Multiple precision integer with arithmetic operations. More...

#include <integer.h>

Inheritance diagram for Integer:

Collaboration diagram for Integer:

Classes
class	DivideByZero
	Exception thrown when division by 0 is encountered. More...

class	OpenPGPDecodeErr
	Exception thrown when an error is encountered decoding an OpenPGP integer. More...

class	RandomNumberNotFound
	Exception thrown when a random number cannot be found that satisfies the condition. More...

Private Member Functions
	Integer (word value, size_t length)

int	PositiveCompare (const Integer &t) const

Private Member Functions inherited from InitializeInteger
	InitializeInteger ()

Private Attributes
IntegerSecBlock	reg

Sign	sign

Friends
class	ModularArithmetic

class	MontgomeryRepresentation

class	HalfMontgomeryRepresentation

CRYPTOPP_DLL friend Integer CRYPTOPP_API	a_times_b_mod_c (const Integer &x, const Integer &y, const Integer &m)
	modular multiplication More...

CRYPTOPP_DLL friend Integer CRYPTOPP_API	a_exp_b_mod_c (const Integer &x, const Integer &e, const Integer &m)
	modular exponentiation More...

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)

ENUMS, EXCEPTIONS, and TYPEDEFS
enum	Sign { POSITIVE =0, NEGATIVE =1 }
	Used internally to represent the integer. More...

enum	Signedness { UNSIGNED, SIGNED }
	Used when importing and exporting integers. More...

enum	RandomNumberType { ANY, PRIME }
	Properties of a random integer. More...

CREATORS
	Integer ()
	Creates the zero integer. More...

	Integer (const Integer &t)
	copy constructor More...

	Integer (signed long value)
	Convert from signed long. More...

	Integer (Sign sign, lword value)
	Convert from lword. More...

	Integer (Sign sign, word highWord, word lowWord)
	Convert from two words. More...

	Integer (const char *str, ByteOrder order=BIG_ENDIAN_ORDER)
	Convert from a C-string. More...

	Integer (const wchar_t *str, ByteOrder order=BIG_ENDIAN_ORDER)
	Convert from a wide C-string. More...

	Integer (const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order=BIG_ENDIAN_ORDER)
	Convert from a big-endian byte array. More...

	Integer (BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order=BIG_ENDIAN_ORDER)
	Convert from a big-endian array. More...

	Integer (BufferedTransformation &bt)
	Convert from a BER encoded byte array. More...

	Integer (RandomNumberGenerator &rng, size_t bitCount)
	Create a random integer. More...

	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 form. More...

static const Integer &CRYPTOPP_API	Zero ()
	Integer representing 0. More...

static const Integer &CRYPTOPP_API	One ()
	Integer representing 1. More...

static const Integer &CRYPTOPP_API	Two ()
	Integer representing 2. More...

static Integer CRYPTOPP_API	Power2 (size_t e)
	Exponentiates to a power of 2. More...

ENCODE/DECODE
size_t	MinEncodedSize (Signedness sign=UNSIGNED) const
	Minimum number of bytes to encode this integer. More...

void	Encode (byte *output, size_t outputLen, Signedness sign=UNSIGNED) const
	Encode in big-endian format. More...

void	Encode (BufferedTransformation &bt, size_t outputLen, Signedness sign=UNSIGNED) const
	Encode in big-endian format. More...

void	DEREncode (BufferedTransformation &bt) const
	Encode in DER format. More...

void	DEREncodeAsOctetString (BufferedTransformation &bt, size_t length) const
	Encode absolute value as big-endian octet string. More...

size_t	OpenPGPEncode (byte *output, size_t bufferSize) const
	Encode absolute value in OpenPGP format. More...

size_t	OpenPGPEncode (BufferedTransformation &bt) const
	Encode absolute value in OpenPGP format. More...

void	Decode (const byte *input, size_t inputLen, Signedness sign=UNSIGNED)
	Decode from big-endian byte array. More...

void	Decode (BufferedTransformation &bt, size_t inputLen, Signedness sign=UNSIGNED)
	Decode nonnegative value from big-endian byte array. More...

void	BERDecode (const byte *input, size_t inputLen)
	Decode from BER format. More...

void	BERDecode (BufferedTransformation &bt)
	Decode from BER format. More...

void	BERDecodeAsOctetString (BufferedTransformation &bt, size_t length)
	Decode nonnegative value from big-endian octet string. More...

void	OpenPGPDecode (const byte *input, size_t inputLen)
	Decode from OpenPGP format. More...

void	OpenPGPDecode (BufferedTransformation &bt)
	Decode from OpenPGP format. More...

ACCESSORS
bool	IsConvertableToLong () const
	Determines if the Integer is convertable to Long. More...

signed long	ConvertToLong () const
	Convert the Integer to Long. More...

unsigned int	BitCount () const
	Determines the number of bits required to represent the Integer. More...

unsigned int	ByteCount () const
	Determines the number of bytes required to represent the Integer. More...

unsigned int	WordCount () const
	Determines the number of words required to represent the Integer. More...

bool	GetBit (size_t i) const
	Provides the i-th bit of the Integer. More...

byte	GetByte (size_t i) const
	Provides the i-th byte of the Integer. More...

lword	GetBits (size_t i, size_t n) const
	Provides the low order bits of the Integer. More...

bool	IsZero () const
	Determines if the Integer is 0. More...

bool	NotZero () const
	Determines if the Integer is non-0. More...

bool	IsNegative () const
	Determines if the Integer is negative. More...

bool	NotNegative () const
	Determines if the Integer is non-negative. More...

bool	IsPositive () const
	Determines if the Integer is positive. More...

bool	NotPositive () const
	Determines if the Integer is non-positive. More...

bool	IsEven () const
	Determines if the Integer is even parity. More...

bool	IsOdd () const
	Determines if the Integer is odd parity. More...

MANIPULATORS
Integer &	operator= (const Integer &t)
	Assignment. More...

Integer &	operator+= (const Integer &t)
	Addition Assignment. More...

Integer &	operator-= (const Integer &t)
	Subtraction Assignment. More...

Integer &	operator*= (const Integer &t)
	Multiplication Assignment. More...

Integer &	operator/= (const Integer &t)
	Division Assignment. More...

Integer &	operator%= (const Integer &t)
	Remainder Assignment. More...

Integer &	operator/= (word t)
	Division Assignment. More...

Integer &	operator%= (word t)
	Remainder Assignment. More...

Integer &	operator<<= (size_t n)
	Left-shift Assignment. More...

Integer &	operator>>= (size_t n)
	Right-shift Assignment. More...

Integer &	operator&= (const Integer &t)
	Bitwise AND Assignment. More...

Integer &	operator\|= (const Integer &t)
	Bitwise OR Assignment. More...

Integer &	operator^= (const Integer &t)
	Bitwise XOR Assignment. More...

void	Randomize (RandomNumberGenerator &rng, size_t bitCount)
	Set this Integer to random integer. More...

void	Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max)
	Set this Integer to random integer. More...

bool	Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One())
	Set this Integer to random integer of special form. More...

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. More...

void	SetByte (size_t n, byte value)
	Set the n-th byte to value. More...

void	Negate ()
	Reverse the Sign of the Integer. More...

void	SetPositive ()
	Sets the Integer to positive. More...

void	SetNegative ()
	Sets the Integer to negative. More...

void	swap (Integer &a)
	Swaps this Integer with another Integer. More...

UNARY OPERATORS
bool	operator! () const
	Negation. More...

Integer	operator+ () const
	Addition. More...

Integer	operator- () const
	Subtraction. More...

Integer &	operator++ ()
	Pre-increment. More...

Integer &	operator-- ()
	Pre-decrement. More...

Integer	operator++ (int)
	Post-increment. More...

Integer	operator-- (int)
	Post-decrement. More...

BINARY OPERATORS
int	Compare (const Integer &a) const
	Perform signed comparison. More...

Integer	Plus (const Integer &b) const
	Addition. More...

Integer	Minus (const Integer &b) const
	Subtraction. More...

Integer	Times (const Integer &b) const
	Multiplication. More...

Integer	DividedBy (const Integer &b) const
	Division. More...

Integer	Modulo (const Integer &b) const
	Remainder. More...

Integer	DividedBy (word b) const
	Division. More...

word	Modulo (word b) const
	Remainder. More...

Integer	And (const Integer &) const
	Bitwise AND. More...

Integer	Or (const Integer &) const
	Bitwise OR. More...

Integer	Xor (const Integer &) const
	Bitwise XOR. More...

Integer	operator>> (size_t n) const
	Right-shift. More...

Integer	operator<< (size_t n) const
	Left-shift. More...

OTHER ARITHMETIC FUNCTIONS
Integer	AbsoluteValue () const
	Retrieve the absolute value of this integer. More...

Integer	Doubled () const
	Add this integer to itself. More...

Integer	Squared () const
	Multiply this integer by itself. More...

Integer	SquareRoot () const
	Extract square root. More...

bool	IsSquare () const
	Determine whether this integer is a perfect square. More...

bool	IsUnit () const
	is 1 or -1 More...

Integer	MultiplicativeInverse () const
	return inverse if 1 or -1, otherwise return 0 More...

Integer	InverseMod (const Integer &n) const
	calculate multiplicative inverse of *this mod n More...

word	InverseMod (word n) const

static void CRYPTOPP_API	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)) More...

static void CRYPTOPP_API	Divide (word &r, Integer &q, const Integer &a, word d)
	use a faster division algorithm when divisor is short More...

static void CRYPTOPP_API	DivideByPowerOf2 (Integer &r, Integer &q, const Integer &a, unsigned int n)
	returns same result as Divide(r, q, a, Power2(n)), but faster More...

static Integer CRYPTOPP_API	Gcd (const Integer &a, const Integer &n)
	greatest common divisor More...

INPUT/OUTPUT
CRYPTOPP_DLL std::istream &CRYPTOPP_API	operator>> (std::istream &in, Integer &a)
	Extraction operator. More...

CRYPTOPP_DLL std::ostream &CRYPTOPP_API	operator<< (std::ostream &out, const Integer &a)
	Insertion operator. More...

Additional Inherited Members
Public Member Functions inherited from ASN1Object
virtual	~ASN1Object ()

virtual void	BEREncode (BufferedTransformation &bt) const
	Encode this object into a BufferedTransformation. More...

Detailed Description

Multiple precision integer with arithmetic operations.

The Integer class can represent positive and negative integers with absolute value less than (256**sizeof(word))^{(256**sizeof(int))}.

Internally, the library uses a sign magnitude representation, and the class has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is used to hold the representation. The second is a Sign (an enumeration), and it is used to track the sign of the Integer.

Since: Crypto++ 1.0

Definition at line 43 of file integer.h.

Member Enumeration Documentation

enum Integer::RandomNumberType

Properties of a random integer.

Enumerator
ANY	a number with no special properties
PRIME	a number which is probabilistically prime

Definition at line 85 of file integer.h.

enum Integer::Sign

Used internally to represent the integer.

Sign is used internally to represent the integer. It is also used in a few API functions.

See also: SetPositive(), SetNegative(), Signedness

Enumerator
POSITIVE	the value is positive or 0
NEGATIVE	the value is negative

Definition at line 67 of file integer.h.

enum Integer::Signedness

Used when importing and exporting integers.

Signedness is usually used in API functions.

See also: Sign

Enumerator
UNSIGNED	an unsigned value
SIGNED	a signed value

Definition at line 77 of file integer.h.

Constructor & Destructor Documentation

Integer::Integer ( )

Creates the zero integer.

Definition at line 2892 of file integer.cpp.

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Integer::Integer ( const Integer & t )

copy constructor

Definition at line 2898 of file integer.cpp.

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Integer::Integer ( signed long value )

Convert from signed long.

Definition at line 2911 of file integer.cpp.

Integer::Integer	(	Sign	sign,
		lword	value
	)

Convert from lword.

Parameters

sign	enumeration indicating Sign
value	the long word

Definition at line 2904 of file integer.cpp.

Integer::Integer	(	Sign	sign,
		word	highWord,
		word	lowWord
	)

Convert from two words.

Parameters

sign	enumeration indicating Sign
highWord	the high word
lowWord	the low word

Definition at line 2925 of file integer.cpp.

Integer::Integer	(	const char *	str,
		ByteOrder	order = `BIG_ENDIAN_ORDER`
	)

explicit

Convert from a C-string.

Parameters

str	C-string value
order	the ByteOrder of the string to be processed

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.

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 3279 of file integer.cpp.

Integer::Integer	(	const wchar_t *	str,
		ByteOrder	order = `BIG_ENDIAN_ORDER`
	)

explicit

Convert from a wide C-string.

Parameters

str	wide C-string value
order	the ByteOrder of the string to be processed

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.

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 3285 of file integer.cpp.

Integer::Integer	(	const byte *	encodedInteger,
		size_t	byteCount,
		Signedness	sign = `UNSIGNED`,
		ByteOrder	order = `BIG_ENDIAN_ORDER`
	)

Convert from a big-endian byte array.

Parameters

encodedInteger	big-endian byte array
byteCount	length of the byte array
sign	enumeration indicating Signedness
order	the ByteOrder of the array to be processed

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 2972 of file integer.cpp.

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Integer::Integer	(	BufferedTransformation &	bt,
		size_t	byteCount,
		Signedness	sign = `UNSIGNED`,
		ByteOrder	order = `BIG_ENDIAN_ORDER`
	)

Convert from a big-endian array.

Parameters

bt	BufferedTransformation object with big-endian byte array
byteCount	length of the byte array
sign	enumeration indicating Signedness
order	the ByteOrder of the data to be processed

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 2955 of file integer.cpp.

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Integer::Integer ( BufferedTransformation & bt )

explicit

Convert from a BER encoded byte array.

Parameters

bt	BufferedTransformation object with BER encoded byte array

Definition at line 2992 of file integer.cpp.

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Integer::Integer	(	RandomNumberGenerator &	rng,
		size_t	bitCount
	)

Create a random integer.

Parameters

rng	RandomNumberGenerator used to generate material
bitCount	the number of bits in the resulting integer

The random integer created is uniformly distributed over [0, 2^bitCount].

Definition at line 2997 of file integer.cpp.

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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 form.

Parameters

rng	RandomNumberGenerator used to generate material
min	the minimum value
max	the maximum value
rnType	RandomNumberType to specify the type
equiv	the equivalence class based on the parameter `mod`
mod	the modulus used to reduce the equivalence class

Exceptions

RandomNumberNotFound if the set is empty.

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.

Definition at line 3002 of file integer.cpp.

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Integer::Integer	(	word	value,
		size_t	length
	)

private

Definition at line 3135 of file integer.cpp.

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Member Function Documentation

Integer Integer::AbsoluteValue ( ) const

Retrieve the absolute value of this integer.

Definition at line 3122 of file integer.cpp.

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Integer Integer::And ( const Integer & t ) const

Bitwise AND.

Parameters

t	the other Integer

Returns: the result of *this & t

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.

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++ 5.7

Definition at line 3738 of file integer.cpp.

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void Integer::BERDecode	(	const byte *	input,
		size_t	inputLen
	)

Decode from BER format.

Parameters

input	big-endian byte array
inputLen	length of the byte array

Definition at line 3398 of file integer.cpp.

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void Integer::BERDecode ( BufferedTransformation & bt )

virtual

Decode from BER format.

Parameters

bt	BufferedTransformation object

Implements ASN1Object.

Definition at line 3404 of file integer.cpp.

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void Integer::BERDecodeAsOctetString	(	BufferedTransformation &	bt,
		size_t	length
	)

Decode nonnegative value from big-endian octet string.

Parameters

bt	BufferedTransformation object
length	length of the byte array

Definition at line 3420 of file integer.cpp.

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unsigned int Integer::BitCount ( ) const

Determines the number of bits required to represent the Integer.

Returns: number of significant bits = floor(log2(abs(*this))) + 1

Definition at line 3305 of file integer.cpp.

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unsigned int Integer::ByteCount ( ) const

Determines the number of bytes required to represent the Integer.

Returns: number of significant bytes = ceiling(BitCount()/8)

Definition at line 3296 of file integer.cpp.

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

Perform signed comparison.

Parameters

a	the Integer to comapre

Return values

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

Definition at line 4302 of file integer.cpp.

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signed long Integer::ConvertToLong ( ) const

Convert the Integer to Long.

Returns: equivalent signed long if possible, otherwise undefined

See also: IsConvertableToLong()

Definition at line 2946 of file integer.cpp.

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void Integer::Decode	(	const byte *	input,
		size_t	inputLen,
		Signedness	sign = `UNSIGNED`
	)

Decode from big-endian byte array.

Parameters

input	big-endian byte array
inputLen	length of the byte array
sign	enumeration indicating Signedness

Definition at line 3314 of file integer.cpp.

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void Integer::Decode	(	BufferedTransformation &	bt,
		size_t	inputLen,
		Signedness	sign = `UNSIGNED`
	)

Decode nonnegative value from big-endian byte array.

Parameters

bt	BufferedTransformation object
inputLen	length of the byte array
sign	enumeration indicating Signedness

Note: bt.MaxRetrievable() >= inputLen.

Definition at line 3320 of file integer.cpp.

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void Integer::DEREncode ( BufferedTransformation & bt ) const

virtual

Encode in DER format.

Parameters

bt	BufferedTransformation object

Encodes the Integer using Distinguished Encoding Rules The result is placed into a BufferedTransformation object

Implements ASN1Object.

Definition at line 3391 of file integer.cpp.

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void Integer::DEREncodeAsOctetString	(	BufferedTransformation &	bt,
		size_t	length
	)		const

Encode absolute value as big-endian octet string.

Parameters

bt	BufferedTransformation object
length	the number of mytes to decode

Definition at line 3413 of file integer.cpp.

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void Integer::Divide	(	Integer &	r,
		Integer &	q,
		const Integer &	a,
		const Integer &	d
	)

static

calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))

Definition at line 4144 of file integer.cpp.

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void Integer::Divide	(	word &	r,
		Integer &	q,
		const Integer &	a,
		word	d
	)

static

use a faster division algorithm when divisor is short

Definition at line 4204 of file integer.cpp.

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void Integer::DivideByPowerOf2	(	Integer &	r,
		Integer &	q,
		const Integer &	a,
		unsigned int	n
	)

static

returns same result as Divide(r, q, a, Power2(n)), but faster

Definition at line 4162 of file integer.cpp.

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Integer Integer::DividedBy ( const Integer & b ) const

Division.

Definition at line 4190 of file integer.cpp.

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Integer Integer::DividedBy ( word b ) const

Division.

Definition at line 4238 of file integer.cpp.

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Integer Integer::Doubled ( ) const

inline

Add this integer to itself.

Definition at line 567 of file integer.h.

void Integer::Encode	(	byte *	output,
		size_t	outputLen,
		Signedness	sign = `UNSIGNED`
	)		const

Encode in big-endian format.

Parameters

output	big-endian byte array
outputLen	length of the byte array
sign	enumeration indicating Signedness

Unsigned means encode absolute value, signed means encode two's complement if negative.

outputLen can be used to ensure an Integer is encoded to an exact size (rather than a minimum size). An exact size is useful, for example, when encoding to a field element size.

Definition at line 3369 of file integer.cpp.

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void Integer::Encode	(	BufferedTransformation &	bt,
		size_t	outputLen,
		Signedness	sign = `UNSIGNED`
	)		const

Encode in big-endian format.

Parameters

bt	BufferedTransformation object
outputLen	length of the encoding
sign	enumeration indicating Signedness

Unsigned means encode absolute value, signed means encode two's complement if negative.

outputLen can be used to ensure an Integer is encoded to an exact size (rather than a minimum size). An exact size is useful, for example, when encoding to a field element size.

Definition at line 3376 of file integer.cpp.

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Integer Integer::Gcd	(	const Integer &	a,
		const Integer &	n
	)

static

greatest common divisor

Definition at line 4365 of file integer.cpp.

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void Integer::GenerateRandom	(	RandomNumberGenerator &	rng,
		const NameValuePairs &	params = `g_nullNameValuePairs`
	)

inline

Definition at line 445 of file integer.h.

bool Integer::GenerateRandomNoThrow	(	RandomNumberGenerator &	rng,
		const NameValuePairs &	params = `g_nullNameValuePairs`
	)

Definition at line 3511 of file integer.cpp.

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bool Integer::GetBit ( size_t i ) const

Provides the i-th bit of the Integer.

Returns: the i-th bit, i=0 being the least significant bit

Definition at line 3065 of file integer.cpp.

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lword Integer::GetBits	(	size_t	i,
		size_t	n
	)		const

Provides the low order bits of the Integer.

Returns: n lowest bits of *this >> i

Definition at line 3106 of file integer.cpp.

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byte Integer::GetByte ( size_t i ) const

Provides the i-th byte of the Integer.

Returns: the i-th byte

Definition at line 3089 of file integer.cpp.

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Integer Integer::InverseMod ( const Integer & n ) const

calculate multiplicative inverse of *this mod n

Definition at line 4370 of file integer.cpp.

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word Integer::InverseMod ( word n ) const

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4395 of file integer.cpp.

bool Integer::IsConvertableToLong ( ) const

Determines if the Integer is convertable to Long.

Returns: true if *this can be represented as a signed long

See also: ConvertToLong()

Definition at line 2932 of file integer.cpp.

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bool Integer::IsEven ( ) const

inline

Determines if the Integer is even parity.

Returns: true if the Integer is even, false otherwise

Definition at line 342 of file integer.h.

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bool Integer::IsNegative ( ) const

inline

Determines if the Integer is negative.

Returns: true if the Integer is negative, false otherwise

Definition at line 330 of file integer.h.

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bool Integer::IsOdd ( ) const

inline

Determines if the Integer is odd parity.

Returns: true if the Integer is odd, false otherwise

Definition at line 345 of file integer.h.

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bool Integer::IsPositive ( ) const

inline

Determines if the Integer is positive.

Returns: true if the Integer is positive, false otherwise

Definition at line 336 of file integer.h.

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bool Integer::IsSquare ( ) const

Determine whether this integer is a perfect square.

Definition at line 4338 of file integer.cpp.

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bool Integer::IsUnit ( ) const

is 1 or -1

Definition at line 4344 of file integer.cpp.

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bool Integer::IsZero ( ) const

inline

Determines if the Integer is 0.

Returns: true if the Integer is 0, false otherwise

Definition at line 324 of file integer.h.

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size_t Integer::MinEncodedSize ( Signedness sign = UNSIGNED ) const

Minimum number of bytes to encode this integer.

Parameters

sign	enumeration indicating Signedness

Note: The MinEncodedSize() of 0 is 1.

Definition at line 3354 of file integer.cpp.

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Integer Integer::Minus ( const Integer & b ) const

Subtraction.

Definition at line 3936 of file integer.cpp.

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Integer Integer::Modulo ( const Integer & b ) const

Remainder.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4197 of file integer.cpp.

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word Integer::Modulo ( word b ) const

Remainder.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4246 of file integer.cpp.

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Integer Integer::MultiplicativeInverse ( ) const

return inverse if 1 or -1, otherwise return 0

Definition at line 4349 of file integer.cpp.

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void Integer::Negate ( )

Reverse the Sign of the Integer.

Definition at line 4285 of file integer.cpp.

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bool Integer::NotNegative ( ) const

inline

Determines if the Integer is non-negative.

Returns: true if the Integer is non-negative, false otherwise

Definition at line 333 of file integer.h.

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bool Integer::NotPositive ( ) const

inline

Determines if the Integer is non-positive.

Returns: true if the Integer is non-positive, false otherwise

Definition at line 339 of file integer.h.

bool Integer::NotZero ( ) const

inline

Determines if the Integer is non-0.

Returns: true if the Integer is non-0, false otherwise

Definition at line 327 of file integer.h.

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const Integer & Integer::One ( )

static

Integer representing 1.

Returns: an Integer representing 1

One() avoids calling constructors for frequently used integers

Definition at line 3035 of file integer.cpp.

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void Integer::OpenPGPDecode	(	const byte *	input,
		size_t	inputLen
	)

Decode from OpenPGP format.

Parameters

input	big-endian byte array
inputLen	length of the byte array

Definition at line 3444 of file integer.cpp.

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void Integer::OpenPGPDecode ( BufferedTransformation & bt )

Decode from OpenPGP format.

Parameters

bt	BufferedTransformation object

Definition at line 3450 of file integer.cpp.

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size_t Integer::OpenPGPEncode	(	byte *	output,
		size_t	bufferSize
	)		const

Encode absolute value in OpenPGP format.

Parameters

output	big-endian byte array
bufferSize	length of the byte array

Returns: length of the output

OpenPGPEncode places result into a BufferedTransformation object and returns the number of bytes used for the encoding

Definition at line 3429 of file integer.cpp.

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size_t Integer::OpenPGPEncode ( BufferedTransformation & bt ) const

Encode absolute value in OpenPGP format.

Parameters

bt	BufferedTransformation object

Returns: length of the output

OpenPGPEncode places result into a BufferedTransformation object and returns the number of bytes used for the encoding

Definition at line 3435 of file integer.cpp.

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bool Integer::operator! ( ) const

Negation.

Definition at line 3048 of file integer.cpp.

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Integer& Integer::operator%= ( const Integer & t )

inline

Remainder Assignment.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 364 of file integer.h.

Integer& Integer::operator%= ( word t )

inline

Remainder Assignment.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 369 of file integer.h.

Integer & Integer::operator&= ( const Integer & t )

Bitwise AND Assignment.

Parameters

t	the other Integer

Returns: the result of *this & t

operator&=() performs a bitwise AND on *this. Missing bits are truncated at the most significant bit positions, so the result is as small as the smaller of the operands.

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++ 5.7

Definition at line 4008 of file integer.cpp.

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Integer& Integer::operator*= ( const Integer & t )

inline

Multiplication Assignment.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 359 of file integer.h.

Integer Integer::operator+ ( ) const

inline

Addition.

Definition at line 477 of file integer.h.

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Integer & Integer::operator++ ( )

Pre-increment.

Definition at line 3696 of file integer.cpp.

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Integer Integer::operator++ ( int )

inline

Post-increment.

Definition at line 485 of file integer.h.

Integer & Integer::operator+= ( const Integer & t )

Addition Assignment.

Definition at line 3913 of file integer.cpp.

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Integer Integer::operator- ( ) const

Subtraction.

Definition at line 3115 of file integer.cpp.

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Integer & Integer::operator-- ( )

Pre-decrement.

Definition at line 3718 of file integer.cpp.

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Integer Integer::operator-- ( int )

inline

Post-decrement.

Definition at line 487 of file integer.h.

Integer & Integer::operator-= ( const Integer & t )

Subtraction Assignment.

Definition at line 3959 of file integer.cpp.

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Integer& Integer::operator/= ( const Integer & t )

inline

Division Assignment.

Definition at line 361 of file integer.h.

Integer& Integer::operator/= ( word t )

inline

Division Assignment.

Definition at line 366 of file integer.h.

Integer Integer::operator<< ( size_t n ) const

inline

Left-shift.

Definition at line 559 of file integer.h.

Integer & Integer::operator<<= ( size_t n )

Left-shift Assignment.

Definition at line 3982 of file integer.cpp.

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Integer & Integer::operator= ( const Integer & t )

Assignment.

Definition at line 3053 of file integer.cpp.

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Integer Integer::operator>> ( size_t n ) const

inline

Right-shift.

Definition at line 557 of file integer.h.

Integer & Integer::operator>>= ( size_t n )

Right-shift Assignment.

Definition at line 3994 of file integer.cpp.

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Integer & Integer::operator^= ( const Integer & t )

Bitwise XOR Assignment.

Parameters

t	the other Integer

Returns: the result of *this ^ t

operator^=() performs a bitwise XOR on *this. Missing bits are shifted in at the most significant bit positions, so the result is as large as the larger of the operands.

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++ 5.7

Definition at line 4041 of file integer.cpp.

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Integer & Integer::operator|= ( const Integer & t )

Bitwise OR Assignment.

Parameters

t	the second Integer

Returns: the result of *this | t

operator|=() performs a bitwise OR on *this. Missing bits are shifted in at the most significant bit positions, so the result is as large as the larger of the operands.

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++ 5.7

Definition at line 4020 of file integer.cpp.

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Integer Integer::Or ( const Integer & t ) const

Bitwise OR.

Parameters

t	the other Integer

Returns: the result of *this | t

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.

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++ 5.7

Definition at line 3764 of file integer.cpp.

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Integer Integer::Plus ( const Integer & b ) const

Addition.

Definition at line 3890 of file integer.cpp.

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int Integer::PositiveCompare ( const Integer & t ) const

private

Definition at line 4291 of file integer.cpp.

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Integer Integer::Power2 ( size_t e )

static

Exponentiates to a power of 2.

Returns: the Integer 2^e

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 3008 of file integer.cpp.

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void Integer::Randomize	(	RandomNumberGenerator &	rng,
		size_t	bitCount
	)

Set this Integer to random integer.

Parameters

rng	RandomNumberGenerator used to generate material
bitCount	the number of bits in the resulting integer

The random integer created is uniformly distributed over [0, 2^bitCount].

Definition at line 3458 of file integer.cpp.

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void Integer::Randomize	(	RandomNumberGenerator &	rng,
		const Integer &	min,
		const Integer &	max
	)

Set this Integer to random integer.

Parameters

rng	RandomNumberGenerator used to generate material
min	the minimum value
max	the maximum value

The random integer created is uniformly distributed over [min, max].

Definition at line 3468 of file integer.cpp.

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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 random integer of special form.

Parameters

rng	RandomNumberGenerator used to generate material
min	the minimum value
max	the maximum value
rnType	RandomNumberType to specify the type
equiv	the equivalence class based on the parameter `mod`
mod	the modulus used to reduce the equivalence class

Exceptions

RandomNumberNotFound if the set is empty.

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.

Definition at line 3485 of file integer.cpp.

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void Integer::SetBit	(	size_t	n,
		bool	value = `1`
	)

Set the n-th bit to value.

0-based numbering.

Definition at line 3075 of file integer.cpp.

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void Integer::SetByte	(	size_t	n,
		byte	value
	)

Set the n-th byte to value.

0-based numbering.

Definition at line 3099 of file integer.cpp.

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void Integer::SetNegative ( )

inline

Sets the Integer to negative.

Definition at line 466 of file integer.h.

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void Integer::SetPositive ( )

inline

Sets the Integer to positive.

Definition at line 463 of file integer.h.

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Integer Integer::Squared ( ) const

inline

Multiply this integer by itself.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 570 of file integer.h.

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Integer Integer::SquareRoot ( ) const

Extract square root.

if negative return 0, else return floor of square root

Definition at line 4320 of file integer.cpp.

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void Integer::swap ( Integer & a )

Swaps this Integer with another Integer.

Definition at line 3129 of file integer.cpp.

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Integer Integer::Times ( const Integer & b ) const

Multiplication.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4086 of file integer.cpp.

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const Integer & Integer::Two ( )

static

Integer representing 2.

Returns: an Integer representing 2

Two() avoids calling constructors for frequently used integers

Definition at line 3043 of file integer.cpp.

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unsigned int Integer::WordCount ( ) const

Determines the number of words required to represent the Integer.

Returns: number of significant words = ceiling(ByteCount()/sizeof(word))

Definition at line 3291 of file integer.cpp.

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Integer Integer::Xor ( const Integer & t ) const

Bitwise XOR.

Parameters

t	the other Integer

Returns: the result of *this ^ t

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.

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++ 5.7

Definition at line 3790 of file integer.cpp.

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const Integer & Integer::Zero ( )

static

Integer representing 0.

Returns: an Integer representing 0

Zero() avoids calling constructors for frequently used integers

Definition at line 3027 of file integer.cpp.

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Friends And Related Function Documentation

CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c	(	const Integer &	x,
		const Integer &	e,
		const Integer &	m
	)

friend

modular exponentiation

Definition at line 4359 of file integer.cpp.

CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c	(	const Integer &	x,
		const Integer &	y,
		const Integer &	m
	)

friend

modular multiplication

Definition at line 4354 of file integer.cpp.

friend class HalfMontgomeryRepresentation

friend

Definition at line 638 of file integer.h.

friend class ModularArithmetic

friend

Definition at line 636 of file integer.h.

friend class MontgomeryRepresentation

friend

Definition at line 637 of file integer.h.

CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<	(	std::ostream &	out,
		const Integer &	a
	)

friend

Insertion operator.

Parameters

out	a reference to a std::ostream
a	a constant reference to an Integer

Returns: a reference to a std::ostream reference

The output integer responds to std::hex, std::oct, std::hex, std::upper and std::lower. The output includes the suffix h (for hex), . (dot, for dec) and o (for octal). There is currently no way to suppress the suffix.

If you want to print an Integer without the suffix or using an arbitrary base, then use IntToString<Integer>().

See also: IntToString<Integer>

Definition at line 3629 of file integer.cpp.

CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>	(	std::istream &	in,
		Integer &	a
	)

friend

Extraction operator.

Parameters

in	a reference to a std::istream
a	a reference to an Integer

Returns: a reference to a std::istream reference

Definition at line 3604 of file integer.cpp.

void PositiveAdd	(	Integer &	sum,
		const Integer &	a,
		const Integer &	b
	)

friend

Definition at line 3814 of file integer.cpp.

void PositiveDivide	(	Integer &	remainder,
		Integer &	quotient,
		const Integer &	dividend,
		const Integer &	divisor
	)

friend

Definition at line 4115 of file integer.cpp.

void PositiveMultiply	(	Integer &	product,
		const Integer &	a,
		const Integer &	b
	)

friend

Definition at line 4066 of file integer.cpp.

void PositiveSubtract	(	Integer &	diff,
		const Integer &	a,
		const Integer &	b
	)

friend

Definition at line 3844 of file integer.cpp.

Member Data Documentation

IntegerSecBlock Integer::reg

private

Definition at line 632 of file integer.h.

Sign Integer::sign

private

Definition at line 633 of file integer.h.

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

src/cryptopp/integer.h
src/cryptopp/integer.cpp

Classes

Private Member Functions

Private Attributes

Friends

ENUMS, EXCEPTIONS, and TYPEDEFS

CREATORS

ENCODE/DECODE

ACCESSORS

MANIPULATORS

UNARY OPERATORS

BINARY OPERATORS

OTHER ARITHMETIC FUNCTIONS

INPUT/OUTPUT

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation