SequentialPrime.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;

namespace FiatShamirIdentification
{
    /// <summary>
    ///     Utility for prime numbers.
    ///     sequential version.
    ///     for internal use.
    /// </summary>
    internal class SequentialPrime : IPrime
    {
        private readonly byte[] _buffer; //used for random number generation
        private readonly Random _generator;
        private readonly uint _precision; //precision of Miller-Rabin primality test


        /// <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>
        public SequentialPrime(int seed, uint precision = 20, uint wordSize = 128)
        {
            if (precision < 5 || wordSize < 8)
                throw new ArgumentException("precision < 5 or wordSize < 8");
            _precision = precision;
            _generator = new Random(seed);
            _buffer = new byte[wordSize];
        }

        /// <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>
        public SequentialPrime(uint precision = 20, uint wordSize = 128)
        {
            if (precision < 5 || wordSize < 8)
                throw new ArgumentException("precision < 5 or wordSize < 8");
            _precision = precision;
            _generator = new Random();
            _buffer = new byte[wordSize];
        }


        /// <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);
        }

        /// <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++;

            while (!MRtest(ref number)) //test primality
                number += 2;

            return number;
        }

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

        private static bool MRpredicate2(ref BigInteger y, ref BigInteger number, ref BigInteger z, uint w)
        {
            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)
        {
            MRscomposition(ref number, out var w, out var z);

            var ris = true;
            uint i = 0;


            while (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;
            }
        }
    }
}