesHelper.SquarePositive(resultNum, ref wkspace);

                    if (!(resultNum.length < mod.length))

                        BarrettReduction(resultNum);



                    if (exp.TestBit(pos))

                    {



                        //

                        // r = r * b % m

                        //



                        fixed (uint* u = resultNum.data)

                        {



                            uint i = 0;

                            ulong mc = 0;



                            do

                            {

                                mc += (ulong)u[i] * (ulong)b;

                                u[i] = (uint)mc;

                                mc >>= 32;

                            } while (++i < resultNum.length);



                            if (resultNum.length < mod.length)

                            {

                                if (mc != 0)

                                {

                                    u[i] = (uint)mc;

                                    resultNum.length++;

                                    while (resultNum >= mod)

                                        PrimitivesHelper.MinusEq(resultNum, mod);

                                }

                            }

                            else if (mc != 0)

                            {



                                //

                                // First, we estimate the quotient by dividing

                                // the first part of each of the numbers. Then

                                // we correct this, if necessary, with a subtraction.

                                //



                                uint cc = (uint)mc;



                                // We would rather have this estimate overshoot,

                                // so we add one to the divisor

                                uint divEstimate = (uint)((((ulong)cc << 32) | (ulong)u[i - 1]) /

                                    (mod.data[mod.length - 1] + 1));



                                uint t;



                                i = 0;

                                mc = 0;

                                do

                                {

                                    mc += (ulong)mod.data[i] * (ulong)divEstimate;

                                    t = u[i];

                                    u[i] -= (uint)mc;

                                    mc >>= 32;

                                    if (u[i] > t) mc++;

                                    i++;

                                } while (i < resultNum.length);

                                cc -= (uint)mc;



                                if (cc != 0)

                                {



                                    uint sc = 0, j = 0;

                                    uint[] s = mod.data;

                                    do

                                    {

                                        uint a = s[j];

                                        if (((a += sc) < sc) | ((u[j] -= a) > ~a)) sc = 1;

                                        else sc = 0;

                                        j++;

                                    } while (j < resultNum.length);

                                    cc -= sc;

                                }

                                while (resultNum >= mod)

                                    PrimitivesHelper.MinusEq(resultNum, mod);

                            }

                            else

                            {

                                while (resultNum >= mod)

                                    PrimitivesHelper.MinusEq(resultNum, mod);

                            }

                        }

                    }

                } while (pos-- > 0);



                return resultNum;

            }



            #endregion

        }



        public class Montgomery

        {



            private Montgomery()

            {

            }



            public static uint Inverse(uint n)

            {

                uint y = n, z;



                while ((z = n * y) != 1)

                    y *= 2 - z;



                return (uint)-y;

            }



            public static FlexInt ToMont(FlexInt n, FlexInt m)

            {

                n.Normalize(); m.Normalize();



                n <<= (int)m.length * 32;

                n %= m;

                return n;

            }



            public static unsafe FlexInt Reduce(FlexInt n, FlexInt m, uint mPrime)

            {

                FlexInt A = n;

                fixed (uint* a = A.data, mm = m.data)

                {

                    for (uint i = 0; i < m.length; i++)

                    {

                        // The mod here is taken care of by the CPU,

                        // since the multiply will overflow.

                        uint u_i = a[0] * mPrime /* % 2^32 */;



                        //

                        // A += u_i * m;

                        // A >>= 32

                        //



                        // mP = Position in mod

                        // aSP = the source of bits from a

                        // aDP = destination for bits

                        uint* mP = mm, aSP = a, aDP = a;



                        ulong c = (ulong)u_i * ((ulong)*(mP++)) + *(aSP++);

                        c >>= 32;

                        uint j = 1;



                        // Multiply and add

                        for (; j < m.length; j++)

                        {

                            c += (ulong)u_i * (ulong)*(mP++) + *(aSP++);

                            *(aDP++) = (uint)c;

                            c >>= 32;

                        }



                        // Account for carry

                        // TODO: use a better loop here, we dont need the ulong stuff

                        for (; j < A.length; j++)

                        {

                            c += *(aSP++);

                            *(aDP++) = (uint)c;

                            c >>= 32;

                            if (c == 0) { j++; break; }

                        }

                        // Copy the rest

                        for (; j < A.length; j++)

                        {

                            *(aDP++) = *(aSP++);

                        }



                        *(aDP++) = (uint)c;

                    }



                    while (A.length > 1 && a[A.length - 1] == 0) A.length--;



                }

                if (A >= m) PrimitivesHelper.MinusEq(A, m);



                return A;

            }

        }



        /// <summary>

        /// Low level functions for the FlexInt

        /// </summary>

        private sealed class PrimitivesHelper

        {



            #region Addition/Subtraction



            /// <summary>

            /// Adds two numbers with the same sign.

            /// </summary>

            /// <param name="bi1">A FlexInt</param>

            /// <param name="bi2">A FlexInt</param>

            /// <returns>bi1 + bi2</returns>

            public static FlexInt AddSameSign(FlexInt bi1, FlexInt bi2)

            {

                uint[] x, y;

                uint yMax, xMax, i = 0;



                // x should be bigger

                if (bi1.length < bi2.length)

                {

                    x = bi2.data;

                    xMax = bi2.length;

                    y = bi1.data;

                    yMax = bi1.length;

                }

                else

                {

                    x = bi1.data;

                    xMax = bi1.length;

                    y = bi2.data;

                    yMax = bi2.length;

                }



                FlexInt result = new FlexInt(Sign.Positive, xMax + 1);



                uint[] r = result.data;



                ulong sum = 0;



                // Add common parts of both numbers

                do

                {

                    sum = ((ulong)x[i]) + ((ulong)y[i]) + sum;

                    r[i] = (uint)sum;

                    sum >>= 32;

                } while (++i < yMax);



                // Copy remainder of longer number while carry propagation is required

                bool carry = (sum != 0);



                if (carry)

                {



                    if (i < xMax)

                    {

                        do

                            carry = ((r[i] = x[i] + 1) == 0);

                        while (++i < xMax && carry);

                    }



                    if (carry)

                    {

                        r[i] = 1;

                        result.length = ++i;

                        return result;

                    }

                }



                // Copy the rest

                if (i < xMax)

                {

                    do

                        r[i] = x[i];

                    while (++i < xMax);

                }



                result.Normalize();

                return result;

            }



            public static FlexInt Subtract(FlexInt big, FlexInt small)

            {

                FlexInt result = new FlexInt(Sign.Positive, big.length);



                uint[] r = result.data, b = big.data, s = small.data;

                uint i = 0, c = 0;



                do

                {



                    uint x = s[i];

                    if (((x += c) < c) | ((r[i] = b[i] - x) > ~x))

                        c = 1;

                    else

                        c = 0;



                } while (++i < small.length);



                if (i == big.length) goto fixup;



                if (c == 1)

                {

                    do

                        r[i] = b[i] - 1;

                    while (b[i++] == 0 && i < big.length);



                    if (i == big.length) goto fixup;

                }



                do

                    r[i] = b[i];

                while (++i < big.length);



            fixup:



                result.Normalize();

                return result;

            }



            public static void MinusEq(FlexInt big, FlexInt small)

            {

                uint[] b = big.data, s = small.data;

                uint i = 0, c = 0;



                do

                {

                    uint x = s[i];

                    if (((x += c) < c) | ((b[i] -= x) > ~x))

                        c = 1;

                    else

                        c = 0;

                } while (++i < small.length);



                if (i == big.length) goto fixup;



                if (c == 1)

                {

                    do

                        b[i]--;

                    while (b[i++] == 0 && i < big.length);

                }



            fixup:



                // Normalize length

                while (big.length > 0 && big.data[big.length - 1] == 0) big.length--;



                // Check for zero

                if (big.length == 0)

                    big.length++;



            }



            public static void PlusEq(FlexInt bi1, FlexInt bi2)

            {

                uint[] x, y;

                uint yMax, xMax, i = 0;

                bool flag = false;



                // x should be bigger

                if (bi1.length < bi2.length)

                {

                    flag = true;

                    x = bi2.data;

                    xMax = bi2.length;

                    y = bi1.data;

                    yMax = bi1.length;

                }

                else

                {

                    x = bi1.data;

                    xMax = bi1.length;

                    y = bi2.data;

                    yMax = bi2.length;

                }



                uint[] r = bi1.data;



                ulong sum = 0;



                // Add common parts of both numbers

                do

                {

                    sum += ((ulong)x[i]) + ((ulong)y[i]);

                    r[i] = (uint)sum;

                    sum >>= 32;

                } while (++i < yMax);



                // Copy remainder of longer number while carry propagation is required

                bool carry = (sum != 0);



                if (carry)

                {



                    if (i < xMax)

                    {

                        do

                            carry = ((r[i] = x[i] + 1) == 0);

                        while (++i < xMax && carry);

                    }



                    if (carry)

                    {

                        r[i] = 1;

                        bi1.length = ++i;

                        return;

                    }

                }



                // Copy the rest

                if (flag && i < xMax - 1)

                {

                    do

                        r[i] = x[i];

                    while (++i < xMax);

                }



                bi1.length = xMax + 1;

                bi1.Normalize();

            }



            #endregion



            #region Compare



            /// <summary>

            /// Compares two FlexInt

            /// </summary>

            /// <param name="bi1">A FlexInt</param>

            /// <param name="bi2">A FlexInt</param>

            /// <returns>The sign of bi1 - bi2</returns>

            public static Sign Compare(FlexInt bi1, FlexInt bi2)

            {

                //

                // Step 1. Compare the lengths

                //

                uint l1 = bi1.length, l2 = bi2.length;



                while (l1 > 0 && bi1.data[l1 - 1] == 0) l1--;

                while (l2 > 0 && bi2.data[l2 - 1] == 0) l2--;



                if (l1 == 0 && l2 == 0) return Sign.Zero;



                // bi1 len < bi2 len

                if (l1 < l2) return Sign.Negative;

                // bi1 len > bi2 len

                else if (l1 > l2) return Sign.Positive;



                //

                // Step 2. Compare the bits

                //



                uint pos = l1 - 1;



                while (pos != 0 && bi1.data[pos] == bi2.data[pos]) pos--;



                if (bi1.data[pos] < bi2.data[pos])

                    return Sign.Negative;

                else if (bi1.data[pos] > bi2.data[pos])

                    return Sign.Positive;

                else

                    return Sign.Zero;

            }



            #endregion



            #region Division



            #region Dword



            /// <summary>

            /// Performs n / d and n % d in one operation.

            /// </summary>

            /// <param name="n">A FlexInt, upon exit this will hold n / d</param>

            /// <param name="d">The divisor</param>

            /// <returns>n % d</returns>

            public static uint SingleByteDivideInPlace(FlexInt n, uint d)

            {

                ulong r = 0;

                uint i = n.length;



                while (i-- > 0)

                {

                    r <<= 32;

                    r |= n.data[i];

                    n.data[i] = (uint)(r / d);

                    r %= d;

                }

                n.Normalize();



                return (uint)r;

            }



            public static uint Dword…