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# integer.h

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    00001 #ifndef CRYPTOPP_INTEGER_H
    00002 #define CRYPTOPP_INTEGER_H
    00003
    00004 /** \file */
    00005
    00006 #include "cryptlib.h"
    00007 #include "secblock.h"
    00008
    00009 #include <iosfwd>
    00010 #include <algorithm>
    00011
    00012 #ifdef CRYPTOPP_X86ASM_AVAILABLE
    00013
    00014 #ifdef _M_IX86
    00015         #if (defined(__INTEL_COMPILER) && (__INTEL_COMPILER >= 500)) || (defined(__ICL) && (__ICL >= 500))
    00016                 #define SSE2_INTRINSICS_AVAILABLE
    00017                 #define CRYPTOPP_MM_MALLOC_AVAILABLE
    00018         #elif defined(_MSC_VER)
    00019                 // _mm_free seems to be the only way to tell if the Processor Pack is installed or not
    00020                 #include <malloc.h>
    00021                 #if defined(_mm_free)
    00022                         #define SSE2_INTRINSICS_AVAILABLE
    00023                         #define CRYPTOPP_MM_MALLOC_AVAILABLE
    00024                 #endif
    00025         #endif
    00026 #endif
    00027
    00028 // SSE2 intrinsics work in GCC 3.3 or later
    00029 #if defined(__SSE2__) && (__GNUC_MAJOR__ > 3 || __GNUC_MINOR__ > 2)
    00030         #define SSE2_INTRINSICS_AVAILABLE
    00031 #endif
    00032
    00033 #endif
    00034
    00035 NAMESPACE_BEGIN(CryptoPP)
    00036
    00037 #if defined(SSE2_INTRINSICS_AVAILABLE)
    00038         template <class T>
    00039         class AlignedAllocator : public AllocatorBase<T>
    00040         {
    00041         public:
    00042                 CRYPTOPP_INHERIT_ALLOCATOR_TYPES
    00043
    00044                 pointer allocate(size_type n, const void *);
    00045                 void deallocate(void *p, size_type n);
    00046                 pointer reallocate(T *p, size_type oldSize, size_type newSize, bool preserve)
    00047                 {
    00048                         return StandardReallocate(*this, p, oldSize, newSize, preserve);
    00049                 }
    00050
    00051         #if !(defined(CRYPTOPP_MALLOC_ALIGNMENT_IS_16) || defined(CRYPTOPP_MEMALIGN_AVAILABLE) || defined(CRYPTOPP_MM_MALLOC_AVAILABLE))
    00052         #define CRYPTOPP_NO_ALIGNED_ALLOC
    00053                 AlignedAllocator() : m_pBlock(NULL) {}
    00054         protected:
    00055                 void *m_pBlock;
    00056         #endif
    00057         };
    00058
    00059         template class CRYPTOPP_DLL AlignedAllocator<word>;
    00060         typedef SecBlock<word, AlignedAllocator<word> > SecAlignedWordBlock;
    00061 #else
    00062         typedef SecWordBlock SecAlignedWordBlock;
    00063 #endif
    00064
    00065 void CRYPTOPP_DLL DisableSSE2();
    00066
    00067 //! multiple precision integer and basic arithmetics
    00068 /*! This class can represent positive and negative integers
    00069         with absolute value less than (256**sizeof(word)) ** (256**sizeof(int)).
    00070         \nosubgrouping
    00071 */
    00072 class CRYPTOPP_DLL Integer : public ASN1Object
    00073 {
    00074 public:
    00075         //! \name ENUMS, EXCEPTIONS, and TYPEDEFS
    00076         //@{
    00077                 //! division by zero exception
    00078                 class DivideByZero : public Exception
    00079                 {
    00080                 public:
    00081                         DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {}
    00082                 };
    00083
    00084                 //!
    00085                 class RandomNumberNotFound : public Exception
    00086                 {
    00087                 public:
    00088                         RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {}
    00089                 };
    00090
    00091                 //!
    00092                 enum Sign {POSITIVE=0, NEGATIVE=1};
    00093
    00094                 //!
    00095                 enum Signedness {
    00096                 //!
    00097                         UNSIGNED,
    00098                 //!
    00099                         SIGNED};
    00100
    00101                 //!
    00102                 enum RandomNumberType {
    00103                 //!
    00104                         ANY,
    00105                 //!
    00106                         PRIME};
    00107         //@}
    00108
    00109         //! \name CREATORS
    00110         //@{
    00111                 //! creates the zero integer
    00112                 Integer();
    00113
    00114                 //! copy constructor
    00115                 Integer(const Integer& t);
    00116
    00117                 //! convert from signed long
    00118                 Integer(signed long value);
    00119
    00120                 //! convert from lword
    00121                 Integer(Sign s, lword value);
    00122
    00123                 //! convert from two words
    00124                 Integer(Sign s, word highWord, word lowWord);
    00125
    00126                 //! convert from string
    00127                 /*! str can be in base 2, 8, 10, or 16.  Base is determined by a
    00128                         case insensitive suffix of 'h', 'o', or 'b'.  No suffix means base 10.
    00129                 */
    00130                 explicit Integer(const char *str);
    00131                 explicit Integer(const wchar_t *str);
    00132
    00133                 //! convert from big-endian byte array
    00134                 Integer(const byte *encodedInteger, unsigned int byteCount, Signedness s=UNSIGNED);
    00135
    00136                 //! convert from big-endian form stored in a BufferedTransformation
    00137                 Integer(BufferedTransformation &bt, unsigned int byteCount, Signedness s=UNSIGNED);
    00138
    00139                 //! convert from BER encoded byte array stored in a BufferedTransformation object
    00140                 explicit Integer(BufferedTransformation &bt);
    00141
    00142                 //! create a random integer
    00143                 /*! The random integer created is uniformly distributed over [0, 2**bitcount). */
    00144                 Integer(RandomNumberGenerator &rng, unsigned int bitcount);
    00145
    00146                 //! avoid calling constructors for these frequently used integers
    00147                 static const Integer &Zero();
    00148                 //! avoid calling constructors for these frequently used integers
    00149                 static const Integer &One();
    00150                 //! avoid calling constructors for these frequently used integers
    00151                 static const Integer &Two();
    00152
    00153                 //! create a random integer of special type
    00154                 /*! Ideally, the random integer created should be uniformly distributed
    00155                         over {x | min <= x <= max and x is of rnType and x % mod == equiv}.
    00156                         However the actual distribution may not be uniform because sequential
    00157                         search is used to find an appropriate number from a random starting
    00158                         point.
    00159                         May return (with very small probability) a pseudoprime when a prime
    00160                         is requested and max > lastSmallPrime*lastSmallPrime (lastSmallPrime
    00161                         is declared in nbtheory.h).
    00162                         \throw RandomNumberNotFound if the set is empty.
    00163                 */
    00164                 Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One());
    00165
    00166                 //! return the integer 2**e
    00167                 static Integer Power2(unsigned int e);
    00168         //@}
    00169
    00170         //! \name ENCODE/DECODE
    00171         //@{
    00172                 //! minimum number of bytes to encode this integer
    00173                 /*! MinEncodedSize of 0 is 1 */
    00174                 unsigned int MinEncodedSize(Signedness=UNSIGNED) const;
    00175                 //! encode in big-endian format
    00176                 /*! unsigned means encode absolute value, signed means encode two's complement if negative.
    00177                         if outputLen < MinEncodedSize, the most significant bytes will be dropped
    00178                         if outputLen > MinEncodedSize, the most significant bytes will be padded
    00179                 */
    00180                 unsigned int Encode(byte *output, unsigned int outputLen, Signedness=UNSIGNED) const;
    00181                 //!
    00182                 unsigned int Encode(BufferedTransformation &bt, unsigned int outputLen, Signedness=UNSIGNED) const;
    00183
    00184                 //! encode using Distinguished Encoding Rules, put result into a BufferedTransformation object
    00185                 void DEREncode(BufferedTransformation &bt) const;
    00186
    00187                 //! encode absolute value as big-endian octet string
    00188                 void DEREncodeAsOctetString(BufferedTransformation &bt, unsigned int length) const;
    00189
    00190                 //! encode absolute value in OpenPGP format, return length of output
    00191                 unsigned int OpenPGPEncode(byte *output, unsigned int bufferSize) const;
    00192                 //! encode absolute value in OpenPGP format, put result into a BufferedTransformation object
    00193                 unsigned int OpenPGPEncode(BufferedTransformation &bt) const;
    00194
    00195                 //!
    00196                 void Decode(const byte *input, unsigned int inputLen, Signedness=UNSIGNED);
    00197                 //!
    00198                 //* Precondition: bt.MaxRetrievable() >= inputLen
    00199                 void Decode(BufferedTransformation &bt, unsigned int inputLen, Signedness=UNSIGNED);
    00200
    00201                 //!
    00202                 void BERDecode(const byte *input, unsigned int inputLen);
    00203                 //!
    00204                 void BERDecode(BufferedTransformation &bt);
    00205
    00206                 //! decode nonnegative value as big-endian octet string
    00207                 void BERDecodeAsOctetString(BufferedTransformation &bt, unsigned int length);
    00208
    00209                 class OpenPGPDecodeErr : public Exception
    00210                 {
    00211                 public:
    00212                         OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {}
    00213                 };
    00214
    00215                 //!
    00216                 void OpenPGPDecode(const byte *input, unsigned int inputLen);
    00217                 //!
    00218                 void OpenPGPDecode(BufferedTransformation &bt);
    00219         //@}
    00220
    00221         //! \name ACCESSORS
    00222         //@{
    00223                 //! return true if *this can be represented as a signed long
    00224                 bool IsConvertableToLong() const;
    00225                 //! return equivalent signed long if possible, otherwise undefined
    00226                 signed long ConvertToLong() const;
    00227
    00228                 //! number of significant bits = floor(log2(abs(*this))) + 1
    00229                 unsigned int BitCount() const;
    00230                 //! number of significant bytes = ceiling(BitCount()/8)
    00231                 unsigned int ByteCount() const;
    00232                 //! number of significant words = ceiling(ByteCount()/sizeof(word))
    00233                 unsigned int WordCount() const;
    00234
    00235                 //! return the i-th bit, i=0 being the least significant bit
    00236                 bool GetBit(unsigned int i) const;
    00237                 //! return the i-th byte
    00238                 byte GetByte(unsigned int i) const;
    00239                 //! return n lowest bits of *this >> i
    00240                 unsigned long GetBits(unsigned int i, unsigned int n) const;
    00241
    00242                 //!
    00243                 bool IsZero() const {return !*this;}
    00244                 //!
    00245                 bool NotZero() const {return !IsZero();}
    00246                 //!
    00247                 bool IsNegative() const {return sign == NEGATIVE;}
    00248                 //!
    00249                 bool NotNegative() const {return !IsNegative();}
    00250                 //!
    00251                 bool IsPositive() const {return NotNegative() && NotZero();}
    00252                 //!
    00253                 bool NotPositive() const {return !IsPositive();}
    00254                 //!
    00255                 bool IsEven() const {return GetBit(0) == 0;}
    00256                 //!
    00257                 bool IsOdd() const      {return GetBit(0) == 1;}
    00258         //@}
    00259
    00260         //! \name MANIPULATORS
    00261         //@{
    00262                 //!
    00263                 Integer&  operator=(const Integer& t);
    00264
    00265                 //!
    00266                 Integer&  operator+=(const Integer& t);
    00267                 //!
    00268                 Integer&  operator-=(const Integer& t);
    00269                 //!
    00270                 Integer&  operator*=(const Integer& t)  {return *this = Times(t);}
    00271                 //!
    00272                 Integer&  operator/=(const Integer& t)  {return *this = DividedBy(t);}
    00273                 //!
    00274                 Integer&  operator%=(const Integer& t)  {return *this = Modulo(t);}
    00275                 //!
    00276                 Integer&  operator/=(word t)  {return *this = DividedBy(t);}
    00277                 //!
    00278                 Integer&  operator%=(word t)  {return *this = Modulo(t);}
    00279
    00280                 //!
    00281                 Integer&  operator<<=(unsigned int);
    00282                 //!
    00283                 Integer&  operator>>=(unsigned int);
    00284
    00285                 //!
    00286                 void Randomize(RandomNumberGenerator &rng, unsigned int bitcount);
    00287                 //!
    00288                 void Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max);
    00289                 //! set this Integer to a random element of {x | min <= x <= max and x is of rnType and x % mod == equiv}
    00290                 /*! returns false if the set is empty */
    00291                 bool Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One());
    00292
    00293                 bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs &params = g_nullNameValuePairs);
    00294                 void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params = g_nullNameValuePairs)
    00295                 {
    00296                         if (!GenerateRandomNoThrow(rng, params))
    00297                                 throw RandomNumberNotFound();
    00298                 }
    00299
    00300                 //! set the n-th bit to value
    00301                 void SetBit(unsigned int n, bool value=1);
    00302                 //! set the n-th byte to value
    00303                 void SetByte(unsigned int n, byte value);
    00304
    00305                 //!
    00306                 void Negate();
    00307                 //!
    00308                 void SetPositive() {sign = POSITIVE;}
    00309                 //!
    00310                 void SetNegative() {if (!!(*this)) sign = NEGATIVE;}
    00311
    00312                 //!
    00313                 void swap(Integer &a);
    00314         //@}
    00315
    00316         //! \name UNARY OPERATORS
    00317         //@{
    00318                 //!
    00319                 bool            operator!() const;
    00320                 //!
    00321                 Integer         operator+() const {return *this;}
    00322                 //!
    00323                 Integer         operator-() const;
    00324                 //!
    00325                 Integer&        operator++();
    00326                 //!
    00327                 Integer&        operator--();
    00328                 //!
    00329                 Integer         operator++(int) {Integer temp = *this; ++*this; return temp;}
    00330                 //!
    00331                 Integer         operator--(int) {Integer temp = *this; --*this; return temp;}
    00332         //@}
    00333
    00334         //! \name BINARY OPERATORS
    00335         //@{
    00336                 //! signed comparison
    00337                 /*! \retval -1 if *this < a
    00338                         \retval  0 if *this = a
    00339                         \retval  1 if *this > a
    00340                 */
    00341                 int Compare(const Integer& a) const;
    00342
    00343                 //!
    00344                 Integer Plus(const Integer &b) const;
    00345                 //!
    00346                 Integer Minus(const Integer &b) const;
    00347                 //!
    00348                 Integer Times(const Integer &b) const;
    00349                 //!
    00350                 Integer DividedBy(const Integer &b) const;
    00351                 //!
    00352                 Integer Modulo(const Integer &b) const;
    00353                 //!
    00354                 Integer DividedBy(word b) const;
    00355                 //!
    00356                 word Modulo(word b) const;
    00357
    00358                 //!
    00359                 Integer operator>>(unsigned int n) const        {return Integer(*this)>>=n;}
    00360                 //!
    00361                 Integer operator<<(unsigned int n) const        {return Integer(*this)<<=n;}
    00362         //@}
    00363
    00364         //! \name OTHER ARITHMETIC FUNCTIONS
    00365         //@{
    00366                 //!
    00367                 Integer AbsoluteValue() const;
    00368                 //!
    00369                 Integer Doubled() const {return Plus(*this);}
    00370                 //!
    00371                 Integer Squared() const {return Times(*this);}
    00372                 //! extract square root, if negative return 0, else return floor of square root
    00373                 Integer SquareRoot() const;
    00374                 //! return whether this integer is a perfect square
    00375                 bool IsSquare() const;
    00376
    00377                 //! is 1 or -1
    00378                 bool IsUnit() const;
    00379                 //! return inverse if 1 or -1, otherwise return 0
    00380                 Integer MultiplicativeInverse() const;
    00381
    00382                 //! modular multiplication
    00383                 CRYPTOPP_DLL friend Integer a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m);
    00384                 //! modular exponentiation
    00385                 CRYPTOPP_DLL friend Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m);
    00386
    00387                 //! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))
    00388                 static void Divide(Integer &r, Integer &q, const Integer &a, const Integer &d);
    00389                 //! use a faster division algorithm when divisor is short
    00390                 static void Divide(word &r, Integer &q, const Integer &a, word d);
    00391
    00392                 //! returns same result as Divide(r, q, a, Power2(n)), but faster
    00393                 static void DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n);
    00394
    00395                 //! greatest common divisor
    00396                 static Integer Gcd(const Integer &a, const Integer &n);
    00397                 //! calculate multiplicative inverse of *this mod n
    00398                 Integer InverseMod(const Integer &n) const;
    00399                 //!
    00400                 word InverseMod(word n) const;
    00401         //@}
    00402
    00403         //! \name INPUT/OUTPUT
    00404         //@{
    00405                 //!
    00406                 friend CRYPTOPP_DLL std::istream& operator>>(std::istream& in, Integer &a);
    00407                 //!
    00408                 friend CRYPTOPP_DLL std::ostream& operator<<(std::ostream& out, const Integer &a);
    00409         //@}
    00410
    00411 private:
    00412         friend class ModularArithmetic;
    00413         friend class MontgomeryRepresentation;
    00414         friend class HalfMontgomeryRepresentation;
    00415
    00416         Integer(word value, unsigned int length);
    00417
    00418         int PositiveCompare(const Integer &t) const;
    00419         friend void PositiveAdd(Integer &sum, const Integer &a, const Integer &b);
    00420         friend void PositiveSubtract(Integer &diff, const Integer &a, const Integer &b);
    00421         friend void PositiveMultiply(Integer &product, const Integer &a, const Integer &b);
    00422         friend void PositiveDivide(Integer &remainder, Integer &quotient, const Integer &dividend, const Integer &divisor);
    00423
    00424         SecAlignedWordBlock reg;
    00425         Sign sign;
    00426 };
    00427
    00428 //!
    00429 inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;}
    00430 //!
    00431 inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;}
    00432 //!
    00433 inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;}
    00434 //!
    00435 inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;}
    00436 //!
    00437 inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;}
    00438 //!
    00439 inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;}
    00440 //!
    00441 inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);}
    00442 //!
    00443 inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);}
    00444 //!
    00445 inline CryptoPP::Integer operator*(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Times(b);}
    00446 //!
    00447 inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);}
    00448 //!
    00449 inline CryptoPP::Integer operator%(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Modulo(b);}
    00450 //!
    00451 inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);}
    00452 //!
    00453 inline CryptoPP::word    operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);}
    00454
    00455 NAMESPACE_END
    00456
    00457 NAMESPACE_BEGIN(std)
    00458 template<> inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b)
    00459 {
    00460         a.swap(b);
    00461 }
    00462 NAMESPACE_END
    00463
    00464 #endif