/src/cryptopp/integer.h

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// integer.h - originally written and placed in the public domain by Wei Dai

/// \file integer.h
/// \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))<sup>(256**sizeof(int))</sup>.
/// \details Internally, the library uses a sign magnitude representation, and the class
///  has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
///  used to hold the representation. The second is a Sign (an enumeration), and it is
///  used to track the sign of the Integer.
/// \details For details on how the Integer class initializes its function pointers using
///  InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
///  Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
/// \since Crypto++ 1.0

#ifndef CRYPTOPP_INTEGER_H
#define CRYPTOPP_INTEGER_H

#include "cryptlib.h"
#include "secblock.h"
#include "stdcpp.h"

#include <iosfwd>

NAMESPACE_BEGIN(CryptoPP)

/// \struct InitializeInteger
/// \brief Performs static initialization of the Integer class
struct InitializeInteger
{
  InitializeInteger();
};

// Always align, http://github.com/weidai11/cryptopp/issues/256
typedef SecBlock<word, AllocatorWithCleanup<word, true> > 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))<sup>(256**sizeof(int))</sup>.
/// \details Internally, the library uses a sign magnitude representation, and the class
///  has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
///  used to hold the representation. The second is a Sign (an enumeration), and it is
///  used to track the sign of the Integer.
/// \details For details on how the Integer class initializes its function pointers using
///  InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
///  Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
/// \since Crypto++ 1.0
/// \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 SetPositive(), SetNegative(), 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 the ByteOrder of the string to be processed
    /// \details \p str can be in base 8, 10, or 16. Base is determined
    ///  by a case insensitive suffix of 'o' (8), '.' (10), or 'h' (16).
    ///  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 the ByteOrder of the string to be processed
    /// \details \p str can be in base 8, 10, or 16. Base is determined
    ///  by a case insensitive suffix of 'o' (8), '.' (10), or 'h' (16).
    ///  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 the ByteOrder of the array to be processed
    /// \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 the ByteOrder of the data to be processed
    /// \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 <tt>[0, 2<sup>bitCount</sup>]</tt>.
    Integer(RandomNumberGenerator &rng, size_t bitCount);

    /// \brief Integer representing 0
    /// \return an Integer representing 0
    /// \details Zero() avoids calling constructors for frequently used integers
    static const Integer & CRYPTOPP_API Zero();
    /// \brief Integer representing 1
    /// \return an Integer representing 1
    /// \details One() avoids calling constructors for frequently used integers
    static const Integer & CRYPTOPP_API One();
    /// \brief Integer representing 2
    /// \return 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 <tt>{x | min \<= x \<= max</tt> and \p x is of rnType and <tt>x \% mod == equiv}</tt>.
    ///  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 <tt>max \> lastSmallPrime*lastSmallPrime</tt>. \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
    /// \return the Integer 2<sup>e</sup>
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    static Integer CRYPTOPP_API Power2(size_t e);
  //@}

  /// \name ENCODE/DECODE
  //@{
    /// \brief 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;

    /// \brief 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
    /// \return length of the output
    /// \details OpenPGPEncode places result into the buffer 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
    /// \return 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 <tt>bt.MaxRetrievable() \>= inputLen</tt>.
    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
    /// \return true if <tt>*this</tt> 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
    /// \return number of significant bits
    /// \details BitCount is calculated as <tt>floor(log2(abs(*this))) + 1</tt>.
    unsigned int BitCount() const;
    /// \brief Determines the number of bytes required to represent the Integer
    /// \return number of significant bytes
    /// \details ByteCount is calculated as <tt>ceiling(BitCount()/8)</tt>.
    unsigned int ByteCount() const;
    /// \brief Determines the number of words required to represent the Integer
    /// \return number of significant words
    /// \details WordCount is calculated as <tt>ceiling(ByteCount()/sizeof(word))</tt>.
    unsigned int WordCount() const;

    /// \brief Provides the i-th bit of the Integer
    /// \return 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
    /// \return the i-th byte
    byte GetByte(size_t i) const;
    /// \brief Provides the low order bits of the Integer
    /// \return n lowest bits of <tt>*this >> i</tt>
    lword GetBits(size_t i, size_t n) const;

    /// \brief Determines if the Integer is 0
    /// \return true if the Integer is 0, false otherwise
    bool IsZero() const {return !*this;}
    /// \brief Determines if the Integer is non-0
    /// \return true if the Integer is non-0, false otherwise
    bool NotZero() const {return !IsZero();}
    /// \brief Determines if the Integer is negative
    /// \return true if the Integer is negative, false otherwise
    bool IsNegative() const {return sign == NEGATIVE;}
    /// \brief Determines if the Integer is non-negative
    /// \return true if the Integer is non-negative, false otherwise
    bool NotNegative() const {return !IsNegative();}
    /// \brief Determines if the Integer is positive
    /// \return true if the Integer is positive, false otherwise
    bool IsPositive() const {return NotNegative() && NotZero();}
    /// \brief Determines if the Integer is non-positive
    /// \return true if the Integer is non-positive, false otherwise
    bool NotPositive() const {return !IsPositive();}
    /// \brief Determines if the Integer is even parity
    /// \return true if the Integer is even, false otherwise
    bool IsEven() const {return GetBit(0) == 0;}
    /// \brief Determines if the Integer is odd parity
    /// \return true if the Integer is odd, false otherwise
    bool IsOdd() const  {return GetBit(0) == 1;}
  //@}

  /// \name MANIPULATORS
  //@{
    /// \brief Assignment
    /// \param t the other Integer
    /// \return the result of assignment
    Integer&  operator=(const Integer& t);
    /// \brief Addition Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this + t</tt>
    Integer&  operator+=(const Integer& t);
    /// \brief Subtraction Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this - t</tt>
    Integer&  operator-=(const Integer& t);
    /// \brief Multiplication Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this * t</tt>
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer&  operator*=(const Integer& t)  {return *this = Times(t);}
    /// \brief Division Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this / t</tt>
    Integer&  operator/=(const Integer& t)  {return *this = DividedBy(t);}
    /// \brief Remainder Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this % t</tt>
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer&  operator%=(const Integer& t)  {return *this = Modulo(t);}
    /// \brief Division Assignment
    /// \param t the other word
    /// \return the result of <tt>*this / t</tt>
    Integer&  operator/=(word t)  {return *this = DividedBy(t);}
    /// \brief Remainder Assignment
    /// \param t the other word
    /// \return the result of <tt>*this % t</tt>
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer&  operator%=(word t)  {return *this = Integer(POSITIVE, 0, Modulo(t));}

    /// \brief Left-shift Assignment
    /// \param n number of bits to shift
    /// \return reference to this Integer
    Integer&  operator<<=(size_t n);
    /// \brief Right-shift Assignment
    /// \param n number of bits to shift
    /// \return reference to this Integer
    Integer&  operator>>=(size_t n);

    /// \brief Bitwise AND Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this & t</tt>
    /// \details operator&=() performs a bitwise AND on <tt>*this</tt>. Missing bits are truncated
    ///  at the most significant bit positions, so the result is as small as the
    ///  smaller of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer& operator&=(const Integer& t);
    /// \brief Bitwise OR Assignment
    /// \param t the second Integer
    /// \return the result of <tt>*this | t</tt>
    /// \details operator|=() performs a bitwise OR on <tt>*this</tt>. Missing bits are shifted in
    ///  at the most significant bit positions, so the result is as large as the
    ///  larger of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer& operator|=(const Integer& t);
    /// \brief Bitwise XOR Assignment
    /// \param t the other Integer
    /// \return the result of <tt>*this ^ t</tt>
    /// \details operator^=() performs a bitwise XOR on <tt>*this</tt>. Missing bits are shifted
    ///  in at the most significant bit positions, so the result is as large as the
    ///  larger of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer& operator^=(const Integer& 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 <tt>[0, 2<sup>bitCount</sup>]</tt>.
    /// \note If \p bitCount is 0, then this Integer is set to 0 (and not 0 or 1).
    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 <tt>[min, max]</tt>.
    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 <tt>{x | min \<= x \<= max</tt> and \p x is of rnType and <tt>x \% mod == equiv}</tt>.
    ///  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 <tt>max \> lastSmallPrime*lastSmallPrime</tt>. \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());

    /// \brief Generate a random number
    /// \param rng RandomNumberGenerator used to generate material
    /// \param params additional parameters that cannot be passed directly to the function
    /// \return true if a random number was generated, false otherwise
    /// \details GenerateRandomNoThrow attempts to generate a random number according to the
    ///  parameters specified in params. The function does not throw RandomNumberNotFound.
    /// \details The example below generates a prime number using NameValuePairs that Integer
    ///  class recognizes. The names are not provided in argnames.h.
    /// <pre>
    ///    AutoSeededRandomPool prng;
    ///    AlgorithmParameters params = MakeParameters("BitLength", 2048)
    ///                                               ("RandomNumberType", Integer::PRIME);
    ///    Integer x;
    ///    if (x.GenerateRandomNoThrow(prng, params) == false)
    ///        throw std::runtime_error("Failed to generate prime number");
    /// </pre>
    bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs &params = g_nullNameValuePairs);

    /// \brief Generate a random number
    /// \param rng RandomNumberGenerator used to generate material
    /// \param params additional parameters that cannot be passed directly to the function
    /// \throw RandomNumberNotFound if a random number is not found
    /// \details GenerateRandom attempts to generate a random number according to the
    ///  parameters specified in params.
    /// \details The example below generates a prime number using NameValuePairs that Integer
    ///  class recognizes. The names are not provided in argnames.h.
    /// <pre>
    ///    AutoSeededRandomPool prng;
    ///    AlgorithmParameters params = MakeParameters("BitLength", 2048)
    ///                                               ("RandomNumberType", Integer::PRIME);
    ///    Integer x;
    ///    try { x.GenerateRandom(prng, params); }
    ///    catch (RandomNumberNotFound&) { x = -1; }
    /// </pre>
    void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params = 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
  //@{
    /// \brief Negation
    bool    operator!() const;
    /// \brief Addition
    Integer   operator+() const {return *this;}
    /// \brief Subtraction
    Integer   operator-() const;
    /// \brief Pre-increment
    Integer&  operator++();
    /// \brief Pre-decrement
    Integer&  operator--();
    /// \brief Post-increment
    Integer   operator++(int) {Integer temp = *this; ++*this; return temp;}
    /// \brief Post-decrement
    Integer   operator--(int) {Integer temp = *this; --*this; return temp;}
  //@}

  /// \name BINARY OPERATORS
  //@{
    /// \brief Perform signed comparison
    /// \param a the Integer to compare
    /// \retval -1 if <tt>*this < a</tt>
    /// \retval  0 if <tt>*this = a</tt>
    /// \retval  1 if <tt>*this > a</tt>
    int Compare(const Integer& a) const;

    /// \brief Addition
    Integer Plus(const Integer &b) const;
    /// \brief Subtraction
    Integer Minus(const Integer &b) const;
    /// \brief Multiplication
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer Times(const Integer &b) const;
    /// \brief Division
    Integer DividedBy(const Integer &b) const;
    /// \brief Remainder
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer Modulo(const Integer &b) const;
    /// \brief Division
    Integer DividedBy(word b) const;
    /// \brief Remainder
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    word Modulo(word b) const;

    /// \brief Bitwise AND
    /// \param t the other Integer
    /// \return the result of <tt>*this & t</tt>
    /// \details And() performs a bitwise AND on the operands. Missing bits are truncated
    ///  at the most significant bit positions, so the result is as small as the
    ///  smaller of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer And(const Integer& t) const;

    /// \brief Bitwise OR
    /// \param t the other Integer
    /// \return the result of <tt>*this | t</tt>
    /// \details Or() performs a bitwise OR on the operands. Missing bits are shifted in
    ///  at the most significant bit positions, so the result is as large as the
    ///  larger of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer Or(const Integer& t) const;

    /// \brief Bitwise XOR
    /// \param t the other Integer
    /// \return the result of <tt>*this ^ t</tt>
    /// \details Xor() performs a bitwise XOR on the operands. Missing bits are shifted in
    ///  at the most significant bit positions, so the result is as large as the
    ///  larger of the operands.
    /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
    ///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
    ///  the integer should be converted to a 2's compliment representation before performing
    ///  the operation.
    /// \since Crypto++ 6.0
    Integer Xor(const Integer& t) const;

    /// \brief Right-shift
    Integer operator>>(size_t n) const  {return Integer(*this)>>=n;}
    /// \brief Left-shift
    Integer operator<<(size_t n) const  {return Integer(*this)<<=n;}
  //@}

  /// \name OTHER ARITHMETIC FUNCTIONS
  //@{
    /// \brief Retrieve the absolute value of this integer
    Integer AbsoluteValue() const;
    /// \brief Add this integer to itself
    Integer Doubled() const {return Plus(*this);}
    /// \brief Multiply this integer by itself
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer Squared() const {return Times(*this);}
    /// \brief Extract square root
    /// \details if negative return 0, else return floor of square root
    Integer SquareRoot() const;
    /// \brief Determine whether this integer is a perfect square
    bool IsSquare() const;

    /// \brief Determine if 1 or -1
    /// \return true if this integer is 1 or -1, false otherwise
    bool IsUnit() const;
    /// \brief Calculate multiplicative inverse
    /// \return MultiplicativeInverse inverse if 1 or -1, otherwise return 0.
    Integer MultiplicativeInverse() const;

    /// \brief Extended Division
    /// \param r a reference for the remainder
    /// \param q a reference for the quotient
    /// \param a reference to the dividend
    /// \param d reference to the divisor
    /// \details Divide calculates 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);

    /// \brief Extended Division
    /// \param r a reference for the remainder
    /// \param q a reference for the quotient
    /// \param a reference to the dividend
    /// \param d reference to the divisor
    /// \details Divide calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)).
    ///  This overload uses a faster division algorithm because the divisor is short.
    static void CRYPTOPP_API Divide(word &r, Integer &q, const Integer &a, word d);

    /// \brief Extended Division
    /// \param r a reference for the remainder
    /// \param q a reference for the quotient
    /// \param a reference to the dividend
    /// \param n reference to the divisor
    /// \details DivideByPowerOf2 calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)).
    ///  It returns same result as Divide(r, q, a, Power2(n)), but faster.
    ///  This overload uses a faster division algorithm because the divisor is a power of 2.
    static void CRYPTOPP_API DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n);

    /// \brief Calculate greatest common divisor
    /// \param a reference to the first number
    /// \param n reference to the secind number
    /// \return the greatest common divisor <tt>a</tt> and <tt>n</tt>.
    static Integer CRYPTOPP_API Gcd(const Integer &a, const Integer &n);

    /// \brief Calculate multiplicative inverse
    /// \param n reference to the modulus
    /// \return an Integer <tt>*this % n</tt>.
    /// \details InverseMod returns the multiplicative inverse of the Integer <tt>*this</tt>
    ///  modulo the Integer <tt>n</tt>. If no Integer exists then Integer 0 is returned.
    /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
    Integer InverseMod(const Integer &n) const;

    /// \brief Calculate multiplicative inverse
    /// \param n the modulus
    /// \return a word <tt>*this % n</tt>.
    /// \details InverseMod returns the multiplicative inverse of the Integer <tt>*this</tt>
    ///  modulo the word <tt>n</tt>. If no Integer exists then word 0 is returned.
    /// \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 reference to a std::istream
    /// \param a reference to an Integer
    /// \return reference to a std::istream reference
    friend CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>(std::istream& in, Integer &a);

    /// \brief Insertion operator
    /// \param out reference to a std::ostream
    /// \param a a constant reference to an Integer
    /// \return reference to a std::ostream reference
    /// \details The output integer responds to hex, std::oct, std::hex, std::upper and
    ///  std::lower. The output includes the suffix \a h (for hex), \a . (\a dot, for dec)
    ///  and \a o (for octal). There is currently no way to suppress the suffix.
    /// \details If you want to print an Integer without the suffix or using an arbitrary base, then
    ///  use IntToString<Integer>().
    /// \sa IntToString<Integer>
    friend CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<(std::ostream& out, const Integer &a);
  //@}

  /// \brief Modular multiplication
  /// \param x reference to the first term
  /// \param y reference to the second term
  /// \param m reference to the modulus
  /// \return an Integer <tt>(a * b) % m</tt>.
  CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m);
  /// \brief Modular exponentiation
  /// \param x reference to the base
  /// \param e reference to the exponent
  /// \param m reference to the modulus
  /// \return an Integer <tt>(a ^ b) % m</tt>.
  CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m);

protected:

  // http://github.com/weidai11/cryptopp/issues/602
  Integer InverseModNext(const Integer &n) const;

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 &quotient, const Integer &dividend, const Integer &divisor);
#endif
};

/// \brief Comparison
inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;}
/// \brief Comparison
inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;}
/// \brief Comparison
inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;}
/// \brief Comparison
inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;}
/// \brief Comparison
inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;}
/// \brief Comparison
inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;}
/// \brief Addition
inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);}
/// \brief Subtraction
inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);}
/// \brief Multiplication
/// \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);}
/// \brief Division
inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);}
/// \brief Remainder
/// \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);}
/// \brief Division
inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);}
/// \brief Remainder
/// \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);}

/// \brief Bitwise AND
/// \param a the first Integer
/// \param b the second Integer
/// \return the result of a & b
/// \details operator&() performs a bitwise AND on the operands. Missing bits are truncated
///  at the most significant bit positions, so the result is as small as the
///  smaller of the operands.
/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
///  the integer should be converted to a 2's compliment representation before performing
///  the operation.
/// \since Crypto++ 6.0
inline CryptoPP::Integer operator&(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.And(b);}

/// \brief Bitwise OR
/// \param a the first Integer
/// \param b the second Integer
/// \return the result of a | b
/// \details operator|() performs a bitwise OR on the operands. Missing bits are shifted in
///  at the most significant bit positions, so the result is as large as the
///  larger of the operands.
/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
///  the integer should be converted to a 2's compliment representation before performing
///  the operation.
/// \since Crypto++ 6.0
inline CryptoPP::Integer operator|(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Or(b);}

/// \brief Bitwise XOR
/// \param a the first Integer
/// \param b the second Integer
/// \return the result of a ^ b
/// \details operator^() performs a bitwise XOR on the operands. Missing bits are shifted
///  in at the most significant bit positions, so the result is as large as the
///  larger of the operands.
/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
///  does not attempt to interpret bits, and the result is always POSITIVE. If needed,
///  the integer should be converted to a 2's compliment representation before performing
///  the operation.
/// \since Crypto++ 6.0
inline CryptoPP::Integer operator^(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Xor(b);}

NAMESPACE_END

#ifndef __BORLANDC__
NAMESPACE_BEGIN(std)
inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b)
{
  a.swap(b);
}
NAMESPACE_END
#endif

#endif

Coverage Report

Created: 2024-11-21 07:03