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-/*
- Copyright (c) 2000, 2014, Oracle and/or its affiliates. All rights reserved.
-
- This program is free software; you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation; version 2 of the License.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program; see the file COPYING. If not, write to the
- Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
- MA 02110-1301 USA.
-*/
-
-/* based on Wei Dai's integer.h from CryptoPP */
-
-
-#ifndef TAO_CRYPT_INTEGER_HPP
-#define TAO_CRYPT_INTEGER_HPP
-
-
-#ifdef _MSC_VER
- // 4250: dominance
- // 4660: explicitly instantiating a class already implicitly instantiated
- // 4661: no suitable definition provided for explicit template request
- // 4786: identifer was truncated in debug information
- // 4355: 'this' : used in base member initializer list
-# pragma warning(disable: 4250 4660 4661 4786 4355)
-#endif
-
-
-#include "misc.hpp"
-#include "block.hpp"
-#include "random.hpp"
-#include "file.hpp"
-#include <string.h>
-#ifdef USE_SYS_STL
- #include <algorithm>
-#else
- #include "algorithm.hpp"
-#endif
-
-
-#ifdef TAOCRYPT_X86ASM_AVAILABLE
- #if defined(__GNUC__) && (__GNUC__ >= 4)
- // GCC 4 or greater optimizes too much inline on recursive for bigint,
- // -O3 just as fast without asm here anyway
- #undef TAOCRYPT_X86ASM_AVAILABLE
- #endif
-#endif
-
-#ifdef TAOCRYPT_X86ASM_AVAILABLE
-
-#ifdef _M_IX86
- #if (defined(__INTEL_COMPILER) && (__INTEL_COMPILER >= 500)) || \
- (defined(__ICL) && (__ICL >= 500))
- #define SSE2_INTRINSICS_AVAILABLE
- #define TAOCRYPT_MM_MALLOC_AVAILABLE
- #elif defined(_MSC_VER)
- // _mm_free seems to be the only way to tell if the Processor Pack is
- //installed or not
- #include <malloc.h>
- #if defined(_mm_free)
- #define SSE2_INTRINSICS_AVAILABLE
- #define TAOCRYPT_MM_MALLOC_AVAILABLE
- #endif
- #endif
-#endif
-
-// SSE2 intrinsics work in GCC 3.3 or later
-#if defined(__SSE2__) && (__GNUC__ == 4 || __GNUC_MAJOR__ > 3 || \
- __GNUC_MINOR__ > 2)
- #define SSE2_INTRINSICS_AVAILABLE
-#endif
-
-#endif // X86ASM
-
-
-
-
-namespace TaoCrypt {
-
-#if defined(SSE2_INTRINSICS_AVAILABLE)
-
- // Allocator handling proper alignment
- template <class T>
- class AlignedAllocator : public AllocatorBase<T>
- {
- public:
- typedef typename AllocatorBase<T>::pointer pointer;
- typedef typename AllocatorBase<T>::size_type size_type;
-
- pointer allocate(size_type n, const void* = 0);
- void deallocate(void* p, size_type n);
- pointer reallocate(T* p, size_type oldSize, size_type newSize,
- bool preserve)
- {
- return StdReallocate(*this, p, oldSize, newSize, preserve);
- }
-
- #if !(defined(TAOCRYPT_MALLOC_ALIGNMENT_IS_16) || \
- defined(TAOCRYPT_MEMALIGN_AVAILABLE) || \
- defined(TAOCRYPT_MM_MALLOC_AVAILABLE))
- #define TAOCRYPT_NO_ALIGNED_ALLOC
- AlignedAllocator() : m_pBlock(0) {}
- protected:
- void *m_pBlock;
- #endif
- };
-
- typedef Block<word, AlignedAllocator<word> > AlignedWordBlock;
-#else
- typedef WordBlock AlignedWordBlock;
-#endif
-
-
-
-#ifdef _WIN32
- #undef max // avoid name clash
-#endif
-// general MAX
-template<typename T> inline
-const T& max(const T& a, const T& b)
-{
- return a > b ? a : b;
-}
-
-
-// Large Integer class
-class Integer {
-public:
- enum Sign {POSITIVE = 0, NEGATIVE = 1 };
- enum Signedness { UNSIGNED, SIGNED };
- enum RandomNumberType { ANY, PRIME };
-
- class DivideByZero {};
-
- Integer();
- Integer(const Integer& t);
- Integer(signed long value);
- Integer(Sign s, word highWord, word lowWord);
-
- // BER Decode Source
- explicit Integer(Source&);
-
- Integer(const byte* encodedInteger, unsigned int byteCount,
- Signedness s = UNSIGNED);
-
- ~Integer() {}
-
- static const Integer& Zero();
- static const Integer& One();
-
- Integer& Ref() { return *this; }
-
- Integer(RandomNumberGenerator& rng, const Integer& min,
- const Integer& max);
-
- static Integer Power2(unsigned int e);
-
- unsigned int MinEncodedSize(Signedness = UNSIGNED) const;
- unsigned int Encode(byte* output, unsigned int outputLen,
- Signedness = UNSIGNED) const;
-
- void Decode(const byte* input, unsigned int inputLen,
- Signedness = UNSIGNED);
- void Decode(Source&);
-
- bool IsConvertableToLong() const;
- signed long ConvertToLong() const;
-
- unsigned int BitCount() const;
- unsigned int ByteCount() const;
- unsigned int WordCount() const;
-
- bool GetBit(unsigned int i) const;
- byte GetByte(unsigned int i) const;
- unsigned long GetBits(unsigned int i, unsigned int n) const;
-
- bool IsZero() const { return !*this; }
- bool NotZero() const { return !IsZero(); }
- bool IsNegative() const { return sign_ == NEGATIVE; }
- bool NotNegative() const { return !IsNegative(); }
- bool IsPositive() const { return NotNegative() && NotZero(); }
- bool NotPositive() const { return !IsPositive(); }
- bool IsEven() const { return GetBit(0) == 0; }
- bool IsOdd() const { return GetBit(0) == 1; }
-
- Integer& operator=(const Integer& t);
- Integer& operator+=(const Integer& t);
- Integer& operator-=(const Integer& t);
- Integer& operator*=(const Integer& t) { return *this = Times(t); }
- Integer& operator/=(const Integer& t)
- { return *this = DividedBy(t);}
- Integer& operator%=(const Integer& t) { return *this = Modulo(t); }
- Integer& operator/=(word t) { return *this = DividedBy(t); }
- Integer& operator%=(word t) { return *this = Modulo(t); }
- Integer& operator<<=(unsigned int);
- Integer& operator>>=(unsigned int);
-
-
- void Randomize(RandomNumberGenerator &rng, unsigned int bitcount);
- void Randomize(RandomNumberGenerator &rng, const Integer &min,
- const Integer &max);
-
- void SetBit(unsigned int n, bool value = 1);
- void SetByte(unsigned int n, byte value);
-
- void Negate();
- void SetPositive() { sign_ = POSITIVE; }
- void SetNegative() { if (!!(*this)) sign_ = NEGATIVE; }
- void Swap(Integer& a);
-
- bool operator!() const;
- Integer operator+() const {return *this;}
- Integer operator-() const;
- Integer& operator++();
- Integer& operator--();
- Integer operator++(int)
- { Integer temp = *this; ++*this; return temp; }
- Integer operator--(int)
- { Integer temp = *this; --*this; return temp; }
-
- int Compare(const Integer& a) const;
-
- Integer Plus(const Integer &b) const;
- Integer Minus(const Integer &b) const;
- Integer Times(const Integer &b) const;
- Integer DividedBy(const Integer &b) const;
- Integer Modulo(const Integer &b) const;
- Integer DividedBy(word b) const;
- word Modulo(word b) const;
-
- Integer operator>>(unsigned int n) const { return Integer(*this)>>=n; }
- Integer operator<<(unsigned int n) const { return Integer(*this)<<=n; }
-
- Integer AbsoluteValue() const;
- Integer Doubled() const { return Plus(*this); }
- Integer Squared() const { return Times(*this); }
- Integer SquareRoot() const;
-
- bool IsSquare() const;
- bool IsUnit() const;
-
- Integer MultiplicativeInverse() const;
-
- friend Integer a_times_b_mod_c(const Integer& x, const Integer& y,
- const Integer& m);
- friend Integer a_exp_b_mod_c(const Integer& x, const Integer& e,
- const Integer& m);
-
- static void Divide(Integer& r, Integer& q, const Integer& a,
- const Integer& d);
- static void Divide(word& r, Integer& q, const Integer& a, word d);
- static void DivideByPowerOf2(Integer& r, Integer& q, const Integer& a,
- unsigned int n);
- static Integer Gcd(const Integer& a, const Integer& n);
-
- Integer InverseMod(const Integer& n) const;
- word InverseMod(word n) const;
-
-private:
- friend class ModularArithmetic;
- friend class MontgomeryRepresentation;
-
- Integer(word value, unsigned int length);
- int PositiveCompare(const Integer& t) const;
-
- friend void PositiveAdd(Integer& sum, const Integer& a, const Integer& b);
- friend void PositiveSubtract(Integer& diff, const Integer& a,
- const Integer& b);
- friend void PositiveMultiply(Integer& product, const Integer& a,
- const Integer& b);
- friend void PositiveDivide(Integer& remainder, Integer& quotient, const
- Integer& dividend, const Integer& divisor);
- AlignedWordBlock reg_;
- Sign sign_;
-};
-
-inline bool operator==(const Integer& a, const Integer& b)
- {return a.Compare(b)==0;}
-inline bool operator!=(const Integer& a, const Integer& b)
- {return a.Compare(b)!=0;}
-inline bool operator> (const Integer& a, const Integer& b)
- {return a.Compare(b)> 0;}
-inline bool operator>=(const Integer& a, const Integer& b)
- {return a.Compare(b)>=0;}
-inline bool operator< (const Integer& a, const Integer& b)
- {return a.Compare(b)< 0;}
-inline bool operator<=(const Integer& a, const Integer& b)
- {return a.Compare(b)<=0;}
-
-inline Integer operator+(const Integer &a, const Integer &b)
- {return a.Plus(b);}
-inline Integer operator-(const Integer &a, const Integer &b)
- {return a.Minus(b);}
-inline Integer operator*(const Integer &a, const Integer &b)
- {return a.Times(b);}
-inline Integer operator/(const Integer &a, const Integer &b)
- {return a.DividedBy(b);}
-inline Integer operator%(const Integer &a, const Integer &b)
- {return a.Modulo(b);}
-inline Integer operator/(const Integer &a, word b) {return a.DividedBy(b);}
-inline word operator%(const Integer &a, word b) {return a.Modulo(b);}
-
-inline void swap(Integer &a, Integer &b)
-{
- a.Swap(b);
-}
-
-
-Integer CRT(const Integer& xp, const Integer& p, const Integer& xq,
- const Integer& q, const Integer& u);
-
-inline Integer ModularExponentiation(const Integer& a, const Integer& e,
- const Integer& m)
-{
- return a_exp_b_mod_c(a, e, m);
-}
-
-Integer ModularRoot(const Integer& a, const Integer& dp, const Integer& dq,
- const Integer& p, const Integer& q, const Integer& u);
-
-
-
-} // namespace
-
-#endif // TAO_CRYPT_INTEGER_HPP