838 lines
38 KiB
C++
838 lines
38 KiB
C++
// integer.h - originally written and placed in the public domain by Wei Dai
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/// \file integer.h
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/// \brief Multiple precision integer with arithmetic operations
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/// \details The Integer class can represent positive and negative integers
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/// with absolute value less than (256**sizeof(word))<sup>(256**sizeof(int))</sup>.
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/// \details Internally, the library uses a sign magnitude representation, and the class
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/// has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
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/// used to hold the representation. The second is a Sign (an enumeration), and it is
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/// used to track the sign of the Integer.
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/// \details For details on how the Integer class initializes its function pointers using
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/// InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
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/// Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
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/// \since Crypto++ 1.0
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#ifndef CRYPTOPP_INTEGER_H
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#define CRYPTOPP_INTEGER_H
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#include "cryptlib.h"
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#include "secblock.h"
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#include "stdcpp.h"
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#include <iosfwd>
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NAMESPACE_BEGIN(CryptoPP)
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/// \struct InitializeInteger
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/// \brief Performs static initialization of the Integer class
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struct InitializeInteger
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{
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InitializeInteger();
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};
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// Always align, http://github.com/weidai11/cryptopp/issues/256
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typedef SecBlock<word, AllocatorWithCleanup<word, true> > IntegerSecBlock;
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/// \brief Multiple precision integer with arithmetic operations
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/// \details The Integer class can represent positive and negative integers
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/// with absolute value less than (256**sizeof(word))<sup>(256**sizeof(int))</sup>.
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/// \details Internally, the library uses a sign magnitude representation, and the class
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/// has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
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/// used to hold the representation. The second is a Sign (an enumeration), and it is
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/// used to track the sign of the Integer.
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/// \details For details on how the Integer class initializes its function pointers using
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/// InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
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/// Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
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/// \since Crypto++ 1.0
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/// \nosubgrouping
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class CRYPTOPP_DLL Integer : private InitializeInteger, public ASN1Object
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{
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public:
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/// \name ENUMS, EXCEPTIONS, and TYPEDEFS
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//@{
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/// \brief Exception thrown when division by 0 is encountered
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class DivideByZero : public Exception
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{
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public:
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DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {}
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};
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/// \brief Exception thrown when a random number cannot be found that
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/// satisfies the condition
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class RandomNumberNotFound : public Exception
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{
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public:
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RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {}
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};
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/// \enum Sign
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/// \brief Used internally to represent the integer
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/// \details Sign is used internally to represent the integer. It is also used in a few API functions.
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/// \sa SetPositive(), SetNegative(), Signedness
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enum Sign {
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/// \brief the value is positive or 0
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POSITIVE=0,
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/// \brief the value is negative
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NEGATIVE=1};
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/// \enum Signedness
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/// \brief Used when importing and exporting integers
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/// \details Signedness is usually used in API functions.
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/// \sa Sign
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enum Signedness {
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/// \brief an unsigned value
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UNSIGNED,
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/// \brief a signed value
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SIGNED};
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/// \enum RandomNumberType
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/// \brief Properties of a random integer
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enum RandomNumberType {
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/// \brief a number with no special properties
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ANY,
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/// \brief a number which is probabilistically prime
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PRIME};
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//@}
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/// \name CREATORS
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//@{
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/// \brief Creates the zero integer
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Integer();
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/// copy constructor
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Integer(const Integer& t);
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/// \brief Convert from signed long
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Integer(signed long value);
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/// \brief Convert from lword
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/// \param sign enumeration indicating Sign
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/// \param value the long word
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Integer(Sign sign, lword value);
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/// \brief Convert from two words
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/// \param sign enumeration indicating Sign
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/// \param highWord the high word
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/// \param lowWord the low word
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Integer(Sign sign, word highWord, word lowWord);
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/// \brief Convert from a C-string
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/// \param str C-string value
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/// \param order the ByteOrder of the string to be processed
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/// \details \p str can be in base 2, 8, 10, or 16. Base is determined by a case
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/// insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
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/// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
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/// integers with curve25519, Poly1305 and Microsoft CAPI.
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explicit Integer(const char *str, ByteOrder order = BIG_ENDIAN_ORDER);
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/// \brief Convert from a wide C-string
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/// \param str wide C-string value
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/// \param order the ByteOrder of the string to be processed
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/// \details \p str can be in base 2, 8, 10, or 16. Base is determined by a case
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/// insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
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/// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
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/// integers with curve25519, Poly1305 and Microsoft CAPI.
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explicit Integer(const wchar_t *str, ByteOrder order = BIG_ENDIAN_ORDER);
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/// \brief Convert from a big-endian byte array
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/// \param encodedInteger big-endian byte array
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/// \param byteCount length of the byte array
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/// \param sign enumeration indicating Signedness
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/// \param order the ByteOrder of the array to be processed
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/// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
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/// integers with curve25519, Poly1305 and Microsoft CAPI.
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Integer(const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER);
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/// \brief Convert from a big-endian array
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/// \param bt BufferedTransformation object with big-endian byte array
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/// \param byteCount length of the byte array
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/// \param sign enumeration indicating Signedness
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/// \param order the ByteOrder of the data to be processed
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/// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
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/// integers with curve25519, Poly1305 and Microsoft CAPI.
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Integer(BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER);
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/// \brief Convert from a BER encoded byte array
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/// \param bt BufferedTransformation object with BER encoded byte array
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explicit Integer(BufferedTransformation &bt);
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/// \brief Create a random integer
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/// \param rng RandomNumberGenerator used to generate material
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/// \param bitCount the number of bits in the resulting integer
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/// \details The random integer created is uniformly distributed over <tt>[0, 2<sup>bitCount</sup>]</tt>.
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Integer(RandomNumberGenerator &rng, size_t bitCount);
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/// \brief Integer representing 0
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/// \return an Integer representing 0
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/// \details Zero() avoids calling constructors for frequently used integers
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static const Integer & CRYPTOPP_API Zero();
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/// \brief Integer representing 1
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/// \return an Integer representing 1
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/// \details One() avoids calling constructors for frequently used integers
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static const Integer & CRYPTOPP_API One();
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/// \brief Integer representing 2
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/// \return an Integer representing 2
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/// \details Two() avoids calling constructors for frequently used integers
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static const Integer & CRYPTOPP_API Two();
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/// \brief Create a random integer of special form
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/// \param rng RandomNumberGenerator used to generate material
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/// \param min the minimum value
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/// \param max the maximum value
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/// \param rnType RandomNumberType to specify the type
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/// \param equiv the equivalence class based on the parameter \p mod
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/// \param mod the modulus used to reduce the equivalence class
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/// \throw RandomNumberNotFound if the set is empty.
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/// \details Ideally, the random integer created should be uniformly distributed
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/// over <tt>{x | min \<= x \<= max</tt> and \p x is of rnType and <tt>x \% mod == equiv}</tt>.
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/// However the actual distribution may not be uniform because sequential
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/// search is used to find an appropriate number from a random starting
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/// point.
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/// \details May return (with very small probability) a pseudoprime when a prime
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/// is requested and <tt>max \> lastSmallPrime*lastSmallPrime</tt>. \p lastSmallPrime
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/// is declared in nbtheory.h.
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Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One());
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/// \brief Exponentiates to a power of 2
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/// \return the Integer 2<sup>e</sup>
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/// \sa a_times_b_mod_c() and a_exp_b_mod_c()
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static Integer CRYPTOPP_API Power2(size_t e);
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//@}
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/// \name ENCODE/DECODE
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//@{
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/// \brief Minimum number of bytes to encode this integer
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/// \param sign enumeration indicating Signedness
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/// \note The MinEncodedSize() of 0 is 1.
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size_t MinEncodedSize(Signedness sign=UNSIGNED) const;
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/// \brief Encode in big-endian format
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/// \param output big-endian byte array
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/// \param outputLen length of the byte array
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/// \param sign enumeration indicating Signedness
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/// \details Unsigned means encode absolute value, signed means encode two's complement if negative.
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/// \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a
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/// minimum size). An exact size is useful, for example, when encoding to a field element size.
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void Encode(byte *output, size_t outputLen, Signedness sign=UNSIGNED) const;
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/// \brief Encode in big-endian format
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/// \param bt BufferedTransformation object
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/// \param outputLen length of the encoding
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/// \param sign enumeration indicating Signedness
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/// \details Unsigned means encode absolute value, signed means encode two's complement if negative.
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/// \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a
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/// minimum size). An exact size is useful, for example, when encoding to a field element size.
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void Encode(BufferedTransformation &bt, size_t outputLen, Signedness sign=UNSIGNED) const;
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/// \brief Encode in DER format
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/// \param bt BufferedTransformation object
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/// \details Encodes the Integer using Distinguished Encoding Rules
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/// The result is placed into a BufferedTransformation object
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void DEREncode(BufferedTransformation &bt) const;
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/// \brief Encode absolute value as big-endian octet string
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/// \param bt BufferedTransformation object
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/// \param length the number of mytes to decode
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void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const;
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/// \brief Encode absolute value in OpenPGP format
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/// \param output big-endian byte array
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/// \param bufferSize length of the byte array
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/// \return length of the output
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/// \details OpenPGPEncode places result into the buffer and returns the
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/// number of bytes used for the encoding
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size_t OpenPGPEncode(byte *output, size_t bufferSize) const;
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/// \brief Encode absolute value in OpenPGP format
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/// \param bt BufferedTransformation object
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/// \return length of the output
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/// \details OpenPGPEncode places result into a BufferedTransformation object and returns the
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/// number of bytes used for the encoding
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size_t OpenPGPEncode(BufferedTransformation &bt) const;
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/// \brief Decode from big-endian byte array
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/// \param input big-endian byte array
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/// \param inputLen length of the byte array
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/// \param sign enumeration indicating Signedness
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void Decode(const byte *input, size_t inputLen, Signedness sign=UNSIGNED);
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/// \brief Decode nonnegative value from big-endian byte array
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/// \param bt BufferedTransformation object
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/// \param inputLen length of the byte array
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/// \param sign enumeration indicating Signedness
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/// \note <tt>bt.MaxRetrievable() \>= inputLen</tt>.
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void Decode(BufferedTransformation &bt, size_t inputLen, Signedness sign=UNSIGNED);
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/// \brief Decode from BER format
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/// \param input big-endian byte array
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/// \param inputLen length of the byte array
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void BERDecode(const byte *input, size_t inputLen);
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/// \brief Decode from BER format
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/// \param bt BufferedTransformation object
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void BERDecode(BufferedTransformation &bt);
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/// \brief Decode nonnegative value from big-endian octet string
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/// \param bt BufferedTransformation object
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/// \param length length of the byte array
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void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length);
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/// \brief Exception thrown when an error is encountered decoding an OpenPGP integer
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class OpenPGPDecodeErr : public Exception
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{
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public:
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OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {}
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};
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/// \brief Decode from OpenPGP format
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/// \param input big-endian byte array
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/// \param inputLen length of the byte array
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void OpenPGPDecode(const byte *input, size_t inputLen);
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/// \brief Decode from OpenPGP format
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/// \param bt BufferedTransformation object
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void OpenPGPDecode(BufferedTransformation &bt);
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//@}
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/// \name ACCESSORS
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//@{
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/// \brief Determines if the Integer is convertable to Long
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/// \return true if *this can be represented as a signed long
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/// \sa ConvertToLong()
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bool IsConvertableToLong() const;
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/// \brief Convert the Integer to Long
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/// \return equivalent signed long if possible, otherwise undefined
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/// \sa IsConvertableToLong()
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signed long ConvertToLong() const;
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/// \brief Determines the number of bits required to represent the Integer
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/// \return number of significant bits
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/// \details BitCount is calculated as <tt>floor(log2(abs(*this))) + 1</tt>.
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unsigned int BitCount() const;
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/// \brief Determines the number of bytes required to represent the Integer
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/// \return number of significant bytes
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/// \details ByteCount is calculated as <tt>ceiling(BitCount()/8)</tt>.
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unsigned int ByteCount() const;
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/// \brief Determines the number of words required to represent the Integer
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/// \return number of significant words
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/// \details WordCount is calculated as <tt>ceiling(ByteCount()/sizeof(word))</tt>.
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unsigned int WordCount() const;
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/// \brief Provides the i-th bit of the Integer
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/// \return the i-th bit, i=0 being the least significant bit
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bool GetBit(size_t i) const;
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/// \brief Provides the i-th byte of the Integer
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/// \return the i-th byte
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byte GetByte(size_t i) const;
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/// \brief Provides the low order bits of the Integer
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/// \return n lowest bits of *this >> i
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lword GetBits(size_t i, size_t n) const;
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/// \brief Determines if the Integer is 0
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/// \return true if the Integer is 0, false otherwise
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bool IsZero() const {return !*this;}
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/// \brief Determines if the Integer is non-0
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/// \return true if the Integer is non-0, false otherwise
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bool NotZero() const {return !IsZero();}
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/// \brief Determines if the Integer is negative
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/// \return true if the Integer is negative, false otherwise
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bool IsNegative() const {return sign == NEGATIVE;}
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/// \brief Determines if the Integer is non-negative
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/// \return true if the Integer is non-negative, false otherwise
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bool NotNegative() const {return !IsNegative();}
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/// \brief Determines if the Integer is positive
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/// \return true if the Integer is positive, false otherwise
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bool IsPositive() const {return NotNegative() && NotZero();}
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/// \brief Determines if the Integer is non-positive
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/// \return true if the Integer is non-positive, false otherwise
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bool NotPositive() const {return !IsPositive();}
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/// \brief Determines if the Integer is even parity
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/// \return true if the Integer is even, false otherwise
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bool IsEven() const {return GetBit(0) == 0;}
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/// \brief Determines if the Integer is odd parity
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/// \return true if the Integer is odd, false otherwise
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bool IsOdd() const {return GetBit(0) == 1;}
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//@}
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/// \name MANIPULATORS
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//@{
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/// \brief Assignment
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/// \param t the other Integer
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/// \return the result of assignment
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Integer& operator=(const Integer& t);
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/// \brief Addition Assignment
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/// \param t the other Integer
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/// \return the result of <tt>*this + t</tt>
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Integer& operator+=(const Integer& t);
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/// \brief Subtraction Assignment
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/// \param t the other Integer
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/// \return the result of <tt>*this - t</tt>
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Integer& operator-=(const Integer& t);
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/// \brief Multiplication Assignment
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/// \param t the other Integer
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/// \return the result of <tt>*this * t</tt>
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/// \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer& operator*=(const Integer& t) {return *this = Times(t);}
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/// \brief Division Assignment
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/// \param t the other Integer
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/// \return the result of <tt>*this / t</tt>
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Integer& operator/=(const Integer& t) {return *this = DividedBy(t);}
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/// \brief Remainder Assignment
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/// \param t the other Integer
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/// \return the result of <tt>*this % t</tt>
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/// \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer& operator%=(const Integer& t) {return *this = Modulo(t);}
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/// \brief Division Assignment
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/// \param t the other word
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/// \return the result of <tt>*this / t</tt>
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Integer& operator/=(word t) {return *this = DividedBy(t);}
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/// \brief Remainder Assignment
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/// \param t the other word
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/// \return the result of <tt>*this % t</tt>
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/// \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer& operator%=(word t) {return *this = Integer(POSITIVE, 0, Modulo(t));}
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/// \brief Left-shift Assignment
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/// \param n number of bits to shift
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/// \return reference to this Integer
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Integer& operator<<=(size_t n);
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/// \brief Right-shift Assignment
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/// \param n number of bits to shift
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/// \return reference to this Integer
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Integer& operator>>=(size_t n);
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/// \brief Bitwise AND Assignment
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/// \param t the other Integer
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/// \return the result of *this & t
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/// \details operator&=() performs a bitwise AND on *this. Missing bits are truncated
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/// at the most significant bit positions, so the result is as small as the
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/// smaller of the operands.
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/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
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/// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
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/// the integer should be converted to a 2's compliment representation before performing
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/// the operation.
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/// \since Crypto++ 6.0
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Integer& operator&=(const Integer& t);
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/// \brief Bitwise OR Assignment
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/// \param t the second Integer
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/// \return the result of *this | t
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/// \details operator|=() performs a bitwise OR on *this. Missing bits are shifted in
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/// at the most significant bit positions, so the result is as large as the
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/// larger of the operands.
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/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
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/// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
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/// the integer should be converted to a 2's compliment representation before performing
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/// the operation.
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/// \since Crypto++ 6.0
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Integer& operator|=(const Integer& t);
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/// \brief Bitwise XOR Assignment
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/// \param t the other Integer
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/// \return the result of *this ^ t
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/// \details operator^=() performs a bitwise XOR on *this. Missing bits are shifted
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/// in at the most significant bit positions, so the result is as large as the
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/// larger of the operands.
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/// \details Internally, Crypto++ uses a sign-magnitude representation. The library
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/// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
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/// the integer should be converted to a 2's compliment representation before performing
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/// the operation.
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/// \since Crypto++ 6.0
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Integer& operator^=(const Integer& t);
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/// \brief Set this Integer to random integer
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/// \param rng RandomNumberGenerator used to generate material
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/// \param bitCount the number of bits in the resulting integer
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/// \details The random integer created is uniformly distributed over <tt>[0, 2<sup>bitCount</sup>]</tt>.
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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 ¶ms = 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 ¶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
|
|
//@{
|
|
/// \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 comapre
|
|
/// \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 a reference to the dividend
|
|
/// \param d a 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 a reference to the dividend
|
|
/// \param d a 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 a reference to the dividend
|
|
/// \param n a 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 a reference to the first number
|
|
/// \param n a 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 a 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 a reference to a std::istream
|
|
/// \param a a reference to an Integer
|
|
/// \return 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
|
|
/// \return 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 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 a reference to the first term
|
|
/// \param y a reference to the second term
|
|
/// \param m a 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 a reference to the base
|
|
/// \param e a reference to the exponent
|
|
/// \param m a 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 "ient, const Integer ÷nd, 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
|