#ifndef CRYPTOPP_INTEGER_H #define CRYPTOPP_INTEGER_H /** \file */ #include "cryptlib.h" #include "secblock.h" #include "stdcpp.h" #include NAMESPACE_BEGIN(CryptoPP) //! \struct InitializeInteger //! Performs static intialization of the Integer class struct InitializeInteger { InitializeInteger(); }; typedef SecBlock > IntegerSecBlock; //! \brief Multiple precision integer with arithmetic operations //! \details The Integer class can represent positive and negative integers //! with absolute value less than (256**sizeof(word))(256**sizeof(int)). //! \details Internally, the library uses a sign magnitude representation, and the class //! has two data members. The first is a IntegerSecBlock (a SecBlock) and it is //! used to hold the representation. The second is a Sign, and its is used to track //! the sign of the Integer. //! \nosubgrouping class CRYPTOPP_DLL Integer : private InitializeInteger, public ASN1Object { public: //! \name ENUMS, EXCEPTIONS, and TYPEDEFS //@{ //! \brief Exception thrown when division by 0 is encountered class DivideByZero : public Exception { public: DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {} }; //! \brief Exception thrown when a random number cannot be found that //! satisfies the condition class RandomNumberNotFound : public Exception { public: RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {} }; //! \enum Sign //! \brief Used internally to represent the integer //! \details Sign is used internally to represent the integer. It is also used in a few API functions. //! \sa Signedness enum Sign { //! \brief the value is positive or 0 POSITIVE=0, //! \brief the value is negative NEGATIVE=1}; //! \enum Signedness //! \brief Used when importing and exporting integers //! \details Signedness is usually used in API functions. //! \sa Sign enum Signedness { //! \brief an unsigned value UNSIGNED, //! \brief a signed value SIGNED}; //! \enum RandomNumberType //! \brief Properties of a random integer enum RandomNumberType { //! \brief a number with no special properties ANY, //! \brief a number which is probabilistically prime PRIME}; //@} //! \name CREATORS //@{ //! \brief Creates the zero integer Integer(); //! copy constructor Integer(const Integer& t); //! \brief Convert from signed long Integer(signed long value); //! \brief Convert from lword //! \param sign enumeration indicating Sign //! \param value the long word Integer(Sign sign, lword value); //! \brief Convert from two words //! \param sign enumeration indicating Sign //! \param highWord the high word //! \param lowWord the low word Integer(Sign sign, word highWord, word lowWord); //! \brief Convert from a C-string //! \param str C-string value //! \param order byte order //! \details \p 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. //! \details Byte order was added at Crypto++ 5.7 to allow use of little-endian //! integers with curve25519, Poly1305 and Microsoft CAPI. explicit Integer(const char *str, ByteOrder order = BIG_ENDIAN_ORDER); //! \brief Convert from a wide C-string //! \param str wide C-string value //! \param order byte order //! \details \p 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. //! \details Byte order was added at Crypto++ 5.7 to allow use of little-endian //! integers with curve25519, Poly1305 and Microsoft CAPI. explicit Integer(const wchar_t *str, ByteOrder order = BIG_ENDIAN_ORDER); //! \brief Convert from a big-endian byte array //! \param encodedInteger big-endian byte array //! \param byteCount length of the byte array //! \param sign enumeration indicating Signedness //! \param order byte order //! \details Byte order was added at Crypto++ 5.7 to allow use of little-endian //! integers with curve25519, Poly1305 and Microsoft CAPI. Integer(const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER); //! \brief Convert from a big-endian array //! \param bt BufferedTransformation object with big-endian byte array //! \param byteCount length of the byte array //! \param sign enumeration indicating Signedness //! \param order byte order //! \details Byte order was added at Crypto++ 5.7 to allow use of little-endian //! integers with curve25519, Poly1305 and Microsoft CAPI. Integer(BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER); //! \brief Convert from a BER encoded byte array //! \param bt BufferedTransformation object with BER encoded byte array explicit Integer(BufferedTransformation &bt); //! \brief Create a random integer //! \param rng RandomNumberGenerator used to generate material //! \param bitCount the number of bits in the resulting integer //! \details The random integer created is uniformly distributed over [0, 2bitCount]. Integer(RandomNumberGenerator &rng, size_t bitCount); //! \brief Integer representing 0 //! \returns an Integer representing 0 //! \details Zero() avoids calling constructors for frequently used integers static const Integer & CRYPTOPP_API Zero(); //! \brief Integer representing 1 //! \returns an Integer representing 1 //! \details One() avoids calling constructors for frequently used integers static const Integer & CRYPTOPP_API One(); //! \brief Integer representing 2 //! \returns an Integer representing 2 //! \details Two() avoids calling constructors for frequently used integers static const Integer & CRYPTOPP_API Two(); //! \brief Create a random integer of special form //! \param rng RandomNumberGenerator used to generate material //! \param min the minimum value //! \param max the maximum value //! \param rnType RandomNumberType to specify the type //! \param equiv the equivalence class based on the parameter \p mod //! \param mod the modulus used to reduce the equivalence class //! \throw RandomNumberNotFound if the set is empty. //! \details Ideally, the random integer created should be uniformly distributed //! over {x | min \<= x \<= max and \p 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. //! \details May return (with very small probability) a pseudoprime when a prime //! is requested and max \> lastSmallPrime*lastSmallPrime. \p lastSmallPrime //! is declared in nbtheory.h. Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One()); //! \brief Exponentiates to a power of 2 //! \returns the Integer 2e //! \sa a_times_b_mod_c() and a_exp_b_mod_c() static Integer CRYPTOPP_API Power2(size_t e); //@} //! \name ENCODE/DECODE //@{ //! \brief The minimum number of bytes to encode this integer //! \param sign enumeration indicating Signedness //! \note The MinEncodedSize() of 0 is 1. size_t MinEncodedSize(Signedness sign=UNSIGNED) const; //! \brief Encode in big-endian format //! \param output big-endian byte array //! \param outputLen length of the byte array //! \param sign enumeration indicating Signedness //! \details Unsigned means encode absolute value, signed means encode two's complement if negative. //! \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a //! minimum size). An exact size is useful, for example, when encoding to a field element size. void Encode(byte *output, size_t outputLen, Signedness sign=UNSIGNED) const; //! \brief Encode in big-endian format //! \param bt BufferedTransformation object //! \param outputLen length of the encoding //! \param sign enumeration indicating Signedness //! \details Unsigned means encode absolute value, signed means encode two's complement if negative. //! \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a //! minimum size). An exact size is useful, for example, when encoding to a field element size. void Encode(BufferedTransformation &bt, size_t outputLen, Signedness sign=UNSIGNED) const; //! \brief Encode in DER format //! \param bt BufferedTransformation object //! \details Encodes the Integer using Distinguished Encoding Rules //! The result is placed into a BufferedTransformation object void DEREncode(BufferedTransformation &bt) const; //! encode absolute value as big-endian octet string //! \param bt BufferedTransformation object //! \param length the number of mytes to decode void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const; //! \brief Encode absolute value in OpenPGP format //! \param output big-endian byte array //! \param bufferSize length of the byte array //! \returns length of the output //! \details OpenPGPEncode places result into a BufferedTransformation object and returns the //! number of bytes used for the encoding size_t OpenPGPEncode(byte *output, size_t bufferSize) const; //! \brief Encode absolute value in OpenPGP format //! \param bt BufferedTransformation object //! \returns length of the output //! \details OpenPGPEncode places result into a BufferedTransformation object and returns the //! number of bytes used for the encoding size_t OpenPGPEncode(BufferedTransformation &bt) const; //! \brief Decode from big-endian byte array //! \param input big-endian byte array //! \param inputLen length of the byte array //! \param sign enumeration indicating Signedness void Decode(const byte *input, size_t inputLen, Signedness sign=UNSIGNED); //! \brief Decode nonnegative value from big-endian byte array //! \param bt BufferedTransformation object //! \param inputLen length of the byte array //! \param sign enumeration indicating Signedness //! \note bt.MaxRetrievable() \>= inputLen. void Decode(BufferedTransformation &bt, size_t inputLen, Signedness sign=UNSIGNED); //! \brief Decode from BER format //! \param input big-endian byte array //! \param inputLen length of the byte array void BERDecode(const byte *input, size_t inputLen); //! \brief Decode from BER format //! \param bt BufferedTransformation object void BERDecode(BufferedTransformation &bt); //! \brief Decode nonnegative value from big-endian octet string //! \param bt BufferedTransformation object //! \param length length of the byte array void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length); //! \brief Exception thrown when an error is encountered decoding an OpenPGP integer class OpenPGPDecodeErr : public Exception { public: OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {} }; //! \brief Decode from OpenPGP format //! \param input big-endian byte array //! \param inputLen length of the byte array void OpenPGPDecode(const byte *input, size_t inputLen); //! \brief Decode from OpenPGP format //! \param bt BufferedTransformation object void OpenPGPDecode(BufferedTransformation &bt); //@} //! \name ACCESSORS //@{ //! \brief Determines if the Integer is convertable to Long //! \returns true if *this can be represented as a signed long //! \sa ConvertToLong() bool IsConvertableToLong() const; //! \brief Convert the Integer to Long //! \return equivalent signed long if possible, otherwise undefined //! \sa IsConvertableToLong() signed long ConvertToLong() const; //! \brief Determines the number of bits required to represent the Integer //! \returns number of significant bits = floor(log2(abs(*this))) + 1 unsigned int BitCount() const; //! \brief Determines the number of bytes required to represent the Integer //! \returns number of significant bytes = ceiling(BitCount()/8) unsigned int ByteCount() const; //! \brief Determines the number of words required to represent the Integer //! \returns number of significant words = ceiling(ByteCount()/sizeof(word)) unsigned int WordCount() const; //! \brief Provides the i-th bit of the Integer //! \returns the i-th bit, i=0 being the least significant bit bool GetBit(size_t i) const; //! \brief Provides the i-th byte of the Integer //! \returns the i-th byte byte GetByte(size_t i) const; //! \brief Provides the low order bits of the Integer //! \returns n lowest bits of *this >> i lword GetBits(size_t i, size_t n) const; //! \brief Determines if the Integer is 0 //! \returns true if the Integer is 0, false otherwise bool IsZero() const {return !*this;} //! \brief Determines if the Integer is non-0 //! \returns true if the Integer is non-0, false otherwise bool NotZero() const {return !IsZero();} //! \brief Determines if the Integer is negative //! \returns true if the Integer is negative, false otherwise bool IsNegative() const {return sign == NEGATIVE;} //! \brief Determines if the Integer is non-negative //! \returns true if the Integer is non-negative, false otherwise bool NotNegative() const {return !IsNegative();} //! \brief Determines if the Integer is positive //! \returns true if the Integer is positive, false otherwise bool IsPositive() const {return NotNegative() && NotZero();} //! \brief Determines if the Integer is non-positive //! \returns true if the Integer is non-positive, false otherwise bool NotPositive() const {return !IsPositive();} //! \brief Determines if the Integer is even parity //! \returns true if the Integer is even, false otherwise bool IsEven() const {return GetBit(0) == 0;} //! \brief Determines if the Integer is odd parity //! \returns true if the Integer is odd, false otherwise bool IsOdd() const {return GetBit(0) == 1;} //@} //! \name MANIPULATORS //@{ //! Integer& operator=(const Integer& t); //! Integer& operator+=(const Integer& t); //! Integer& operator-=(const Integer& t); //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer& operator*=(const Integer& t) {return *this = Times(t);} //! Integer& operator/=(const Integer& t) {return *this = DividedBy(t);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer& operator%=(const Integer& t) {return *this = Modulo(t);} //! Integer& operator/=(word t) {return *this = DividedBy(t);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer& operator%=(word t) {return *this = Integer(POSITIVE, 0, Modulo(t));} //! Integer& operator<<=(size_t); //! Integer& operator>>=(size_t); //! \brief Set this Integer to random integer //! \param rng RandomNumberGenerator used to generate material //! \param bitCount the number of bits in the resulting integer //! \details The random integer created is uniformly distributed over [0, 2bitCount]. void Randomize(RandomNumberGenerator &rng, size_t bitCount); //! \brief Set this Integer to random integer //! \param rng RandomNumberGenerator used to generate material //! \param min the minimum value //! \param max the maximum value //! \details The random integer created is uniformly distributed over [min, max]. void Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max); //! \brief Set this Integer to random integer of special form //! \param rng RandomNumberGenerator used to generate material //! \param min the minimum value //! \param max the maximum value //! \param rnType RandomNumberType to specify the type //! \param equiv the equivalence class based on the parameter \p mod //! \param mod the modulus used to reduce the equivalence class //! \throw RandomNumberNotFound if the set is empty. //! \details Ideally, the random integer created should be uniformly distributed //! over {x | min \<= x \<= max and \p 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. //! \details May return (with very small probability) a pseudoprime when a prime //! is requested and max \> lastSmallPrime*lastSmallPrime. \p lastSmallPrime //! is declared in nbtheory.h. 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(); } //! \brief Set the n-th bit to value //! \details 0-based numbering. void SetBit(size_t n, bool value=1); //! \brief Set the n-th byte to value //! \details 0-based numbering. void SetByte(size_t n, byte value); //! \brief Reverse the Sign of the Integer void Negate(); //! \brief Sets the Integer to positive void SetPositive() {sign = POSITIVE;} //! \brief Sets the Integer to negative void SetNegative() {if (!!(*this)) sign = NEGATIVE;} //! \brief Swaps this Integer with another Integer 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 //@{ //! \brief Perform signed comparison //! \param a the Integer to comapre //! \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; //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer Times(const Integer &b) const; //! Integer DividedBy(const Integer &b) const; //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer Modulo(const Integer &b) const; //! Integer DividedBy(word b) const; //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() word Modulo(word b) const; //! Integer operator>>(size_t n) const {return Integer(*this)>>=n;} //! Integer operator<<(size_t n) const {return Integer(*this)<<=n;} //@} //! \name OTHER ARITHMETIC FUNCTIONS //@{ //! Integer AbsoluteValue() const; //! Integer Doubled() const {return Plus(*this);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() 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; //! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d)) static void CRYPTOPP_API Divide(Integer &r, Integer &q, const Integer &a, const Integer &d); //! use a faster division algorithm when divisor is short static void CRYPTOPP_API Divide(word &r, Integer &q, const Integer &a, word d); //! returns same result as Divide(r, q, a, Power2(n)), but faster static void CRYPTOPP_API DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n); //! greatest common divisor static Integer CRYPTOPP_API Gcd(const Integer &a, const Integer &n); //! calculate multiplicative inverse of *this mod n //! \sa a_times_b_mod_c() and a_exp_b_mod_c() Integer InverseMod(const Integer &n) const; //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() word InverseMod(word n) const; //@} //! \name INPUT/OUTPUT //@{ //! \brief Extraction operator //! \param in a reference to a std::istream //! \param a a reference to an Integer //! \returns a reference to a std::istream reference friend CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>(std::istream& in, Integer &a); //! //! \brief Insertion operator //! \param out a reference to a std::ostream //! \param a a constant reference to an Integer //! \returns a reference to a std::ostream reference //! \details The output integer responds to std::hex, std::oct, std::hex, std::upper and //! std::lower. The output includes the suffix \a \b h (for hex), \a \b . (\a \b dot, for dec) //! and \a \b o (for octal). There is currently no way to supress the suffix. //! \details If you want to print an Integer without the suffix or using an arbitrary base, then //! use IntToString(). //! \sa IntToString friend CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<(std::ostream& out, const Integer &a); //@} #ifndef CRYPTOPP_DOXYGEN_PROCESSING //! modular multiplication CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m); //! modular exponentiation CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m); #endif private: Integer(word value, size_t length); int PositiveCompare(const Integer &t) const; IntegerSecBlock reg; Sign sign; #ifndef CRYPTOPP_DOXYGEN_PROCESSING friend class ModularArithmetic; friend class MontgomeryRepresentation; friend class HalfMontgomeryRepresentation; 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); #endif }; //! 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);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() 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);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() 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);} //! //! \sa a_times_b_mod_c() and a_exp_b_mod_c() inline CryptoPP::word operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);} NAMESPACE_END #ifndef __BORLANDC__ NAMESPACE_BEGIN(std) inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b) { a.swap(b); } NAMESPACE_END #endif #endif