571 lines
22 KiB
C++
571 lines
22 KiB
C++
#ifndef CRYPTOPP_INTEGER_H
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#define CRYPTOPP_INTEGER_H
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/** \file */
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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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//! Performs static intialization 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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typedef SecBlock<word, AllocatorWithCleanup<word, CRYPTOPP_BOOL_X86> > 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 i
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//! used to hold the representation. The second is a Sign, and its is used to track
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//! the sign of the Integer.
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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 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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//! \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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explicit Integer(const char *str);
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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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//! \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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explicit Integer(const wchar_t *str);
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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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Integer(const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED);
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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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Integer(BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED);
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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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//! \returns 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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//! \returns 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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//! \returns 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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//! \returns 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 The 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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//! 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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//! \returns 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(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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//! \returns 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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//! return true if *this can be represented as a signed long
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bool IsConvertableToLong() const;
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//! return equivalent signed long if possible, otherwise undefined
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signed long ConvertToLong() const;
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//! number of significant bits = floor(log2(abs(*this))) + 1
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unsigned int BitCount() const;
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//! number of significant bytes = ceiling(BitCount()/8)
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unsigned int ByteCount() const;
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//! number of significant words = ceiling(ByteCount()/sizeof(word))
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unsigned int WordCount() const;
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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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//! return the i-th byte
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byte GetByte(size_t i) const;
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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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//!
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bool IsZero() const {return !*this;}
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//!
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bool NotZero() const {return !IsZero();}
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//!
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bool IsNegative() const {return sign == NEGATIVE;}
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//!
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bool NotNegative() const {return !IsNegative();}
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//!
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bool IsPositive() const {return NotNegative() && NotZero();}
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//!
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bool NotPositive() const {return !IsPositive();}
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//!
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bool IsEven() const {return GetBit(0) == 0;}
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//!
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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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//!
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Integer& operator=(const Integer& t);
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//!
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Integer& operator+=(const Integer& t);
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//!
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Integer& operator-=(const Integer& t);
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//!
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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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//!
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Integer& operator/=(const Integer& t) {return *this = DividedBy(t);}
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//!
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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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//!
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Integer& operator/=(word t) {return *this = DividedBy(t);}
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//!
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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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//!
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Integer& operator<<=(size_t);
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//!
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Integer& operator>>=(size_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);
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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 min the minimum value
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//! \param max the maximum value
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//! \details The random integer created is uniformly distributed over <tt>[min, max]</tt>.
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void Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max);
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//! \brief Set this Integer to 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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bool Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One());
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bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs);
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void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs)
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{
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if (!GenerateRandomNoThrow(rng, params))
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throw RandomNumberNotFound();
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}
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//! \brief Set the n-th bit to value
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//! \details 0-based numbering.
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void SetBit(size_t n, bool value=1);
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//! \brief Set the n-th byte to value
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//! \details 0-based numbering.
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void SetByte(size_t n, byte value);
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//! \brief Reverse the Sign of the Integer
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void Negate();
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//! \brief Sets the Integer to positive
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void SetPositive() {sign = POSITIVE;}
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//! \brief Sets the Integer to negative
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void SetNegative() {if (!!(*this)) sign = NEGATIVE;}
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//! \brief Swaps this Integer with another Integer
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void swap(Integer &a);
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//@}
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//! \name UNARY OPERATORS
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//@{
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//!
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bool operator!() const;
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//!
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Integer operator+() const {return *this;}
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//!
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Integer operator-() const;
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//!
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Integer& operator++();
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//!
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Integer& operator--();
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//!
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Integer operator++(int) {Integer temp = *this; ++*this; return temp;}
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//!
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Integer operator--(int) {Integer temp = *this; --*this; return temp;}
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//@}
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//! \name BINARY OPERATORS
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//@{
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//! \brief Perform signed comparison
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//! \param a the Integer to comapre
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//! \retval -1 if <tt>*this < a</tt>
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//! \retval 0 if <tt>*this = a</tt>
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//! \retval 1 if <tt>*this > a</tt>
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int Compare(const Integer& a) const;
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//!
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Integer Plus(const Integer &b) const;
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//!
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Integer Minus(const Integer &b) const;
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//!
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer Times(const Integer &b) const;
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//!
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Integer DividedBy(const Integer &b) const;
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//!
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer Modulo(const Integer &b) const;
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//!
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Integer DividedBy(word b) const;
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//!
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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word Modulo(word b) const;
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//!
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Integer operator>>(size_t n) const {return Integer(*this)>>=n;}
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//!
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Integer operator<<(size_t n) const {return Integer(*this)<<=n;}
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//@}
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//! \name OTHER ARITHMETIC FUNCTIONS
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//@{
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//!
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Integer AbsoluteValue() const;
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//!
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Integer Doubled() const {return Plus(*this);}
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//!
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer Squared() const {return Times(*this);}
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//! extract square root, if negative return 0, else return floor of square root
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Integer SquareRoot() const;
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//! return whether this integer is a perfect square
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bool IsSquare() const;
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//! is 1 or -1
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bool IsUnit() const;
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//! return inverse if 1 or -1, otherwise return 0
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Integer MultiplicativeInverse() const;
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//! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))
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static void CRYPTOPP_API Divide(Integer &r, Integer &q, const Integer &a, const Integer &d);
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//! use a faster division algorithm when divisor is short
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static void CRYPTOPP_API Divide(word &r, Integer &q, const Integer &a, word d);
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//! returns same result as Divide(r, q, a, Power2(n)), but faster
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static void CRYPTOPP_API DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n);
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//! greatest common divisor
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static Integer CRYPTOPP_API Gcd(const Integer &a, const Integer &n);
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//! calculate multiplicative inverse of *this mod n
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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Integer InverseMod(const Integer &n) const;
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//!
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//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
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word InverseMod(word n) const;
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//@}
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//! \name INPUT/OUTPUT
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//@{
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//! \brief Extraction operator
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//! \param in a reference to a std::istream
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//! \param a a reference to an Integer
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//! \returns a reference to a std::istream reference
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friend CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>(std::istream& in, Integer &a);
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//!
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//! \brief Insertion operator
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//! \param out a reference to a std::ostream
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//! \param a a constant reference to an Integer
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//! \returns a reference to a std::ostream reference
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//! \details The output integer responds to std::hex, std::oct, std::hex, std::upper and
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//! std::lower. The output includes the suffix \a \b h (for hex), \a \b . (\a \b dot, for dec)
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//! and \a \b o (for octal). There is currently no way to supress the suffix.
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//! \details If you want to print an Integer without the suffix or using an arbitrary base, then
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//! use IntToString<Integer>().
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//! \sa IntToString<Integer>
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friend CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<(std::ostream& out, const Integer &a);
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//@}
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#ifndef CRYPTOPP_DOXYGEN_PROCESSING
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//! modular multiplication
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CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m);
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//! modular exponentiation
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CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m);
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#endif
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private:
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Integer(word value, size_t length);
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int PositiveCompare(const Integer &t) const;
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IntegerSecBlock reg;
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Sign sign;
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|
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#ifndef CRYPTOPP_DOXYGEN_PROCESSING
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friend class ModularArithmetic;
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friend class MontgomeryRepresentation;
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friend class HalfMontgomeryRepresentation;
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|
|
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friend void PositiveAdd(Integer &sum, const Integer &a, const Integer &b);
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friend void PositiveSubtract(Integer &diff, const Integer &a, const Integer &b);
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friend void PositiveMultiply(Integer &product, const Integer &a, const Integer &b);
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friend void PositiveDivide(Integer &remainder, Integer "ient, const Integer ÷nd, const Integer &divisor);
|
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#endif
|
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};
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|
|
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//!
|
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inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;}
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//!
|
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inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;}
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//!
|
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inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;}
|
|
//!
|
|
inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;}
|
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//!
|
|
inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;}
|
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//!
|
|
inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;}
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//!
|
|
inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);}
|
|
//!
|
|
inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);}
|
|
//!
|
|
//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
|
|
inline CryptoPP::Integer operator*(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Times(b);}
|
|
//!
|
|
inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);}
|
|
//!
|
|
//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
|
|
inline CryptoPP::Integer operator%(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Modulo(b);}
|
|
//!
|
|
inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);}
|
|
//!
|
|
//! \sa a_times_b_mod_c() and a_exp_b_mod_c()
|
|
inline CryptoPP::word operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);}
|
|
|
|
NAMESPACE_END
|
|
|
|
#ifndef __BORLANDC__
|
|
NAMESPACE_BEGIN(std)
|
|
inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b)
|
|
{
|
|
a.swap(b);
|
|
}
|
|
NAMESPACE_END
|
|
#endif
|
|
|
|
#endif
|