ParallelPrime.cs

/*
    FiatShamirIdentification

    Copyright 2015 Ivan Sarno

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
//version V.2.2

using System;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Threading;

namespace FiatShamirIdentification
{
    /// <summary>
    ///     Utility for prime numbers.
    ///     parallel version.
    ///     for internal use.
    /// </summary>
    internal class ParallelPrime : IPrime
    {
        private readonly Random _generator;
        private readonly uint _precision; //precision of Miller-Rabin primality test
        private readonly uint _size;
        private readonly int _threads;
        private readonly AutoResetEvent _wait;
        private bool _continue;
        private BigInteger _current;
        private int _pass;

        /// <summary>
        /// </summary>
        /// <param name="seed">seed of random number generator</param>
        /// <param name="precision">precision of Miller-Rabin test, error = 1/2^(2*precision)</param>
        /// <param name="wordSize">length in bytes of number generated</param>
        /// <param name="threads">number of threads to use</param>
        public ParallelPrime(int seed, uint precision = 20, uint wordSize = 128, int threads = 2)
        {
            if (precision < 5 || wordSize < 8 || threads < 2)
                throw new ArgumentException("precision < 5 or wordSize < 8 or threads < 2");
            _precision = precision;
            _generator = new Random(seed);
            _size = wordSize;
            _wait = new AutoResetEvent(false);
            _threads = threads;
        }

        /// <summary>
        /// </summary>
        /// <param name="precision">precision of Miller-Rabin test, error = 1/2^(2*precision)</param>
        /// <param name="wordSize">length in bytes of number generated</param>
        /// <param name="threads">number of threads to use</param>
        public ParallelPrime(uint precision = 20, uint wordSize = 128, int threads = 2)
        {
            if (precision < 5 || wordSize < 8 || threads < 2)
                throw new ArgumentException("precision < 5 or wordSize < 8 or threads < 2");
            _precision = precision;
            _generator = new Random();
            _size = wordSize;
            _wait = new AutoResetEvent(false);
            _threads = threads;
        }


        /// <summary>
        ///     Primality test.
        /// </summary>
        /// <param name="number">number to test</param>
        /// <returns>true if number is prime</returns>
        public bool IsPrime(ref BigInteger number)
        {
            if (number == 2)
                return true;
            if (number.IsEven)
                return false;

            return number > 2 && MRtest(ref number, new byte[_size], _generator);
        }

        /// <summary>
        ///     Return the first prime number following the argument.
        /// </summary>
        /// <param name="number">current number</param>
        /// <returns>next prime number</returns>
        public BigInteger NextPrime(BigInteger number)
        {
            if (number < 2)
                return 2;
            if (number.IsEven)
                number++;
            _current = number;
            _continue = true;
            _pass = 1;

            for (var i = 0; i < _threads; i++) ThreadPool.QueueUserWorkItem(Routine, i);

            _wait.WaitOne();
            return _current;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private bool MRpredicate1(ref BigInteger y, ref BigInteger z, ref BigInteger number)
        {
            return _continue && BigInteger.ModPow(y, z, number) == 1;
        }

        private bool MRpredicate2(ref BigInteger y, ref BigInteger number, ref BigInteger z, uint w)
        {
            if (!_continue)
                return false;
            uint i = 0;
            BigInteger pow2 = 1;
            var cond = BigInteger.ModPow(y, z, number) == number - 1;

            while (!cond && i < w)
            {
                i++;
                pow2 <<= 1;
                cond = BigInteger.ModPow(y, pow2 * z, number) == number - 1;
            }

            return i != w;
        }

        private bool MRtest(ref BigInteger number, byte[] buffer, Random generator)
        {
            MRscomposition(ref number, out var w, out var z);

            var ris = true;
            uint i = 0;

            while (_continue && ris && i < _precision)
            {
                //extract a random number
                generator.NextBytes(buffer);
                buffer[buffer.Length - 1] &= 127; //forces a positive number
                var y = new BigInteger(buffer);
                ////
                y = y % number;
                while (y < 2) //avoids extraction of 0 and 1
                {
                    y += generator.Next();
                    y = y % number;
                }

                //test
                ris = BigInteger.GreatestCommonDivisor(y, number) == 1 &&
                      (MRpredicate1(ref y, ref z, ref number) || MRpredicate2(ref y, ref number, ref z, w));
                i++;
            }

            return ris;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static void MRscomposition(ref BigInteger number, out uint w, out BigInteger z)
        {
            z = number - 1;
            w = 0;
            while (z.IsEven)
            {
                w++;
                z >>= 1;
            }
        }


        //thread's routine
        private void Routine(object threadId)
        {
            var id = (int) threadId;
            var increment = _threads * 2;
            var number = _current + 2 * id;
            var buffer = new byte[_size];
            var generator = new Random(_generator.Next()); //local generator

            while (_continue && !MRtest(ref number, buffer, generator))
                number += increment;

            var pass = Interlocked.CompareExchange(ref _pass, 0, 1);
            if (pass == 0) return;
            _continue = false;
            _current = number;
            _wait.Set();
        }
    }
}