# Integer Class Reference

`#include <integer.h>`

Inheritance diagram for Integer:

List of all members.

## Detailed Description

multiple precision integer and basic arithmetics

This class can represent positive and negative integers with absolute value less than (256**sizeof(word)) ** (256**sizeof(int)).

Definition at line 26 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 &params=g_nullNameValuePairs)
void | GenerateRandom (RandomNumberGenerator &rng, const NameValuePairs &params=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 &quotient, const Integer &dividend, const Integer &divisor)
## Classes
class | DivideByZero
| division by zero exception More...
class | OpenPGPDecodeErr
class | RandomNumberNotFound

## Constructor & Destructor Documentation

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 3038 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 2845 of file integer.cpp.

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).

Exceptions:

  | RandomNumberNotFound | if the set is empty.

Definition at line 2850 of file integer.cpp.

## Member Function Documentation

size_t Integer::MinEncodedSize | ( | Signedness | signedness = `UNSIGNED` | ) | const

minimum number of bytes to encode this integer

MinEncodedSize of 0 is 1

Definition at line 3110 of file integer.cpp.

References ByteCount(), GetByte(), and Power2().

Referenced by DEREncode().

void Integer::Encode | ( | byte * | output,
|  | size_t | outputLen,
|  | Signedness | 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 3122 of file integer.cpp.

Referenced by TF_DecryptorBase::Decrypt(), DEREncode(), DEREncodeAsOctetString(), DSAConvertSignatureFormat(), TF_EncryptorBase::Encrypt(), XTR_DH::GeneratePrivateKey(), DL_SimpleKeyAgreementDomainBase< GROUP_PARAMETERS::Element >::GeneratePrivateKey(), MQV_Domain< GROUP_PARAMETERS, COFACTOR_OPTION >::GenerateStaticPrivateKey(), TF_VerifierBase::InputSignature(), OpenPGPEncode(), DL_VerifierBase< SCHEME_OPTIONS::Element >::RecoverAndRestart(), and TF_SignerBase::SignAndRestart().

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 3237 of file integer.cpp.

int Integer::Compare | ( | const Integer & | a | ) | const

signed comparison

Return values:

  | -1 | if *this < a
  | 0 | if *this = a
  | 1 | if *this > a

Definition at line 3900 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 1657 of file cryptlib.h.

The documentation for this class was generated from the following files:

- integer.h
- integer.cpp