Common/Security/BigInteger.cs

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//************************************************************************************
// BigInteger Class Version 1.03
//
// Copyright (c) 2002 Chew Keong TAN
// All rights reserved.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the
// "Software"), to deal in the Software without restriction, including
// without limitation the rights to use, copy, modify, merge, publish,
// distribute, and/or sell copies of the Software, and to permit persons
// to whom the Software is furnished to do so, provided that the above
// copyright notice(s) and this permission notice appear in all copies of
// the Software and that both the above copyright notice(s) and this
// permission notice appear in supporting documentation.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
// OF THIRD PARTY RIGHTS. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
// HOLDERS INCLUDED IN THIS NOTICE BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL
// INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING
// FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
// NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
// WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
//
//
// Disclaimer
// ----------
// Although reasonable care has been taken to ensure the correctness of this
// implementation, this code should never be used in any application without
// proper verification and testing.  I disclaim all liability and responsibility
// to any person or entity with respect to any loss or damage caused, or alleged
// to be caused, directly or indirectly, by the use of this BigInteger class.
//
// Comments, bugs and suggestions to
// (http://www.codeproject.com/csharp/biginteger.asp)
//
//
// Overloaded Operators +, -, *, /, %, >>, <<, ==, !=, >, <, >=, <=, &, |, ^, ++, --, ~
//
// Features
// --------
// 1) Arithmetic operations involving large signed integers (2's complement).
// 2) Primality test using Fermat little theorm, Rabin Miller's method,
//    Solovay Strassen's method and Lucas strong pseudoprime.
// 3) Modulo exponential with Barrett's reduction.
// 4) Inverse modulo.
// 5) Pseudo prime generation.
// 6) Co-prime generation.
//
//
// Known Problem
// -------------
// This pseudoprime passes my implementation of
// primality test but failed in JDK's isProbablePrime test.
//
//       byte[] pseudoPrime1 = { (byte)0x00,
//             (byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
//             (byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,