#include <integer.h>
Inheritance diagram for Integer:
This class can represent positive and negative integers with absolute value less than (256**sizeof(word)) ** (256**sizeof(int)).
Definition at line 80 of file integer.h.
ENUMS, EXCEPTIONS, and TYPEDEFS | |
| enum | Sign { POSITIVE = 0, NEGATIVE = 1 } |
| enum | Signedness { UNSIGNED, SIGNED } |
| enum | RandomNumberType { ANY, PRIME } |
OTHER ARITHMETIC FUNCTIONS | |
| Integer __cdecl | a_times_b_mod_c (const Integer &x, const Integer &y, const Integer &m) |
| modular multiplication | |
| Integer __cdecl | a_exp_b_mod_c (const Integer &x, const Integer &e, const Integer &m) |
| modular exponentiation | |
| Integer | AbsoluteValue () const |
| Integer | Doubled () const |
| Integer | Squared () const |
| Integer | SquareRoot () const |
| extract square root, if negative return 0, else return floor of square root | |
| bool | IsSquare () const |
| return whether this integer is a perfect square | |
| bool | IsUnit () const |
| is 1 or -1 | |
| Integer | MultiplicativeInverse () const |
| return inverse if 1 or -1, otherwise return 0 | |
| Integer | InverseMod (const Integer &n) const |
| calculate multiplicative inverse of *this mod n | |
| word | InverseMod (word n) const |
| static void __cdecl | Divide (Integer &r, Integer &q, const Integer &a, const Integer &d) |
| calculate r and q such that (a == d*q + r) && (0 <= r < abs(d)) | |
| static void __cdecl | Divide (word &r, Integer &q, const Integer &a, word d) |
| use a faster division algorithm when divisor is short | |
| static void __cdecl | DivideByPowerOf2 (Integer &r, Integer &q, const Integer &a, unsigned int n) |
| returns same result as Divide(r, q, a, Power2(n)), but faster | |
| static Integer __cdecl | Gcd (const Integer &a, const Integer &n) |
| greatest common divisor | |
INPUT/OUTPUT | |
| std::istream &__cdecl | operator>> (std::istream &in, Integer &a) |
| std::ostream &__cdecl | operator<< (std::ostream &out, const Integer &a) |
CREATORS | |
| Integer () | |
| creates the zero integer | |
| Integer (const Integer &t) | |
| copy constructor | |
| Integer (signed long value) | |
| convert from signed long | |
| Integer (Sign s, lword value) | |
| convert from lword | |
| Integer (Sign s, word highWord, word lowWord) | |
| convert from two words | |
| Integer (const char *str) | |
| convert from string | |
| Integer (const wchar_t *str) | |
| Integer (const byte *encodedInteger, size_t byteCount, Signedness s=UNSIGNED) | |
| convert from big-endian byte array | |
| Integer (BufferedTransformation &bt, size_t byteCount, Signedness s=UNSIGNED) | |
| convert from big-endian form stored in a BufferedTransformation | |
| Integer (BufferedTransformation &bt) | |
| convert from BER encoded byte array stored in a BufferedTransformation object | |
| Integer (RandomNumberGenerator &rng, size_t bitcount) | |
| create a random integer | |
| Integer (RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One()) | |
| create a random integer of special type | |
| static const Integer &__cdecl | Zero () |
| avoid calling constructors for these frequently used integers | |
| static const Integer &__cdecl | One () |
| avoid calling constructors for these frequently used integers | |
| static const Integer &__cdecl | Two () |
| avoid calling constructors for these frequently used integers | |
| static Integer __cdecl | Power2 (size_t e) |
| return the integer 2**e | |
ENCODE/DECODE | |
| size_t | MinEncodedSize (Signedness=UNSIGNED) const |
| minimum number of bytes to encode this integer | |
| void | Encode (byte *output, size_t outputLen, Signedness=UNSIGNED) const |
| encode in big-endian format | |
| void | Encode (BufferedTransformation &bt, size_t outputLen, Signedness=UNSIGNED) const |
| void | DEREncode (BufferedTransformation &bt) const |
| encode using Distinguished Encoding Rules, put result into a BufferedTransformation object | |
| void | DEREncodeAsOctetString (BufferedTransformation &bt, size_t length) const |
| encode absolute value as big-endian octet string | |
| size_t | OpenPGPEncode (byte *output, size_t bufferSize) const |
| encode absolute value in OpenPGP format, return length of output | |
| size_t | OpenPGPEncode (BufferedTransformation &bt) const |
| encode absolute value in OpenPGP format, put result into a BufferedTransformation object | |
| void | Decode (const byte *input, size_t inputLen, Signedness=UNSIGNED) |
| void | Decode (BufferedTransformation &bt, size_t inputLen, Signedness=UNSIGNED) |
| void | BERDecode (const byte *input, size_t inputLen) |
| void | BERDecode (BufferedTransformation &bt) |
| decode this object from a BufferedTransformation, using BER (Basic Encoding Rules) | |
| void | BERDecodeAsOctetString (BufferedTransformation &bt, size_t length) |
| decode nonnegative value as big-endian octet string | |
| void | OpenPGPDecode (const byte *input, size_t inputLen) |
| void | OpenPGPDecode (BufferedTransformation &bt) |
ACCESSORS | |
| bool | IsConvertableToLong () const |
| return true if *this can be represented as a signed long | |
| signed long | ConvertToLong () const |
| return equivalent signed long if possible, otherwise undefined | |
| unsigned int | BitCount () const |
| number of significant bits = floor(log2(abs(*this))) + 1 | |
| unsigned int | ByteCount () const |
| number of significant bytes = ceiling(BitCount()/8) | |
| unsigned int | WordCount () const |
| number of significant words = ceiling(ByteCount()/sizeof(word)) | |
| bool | GetBit (size_t i) const |
| return the i-th bit, i=0 being the least significant bit | |
| byte | GetByte (size_t i) const |
| return the i-th byte | |
| lword | GetBits (size_t i, size_t n) const |
| return n lowest bits of *this >> i | |
| bool | IsZero () const |
| bool | NotZero () const |
| bool | IsNegative () const |
| bool | NotNegative () const |
| bool | IsPositive () const |
| bool | NotPositive () const |
| bool | IsEven () const |
| bool | IsOdd () const |
MANIPULATORS | |
| Integer & | operator= (const Integer &t) |
| Integer & | operator+= (const Integer &t) |
| Integer & | operator-= (const Integer &t) |
| Integer & | operator *= (const Integer &t) |
| Integer & | operator/= (const Integer &t) |
| Integer & | operator%= (const Integer &t) |
| Integer & | operator/= (word t) |
| Integer & | operator%= (word t) |
| Integer & | operator<<= (size_t) |
| Integer & | operator>>= (size_t) |
| void | Randomize (RandomNumberGenerator &rng, size_t bitcount) |
| void | Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max) |
| bool | Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One()) |
| set this Integer to a random element of {x | min <= x <= max and x is of rnType and x % mod == equiv} | |
| bool | GenerateRandomNoThrow (RandomNumberGenerator &rng, const NameValuePairs ¶ms=g_nullNameValuePairs) |
| void | GenerateRandom (RandomNumberGenerator &rng, const NameValuePairs ¶ms=g_nullNameValuePairs) |
| void | SetBit (size_t n, bool value=1) |
| set the n-th bit to value | |
| void | SetByte (size_t n, byte value) |
| set the n-th byte to value | |
| void | Negate () |
| void | SetPositive () |
| void | SetNegative () |
| void | swap (Integer &a) |
UNARY OPERATORS | |
| bool | operator! () const |
| Integer | operator+ () const |
| Integer | operator- () const |
| Integer & | operator++ () |
| Integer & | operator-- () |
| Integer | operator++ (int) |
| Integer | operator-- (int) |
BINARY OPERATORS | |
| int | Compare (const Integer &a) const |
| signed comparison | |
| Integer | Plus (const Integer &b) const |
| Integer | Minus (const Integer &b) const |
| Integer | Times (const Integer &b) const |
| Integer | DividedBy (const Integer &b) const |
| Integer | Modulo (const Integer &b) const |
| Integer | DividedBy (word b) const |
| word | Modulo (word b) const |
| Integer | operator>> (size_t n) const |
| Integer | operator<< (size_t n) const |
Public Member Functions | |
| virtual void | BEREncode (BufferedTransformation &bt) const |
| encode this object into a BufferedTransformation, using BER | |
Friends | |
| class | ModularArithmetic |
| class | MontgomeryRepresentation |
| class | HalfMontgomeryRepresentation |
| void | PositiveAdd (Integer &sum, const Integer &a, const Integer &b) |
| void | PositiveSubtract (Integer &diff, const Integer &a, const Integer &b) |
| void | PositiveMultiply (Integer &product, const Integer &a, const Integer &b) |
| void | PositiveDivide (Integer &remainder, Integer "ient, const Integer ÷nd, const Integer &divisor) |
Classes | |
| class | DivideByZero |
| division by zero exception More... | |
| class | OpenPGPDecodeErr |
| class | RandomNumberNotFound |
| Integer::Integer | ( | const char * | str | ) | [explicit] |
convert from string
str can be in base 2, 8, 10, or 16. Base is determined by a case insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
Definition at line 3021 of file integer.cpp.
| Integer::Integer | ( | RandomNumberGenerator & | rng, | |
| size_t | bitcount | |||
| ) |
create a random integer
The random integer created is uniformly distributed over [0, 2**bitcount).
Definition at line 2829 of file integer.cpp.
References Randomize().
| Integer::Integer | ( | RandomNumberGenerator & | rng, | |
| const Integer & | min, | |||
| const Integer & | max, | |||
| RandomNumberType | rnType = ANY, |
|||
| const Integer & | equiv = Zero(), |
|||
| const Integer & | mod = One() | |||
| ) |
create a random integer of special type
Ideally, the random integer created should be uniformly distributed over {x | min <= x <= max and x is of rnType and x % mod == equiv}. However the actual distribution may not be uniform because sequential search is used to find an appropriate number from a random starting point. May return (with very small probability) a pseudoprime when a prime is requested and max > lastSmallPrime*lastSmallPrime (lastSmallPrime is declared in nbtheory.h).
| RandomNumberNotFound | if the set is empty. |
Definition at line 2834 of file integer.cpp.
References Randomize().
| size_t Integer::MinEncodedSize | ( | Signedness | = UNSIGNED |
) | const |
minimum number of bytes to encode this integer
MinEncodedSize of 0 is 1
Definition at line 3093 of file integer.cpp.
References ByteCount(), GetByte(), IsNegative(), NotNegative(), and Power2().
Referenced by DEREncode().
| void Integer::Encode | ( | byte * | output, | |
| size_t | outputLen, | |||
| Signedness | = UNSIGNED | |||
| ) | const |
encode in big-endian format
unsigned means encode absolute value, signed means encode two's complement if negative. if outputLen < MinEncodedSize, the most significant bytes will be dropped if outputLen > MinEncodedSize, the most significant bytes will be padded
Definition at line 3105 of file integer.cpp.
Referenced by DL_SignatureMessageEncodingMethod_NR::ComputeMessageRepresentative(), DL_SignatureMessageEncodingMethod_DSA::ComputeMessageRepresentative(), TF_DecryptorBase::Decrypt(), DEREncode(), DEREncodeAsOctetString(), ElGamalBase::Derive(), DSAConvertSignatureFormat(), Encode(), DL_GroupParameters_IntegerBased::EncodeElement(), TF_EncryptorBase::Encrypt(), XTR_DH::GeneratePrivateKey(), DL_SimpleKeyAgreementDomainBase< GROUP_PARAMETERS::Element >::GeneratePrivateKey(), MQV_Domain< GROUP_PARAMETERS, COFACTOR_OPTION >::GenerateStaticPrivateKey(), TF_VerifierBase::InputSignature(), OpenPGPEncode(), DL_SignerBase< SCHEME_OPTIONS::Element >::SignAndRestart(), TF_SignerBase::SignAndRestart(), ElGamalBase::SymmetricDecrypt(), and ElGamalBase::SymmetricEncrypt().
| bool Integer::Randomize | ( | RandomNumberGenerator & | rng, | |
| const Integer & | min, | |||
| const Integer & | max, | |||
| RandomNumberType | rnType, | |||
| const Integer & | equiv = Zero(), |
|||
| const Integer & | mod = One() | |||
| ) |
set this Integer to a random element of {x | min <= x <= max and x is of rnType and x % mod == equiv}
returns false if the set is empty
Definition at line 3220 of file integer.cpp.
References GenerateRandomNoThrow().
| int Integer::Compare | ( | const Integer & | a | ) | const |
signed comparison
| -1 | if *this < a | |
| 0 | if *this = a | |
| 1 | if *this > a |
Definition at line 3886 of file integer.cpp.
References NotNegative().
| virtual void ASN1Object::BEREncode | ( | BufferedTransformation & | bt | ) | const [inline, virtual, inherited] |
encode this object into a BufferedTransformation, using BER
this may be useful if DEREncode() would be too inefficient
Definition at line 1579 of file cryptlib.h.
Referenced by ASN1CryptoMaterial< PublicKey >::Save().
1.5.1-p1