#ifndef CRYPTOPP_INTEGER_H #define CRYPTOPP_INTEGER_H /** \file */ #include "cryptlib.h" #include "secblock.h" #include #include #ifdef _M_IX86 # if (defined(__INTEL_COMPILER) && (__INTEL_COMPILER >= 500)) || (defined(__ICL) && (__ICL >= 500)) # define SSE2_INTRINSICS_AVAILABLE # elif defined(_MSC_VER) // _mm_free seems to be the only way to tell if the Processor Pack is installed or not # include # if defined(_mm_free) # define SSE2_INTRINSICS_AVAILABLE # endif # endif #endif NAMESPACE_BEGIN(CryptoPP) #ifdef SSE2_INTRINSICS_AVAILABLE template class AlignedAllocator : public AllocatorBase { public: CRYPTOPP_INHERIT_ALLOCATOR_TYPES pointer allocate(size_type n, const void *); void deallocate(void *p, size_type n); pointer reallocate(T *p, size_type oldSize, size_type newSize, bool preserve) { return StandardReallocate(*this, p, oldSize, newSize, preserve); } }; typedef SecBlock > SecAlignedWordBlock; #else typedef SecWordBlock SecAlignedWordBlock; #endif //! multiple precision integer and basic arithmetics /*! This class can represent positive and negative integers with absolute value less than (256**sizeof(word)) ** (256**sizeof(int)). \nosubgrouping */ class Integer : public ASN1Object { public: //! \name ENUMS, EXCEPTIONS, and TYPEDEFS //@{ //! division by zero exception class DivideByZero : public Exception { public: DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {} }; //! class RandomNumberNotFound : public Exception { public: RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {} }; //! enum Signedness { //! UNSIGNED, //! SIGNED}; //! enum RandomNumberType { //! ANY, //! PRIME}; //@} //! \name CREATORS //@{ //! creates the zero integer Integer(); //! copy constructor Integer(const Integer& t); //! convert from signed long Integer(signed long value); //! convert from string /*! str can be in base 2, 8, 10, or 16. Base is determined by a case insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10. */ explicit Integer(const char *str); explicit Integer(const wchar_t *str); //! convert from big-endian byte array Integer(const byte *encodedInteger, unsigned int byteCount, Signedness s=UNSIGNED); //! convert from big-endian form stored in a BufferedTransformation Integer(BufferedTransformation &bt, unsigned int byteCount, Signedness s=UNSIGNED); //! convert from BER encoded byte array stored in a BufferedTransformation object explicit Integer(BufferedTransformation &bt); //! create a random integer /*! The random integer created is uniformly distributed over [0, 2**bitcount). */ Integer(RandomNumberGenerator &rng, unsigned int bitcount); //! avoid calling constructors for these frequently used integers static const Integer &Zero(); //! avoid calling constructors for these frequently used integers static const Integer &One(); //! avoid calling constructors for these frequently used integers static const Integer &Two(); //! create a random integer of special type /*! Ideally, the random integer created should be uniformly distributed over {x | min <= x <= max and x is of rnType and x % mod == equiv}. However the actual distribution may not be uniform because sequential search is used to find an appropriate number from a random starting point. May return (with very small probability) a pseudoprime when a prime is requested and max > lastSmallPrime*lastSmallPrime (lastSmallPrime is declared in nbtheory.h). \throw RandomNumberNotFound if the set is empty. */ Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One()); //! return the integer 2**e static Integer Power2(unsigned int e); //@} //! \name ENCODE/DECODE //@{ //! minimum number of bytes to encode this integer /*! MinEncodedSize of 0 is 1 */ unsigned int MinEncodedSize(Signedness=UNSIGNED) const; //! encode in big-endian format /*! unsigned means encode absolute value, signed means encode two's complement if negative. if outputLen < MinEncodedSize, the most significant bytes will be dropped if outputLen > MinEncodedSize, the most significant bytes will be padded */ unsigned int Encode(byte *output, unsigned int outputLen, Signedness=UNSIGNED) const; //! unsigned int Encode(BufferedTransformation &bt, unsigned int outputLen, Signedness=UNSIGNED) const; //! encode using Distinguished Encoding Rules, put result into a BufferedTransformation object void DEREncode(BufferedTransformation &bt) const; //! encode absolute value as big-endian octet string void DEREncodeAsOctetString(BufferedTransformation &bt, unsigned int length) const; //! encode absolute value in OpenPGP format, return length of output unsigned int OpenPGPEncode(byte *output, unsigned int bufferSize) const; //! encode absolute value in OpenPGP format, put result into a BufferedTransformation object unsigned int OpenPGPEncode(BufferedTransformation &bt) const; //! void Decode(const byte *input, unsigned int inputLen, Signedness=UNSIGNED); //! //* Precondition: bt.MaxRetrievable() >= inputLen void Decode(BufferedTransformation &bt, unsigned int inputLen, Signedness=UNSIGNED); //! void BERDecode(const byte *input, unsigned int inputLen); //! void BERDecode(BufferedTransformation &bt); //! decode nonnegative value as big-endian octet string void BERDecodeAsOctetString(BufferedTransformation &bt, unsigned int length); class OpenPGPDecodeErr : public Exception { public: OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {} }; //! void OpenPGPDecode(const byte *input, unsigned int inputLen); //! void OpenPGPDecode(BufferedTransformation &bt); //@} //! \name ACCESSORS //@{ //! return true if *this can be represented as a signed long bool IsConvertableToLong() const; //! return equivalent signed long if possible, otherwise undefined signed long ConvertToLong() const; //! number of significant bits = floor(log2(abs(*this))) + 1 unsigned int BitCount() const; //! number of significant bytes = ceiling(BitCount()/8) unsigned int ByteCount() const; //! number of significant words = ceiling(ByteCount()/sizeof(word)) unsigned int WordCount() const; //! return the i-th bit, i=0 being the least significant bit bool GetBit(unsigned int i) const; //! return the i-th byte byte GetByte(unsigned int i) const; //! return n lowest bits of *this >> i 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;} //@} //! \name MANIPULATORS //@{ //! 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); //! set this Integer to a random element of {x | min <= x <= max and x is of rnType and x % mod == equiv} /*! returns false if the set is empty */ bool Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One()); bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs); void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs) { if (!GenerateRandomNoThrow(rng, params)) throw RandomNumberNotFound(); } //! set the n-th bit to value void SetBit(unsigned int n, bool value=1); //! set the n-th byte to value void SetByte(unsigned int n, byte value); //! void Negate(); //! void SetPositive() {sign = POSITIVE;} //! void SetNegative() {if (!!(*this)) sign = NEGATIVE;} //! void swap(Integer &a); //@} //! \name UNARY OPERATORS //@{ //! 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;} //@} //! \name BINARY OPERATORS //@{ //! signed comparison /*! \retval -1 if *this < a \retval 0 if *this = a \retval 1 if *this > a */ 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;} //@} //! \name OTHER ARITHMETIC FUNCTIONS //@{ //! Integer AbsoluteValue() const; //! Integer Doubled() const {return Plus(*this);} //! Integer Squared() const {return Times(*this);} //! extract square root, if negative return 0, else return floor of square root Integer SquareRoot() const; //! return whether this integer is a perfect square bool IsSquare() const; //! is 1 or -1 bool IsUnit() const; //! return inverse if 1 or -1, otherwise return 0 Integer MultiplicativeInverse() const; //! modular multiplication friend Integer a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m); //! modular exponentiation friend Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m); //! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d)) static void Divide(Integer &r, Integer &q, const Integer &a, const Integer &d); //! use a faster division algorithm when divisor is short static void Divide(word &r, Integer &q, const Integer &a, word d); //! returns same result as Divide(r, q, a, Power2(n)), but faster static void DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n); //! greatest common divisor static Integer Gcd(const Integer &a, const Integer &n); //! calculate multiplicative inverse of *this mod n Integer InverseMod(const Integer &n) const; //! word InverseMod(word n) const; //@} //! \name INPUT/OUTPUT //@{ //! friend std::istream& operator>>(std::istream& in, Integer &a); //! friend std::ostream& operator<<(std::ostream& out, const Integer &a); //@} private: friend class ModularArithmetic; friend class MontgomeryRepresentation; friend class HalfMontgomeryRepresentation; 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 "ient, const Integer ÷nd, const Integer &divisor); enum Sign {POSITIVE=0, NEGATIVE=1}; SecAlignedWordBlock reg; Sign sign; }; //! inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;} //! inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;} //! inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;} //! inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;} //! inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;} //! inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;} //! inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);} //! inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);} //! inline CryptoPP::Integer operator*(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Times(b);} //! inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);} //! inline CryptoPP::Integer operator%(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Modulo(b);} //! inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);} //! inline CryptoPP::word operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);} NAMESPACE_END NAMESPACE_BEGIN(std) template<> inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b) { a.swap(b); } NAMESPACE_END #endif