Multiple precision integer with arithmetic operations. More...

#include <integer.h>

Inheritance 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...

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...

INPUT/OUTPUT
class	ModularArithmetic

class	MontgomeryRepresentation

class	HalfMontgomeryRepresentation

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

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

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

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

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)

Integer	InverseModNext (const Integer &n) const

CREATORS
	Integer ()
	Creates the zero integer.

	Integer (const Integer &t)
	copy constructor

	Integer (signed long value)
	Convert from signed long.

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

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

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

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

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

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

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

	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 form.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

bool	GenerateRandomNoThrow (RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
	Generate a random number.

void	GenerateRandom (RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
	Generate a random number.

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 ()
	Reverse the Sign of the Integer.

void	SetPositive ()
	Sets the Integer to positive.

void	SetNegative ()
	Sets the Integer to negative.

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

UNARY OPERATORS
bool	operator! () const
	Negation.

Integer	operator+ () const
	Addition.

Integer	operator- () const
	Subtraction.

Integer &	operator++ ()
	Pre-increment.

Integer &	operator-- ()
	Pre-decrement.

Integer	operator++ (int)
	Post-increment.

Integer	operator-- (int)
	Post-decrement.

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

Integer	Plus (const Integer &b) const
	Addition.

Integer	Minus (const Integer &b) const
	Subtraction.

Integer	Times (const Integer &b) const
	Multiplication.

Integer	DividedBy (const Integer &b) const
	Division.

Integer	Modulo (const Integer &b) const
	Remainder.

Integer	DividedBy (word b) const
	Division.

word	Modulo (word b) const
	Remainder.

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

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

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

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

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

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

Integer	Doubled () const
	Add this integer to itself.

Integer	Squared () const
	Multiply this integer by itself.

Integer	SquareRoot () const
	Extract square root.

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

bool	IsUnit () const
	Determine if 1 or -1.

Integer	MultiplicativeInverse () const
	Calculate multiplicative inverse.

Integer	InverseMod (const Integer &n) const
	Calculate multiplicative inverse.

word	InverseMod (word n) const
	Calculate multiplicative inverse.

static void CRYPTOPP_API	Divide (Integer &r, Integer &q, const Integer &a, const Integer &d)
	Extended Division.

static void CRYPTOPP_API	Divide (word &r, Integer &q, const Integer &a, word d)
	Extended Division.

static void CRYPTOPP_API	DivideByPowerOf2 (Integer &r, Integer &q, const Integer &a, unsigned int n)
	Extended Division.

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

Additional Inherited Members
Public Member Functions inherited from ASN1Object
virtual void	BEREncode (BufferedTransformation &bt) const
	Encode this object into a BufferedTransformation.

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.

For details on how the Integer class initializes its function pointers using InitializeInteger and how it creates Integer::Zero(), Integer::One(), and Integer::Two(), then see the comments at the top of integer.cpp.

Since: Crypto++ 1.0

Definition at line 49 of file integer.h.

Member Enumeration Documentation

◆ RandomNumberType

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 91 of file integer.h.

◆ Sign

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 73 of file integer.h.

◆ Signedness

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 83 of file integer.h.

Constructor & Destructor Documentation

◆ Integer() [1/12]

Integer::Integer ( )

Creates the zero integer.

Definition at line 2966 of file integer.cpp.

◆ Integer() [2/12]

Integer::Integer ( const Integer & t )

copy constructor

Definition at line 2972 of file integer.cpp.

◆ Integer() [3/12]

Integer::Integer ( signed long value )

Convert from signed long.

Definition at line 2985 of file integer.cpp.

◆ Integer() [4/12]

Integer::Integer	(	Sign	sign,
		lword	value
	)

Convert from lword.

Parameters

sign	enumeration indicating Sign
value	the long word

Definition at line 2978 of file integer.cpp.

◆ Integer() [5/12]

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 2999 of file integer.cpp.

◆ Integer() [6/12]

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 8, 10, or 16. Base is determined by a case insensitive suffix of 'o' (8), '.' (10), or 'h' (16). 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 3338 of file integer.cpp.

◆ Integer() [7/12]

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 8, 10, or 16. Base is determined by a case insensitive suffix of 'o' (8), '.' (10), or 'h' (16). 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 3344 of file integer.cpp.

◆ Integer() [8/12]

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 3047 of file integer.cpp.

◆ Integer() [9/12]

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 3029 of file integer.cpp.

◆ Integer() [10/12]

Integer::Integer ( BufferedTransformation & bt )

explicit

Convert from a BER encoded byte array.

Parameters

bt	BufferedTransformation object with BER encoded byte array

Definition at line 3070 of file integer.cpp.

◆ Integer() [11/12]

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 3076 of file integer.cpp.

◆ Integer() [12/12]

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 3081 of file integer.cpp.

Member Function Documentation

◆ AbsoluteValue()

Integer Integer::AbsoluteValue ( ) const

Retrieve the absolute value of this integer.

Definition at line 3166 of file integer.cpp.

◆ And()

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++ 6.0

Definition at line 3800 of file integer.cpp.

◆ BERDecode() [1/2]

void Integer::BERDecode ( BufferedTransformation & bt )

virtual

Decode from BER format.

Parameters

bt	BufferedTransformation object

Implements ASN1Object.

Definition at line 3463 of file integer.cpp.

◆ BERDecode() [2/2]

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 3456 of file integer.cpp.

◆ BERDecodeAsOctetString()

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 3479 of file integer.cpp.

◆ BitCount()

unsigned int Integer::BitCount ( ) const

Determines the number of bits required to represent the Integer.

Returns: number of significant bits

BitCount is calculated as floor(log2(abs(*this))) + 1.

Definition at line 3364 of file integer.cpp.

◆ ByteCount()

unsigned int Integer::ByteCount ( ) const

Determines the number of bytes required to represent the Integer.

Returns: number of significant bytes

ByteCount is calculated as ceiling(BitCount()/8).

Definition at line 3355 of file integer.cpp.

◆ Compare()

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

Perform signed comparison.

Parameters

a	the Integer to compare

Return values

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

Definition at line 4397 of file integer.cpp.

◆ ConvertToLong()

signed long Integer::ConvertToLong ( ) const

Convert the Integer to Long.

Returns: equivalent signed long if possible, otherwise undefined

See also: IsConvertableToLong()

Definition at line 3020 of file integer.cpp.

◆ Decode() [1/2]

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 3380 of file integer.cpp.

◆ Decode() [2/2]

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 3373 of file integer.cpp.

◆ DEREncode()

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 3449 of file integer.cpp.

◆ DEREncodeAsOctetString()

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 3472 of file integer.cpp.

◆ Divide() [1/2]

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

static

Extended Division.

Parameters

r	a reference for the remainder
q	a reference for the quotient
a	reference to the dividend
d	reference to the divisor

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

Definition at line 4240 of file integer.cpp.

◆ Divide() [2/2]

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

static

Extended Division.

Parameters

r	a reference for the remainder
q	a reference for the quotient
a	reference to the dividend
d	reference to the divisor

Divide calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)). This overload uses a faster division algorithm because the divisor is short.

Definition at line 4300 of file integer.cpp.

◆ DivideByPowerOf2()

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

static

Extended Division.

Parameters

r	a reference for the remainder
q	a reference for the quotient
a	reference to the dividend
n	reference to the divisor

DivideByPowerOf2 calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)). It returns same result as Divide(r, q, a, Power2(n)), but faster. This overload uses a faster division algorithm because the divisor is a power of 2.

Definition at line 4258 of file integer.cpp.

◆ DividedBy() [1/2]

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

Division.

Definition at line 4286 of file integer.cpp.

◆ DividedBy() [2/2]

Integer Integer::DividedBy ( word b ) const

Division.

Definition at line 4336 of file integer.cpp.

◆ Doubled()

Integer Integer::Doubled ( ) const

inline

Add this integer to itself.

Definition at line 630 of file integer.h.

◆ Encode() [1/2]

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 3434 of file integer.cpp.

◆ Encode() [2/2]

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 3427 of file integer.cpp.

◆ Gcd()

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

static

Calculate greatest common divisor.

Parameters

a	reference to the first number
n	reference to the secind number

Returns: the greatest common divisor a and n.

Definition at line 4468 of file integer.cpp.

◆ GenerateRandom()

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

inline

Generate a random number.

Parameters

rng	RandomNumberGenerator used to generate material
params	additional parameters that cannot be passed directly to the function

Exceptions

RandomNumberNotFound if a random number is not found

GenerateRandom attempts to generate a random number according to the parameters specified in params.

The example below generates a prime number using NameValuePairs that Integer class recognizes. The names are not provided in argnames.h.

   AutoSeededRandomPool prng;
   AlgorithmParameters params = MakeParameters("BitLength", 2048)
                                              ("RandomNumberType", Integer::PRIME);
   Integer x;
   try { x.GenerateRandom(prng, params); }
   catch (RandomNumberNotFound&) { x = -1; }

Definition at line 508 of file integer.h.

◆ GenerateRandomNoThrow()

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

Generate a random number.

Parameters

rng	RandomNumberGenerator used to generate material
params	additional parameters that cannot be passed directly to the function

Returns: true if a random number was generated, false otherwise

GenerateRandomNoThrow attempts to generate a random number according to the parameters specified in params. The function does not throw RandomNumberNotFound.

The example below generates a prime number using NameValuePairs that Integer class recognizes. The names are not provided in argnames.h.

   AutoSeededRandomPool prng;
   AlgorithmParameters params = MakeParameters("BitLength", 2048)
                                              ("RandomNumberType", Integer::PRIME);
   Integer x;
   if (x.GenerateRandomNoThrow(prng, params) == false)
       throw std::runtime_error("Failed to generate prime number");

Definition at line 3584 of file integer.cpp.

◆ GetBit()

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 3111 of file integer.cpp.

◆ GetBits()

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 3150 of file integer.cpp.

◆ GetByte()

byte Integer::GetByte ( size_t i ) const

Provides the i-th byte of the Integer.

Returns: the i-th byte

Definition at line 3134 of file integer.cpp.

◆ InverseMod() [1/2]

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

Calculate multiplicative inverse.

Parameters

n	reference to the modulus

Returns: an Integer *this % n.

InverseMod returns the multiplicative inverse of the Integer *this modulo the Integer n. If no Integer exists then Integer 0 is returned.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4473 of file integer.cpp.

◆ InverseMod() [2/2]

word Integer::InverseMod ( word n ) const

Calculate multiplicative inverse.

Parameters

n	the modulus

Returns: a word *this % n.

InverseMod returns the multiplicative inverse of the Integer *this modulo the word n. If no Integer exists then word 0 is returned.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4512 of file integer.cpp.

◆ InverseModNext()

Integer Integer::InverseModNext ( const Integer & n ) const

protected

Definition at line 4488 of file integer.cpp.

◆ IsConvertableToLong()

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 3006 of file integer.cpp.

◆ IsEven()

bool Integer::IsEven ( ) const

inline

Determines if the Integer is even parity.

Returns: true if the Integer is even, false otherwise

Definition at line 353 of file integer.h.

◆ IsNegative()

bool Integer::IsNegative ( ) const

inline

Determines if the Integer is negative.

Returns: true if the Integer is negative, false otherwise

Definition at line 341 of file integer.h.

◆ IsOdd()

bool Integer::IsOdd ( ) const

inline

Determines if the Integer is odd parity.

Returns: true if the Integer is odd, false otherwise

Definition at line 356 of file integer.h.

◆ IsPositive()

bool Integer::IsPositive ( ) const

inline

Determines if the Integer is positive.

Returns: true if the Integer is positive, false otherwise

Definition at line 347 of file integer.h.

◆ IsSquare()

bool Integer::IsSquare ( ) const

Determine whether this integer is a perfect square.

Definition at line 4433 of file integer.cpp.

◆ IsUnit()

bool Integer::IsUnit ( ) const

Determine if 1 or -1.

Returns: true if this integer is 1 or -1, false otherwise

Definition at line 4439 of file integer.cpp.

◆ IsZero()

bool Integer::IsZero ( ) const

inline

Determines if the Integer is 0.

Returns: true if the Integer is 0, false otherwise

Definition at line 335 of file integer.h.

◆ MinEncodedSize()

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 3412 of file integer.cpp.

◆ Minus()

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

Subtraction.

Definition at line 4032 of file integer.cpp.

◆ Modulo() [1/2]

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

Remainder.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4293 of file integer.cpp.

◆ Modulo() [2/2]

word Integer::Modulo ( word b ) const

Remainder.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4344 of file integer.cpp.

◆ MultiplicativeInverse()

Integer Integer::MultiplicativeInverse ( ) const

Calculate multiplicative inverse.

Returns: MultiplicativeInverse inverse if 1 or -1, otherwise return 0.

Definition at line 4444 of file integer.cpp.

◆ Negate()

void Integer::Negate ( )

Reverse the Sign of the Integer.

Definition at line 4381 of file integer.cpp.

◆ NotNegative()

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 344 of file integer.h.

◆ NotPositive()

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 350 of file integer.h.

◆ NotZero()

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 338 of file integer.h.

◆ One()

const Integer & Integer::One ( )

static

Integer representing 1.

Returns: an Integer representing 1

One() avoids calling constructors for frequently used integers

Definition at line 4920 of file integer.cpp.

◆ OpenPGPDecode() [1/2]

void Integer::OpenPGPDecode ( BufferedTransformation & bt )

Decode from OpenPGP format.

Parameters

bt	BufferedTransformation object

Definition at line 3512 of file integer.cpp.

◆ OpenPGPDecode() [2/2]

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 3505 of file integer.cpp.

◆ OpenPGPEncode() [1/2]

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 3496 of file integer.cpp.

◆ OpenPGPEncode() [2/2]

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 the buffer and returns the number of bytes used for the encoding

Definition at line 3488 of file integer.cpp.

◆ operator!()

bool Integer::operator! ( ) const

Negation.

Definition at line 3094 of file integer.cpp.

◆ operator%=() [1/2]

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

inline

Remainder Assignment.

Parameters

t	the other Integer

Returns: the result of *this % t

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 386 of file integer.h.

◆ operator%=() [2/2]

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

inline

Remainder Assignment.

Parameters

t	the other word

Returns: the result of *this % t

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 395 of file integer.h.

◆ operator&=()

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++ 6.0

Definition at line 4104 of file integer.cpp.

◆ operator*=()

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

inline

Multiplication Assignment.

Parameters

t	the other Integer

Returns: the result of *this * t

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 377 of file integer.h.

◆ operator+()

Integer Integer::operator+ ( ) const

inline

Addition.

Definition at line 540 of file integer.h.

◆ operator++() [1/2]

Integer & Integer::operator++ ( )

Pre-increment.

Definition at line 3759 of file integer.cpp.

◆ operator++() [2/2]

Integer Integer::operator++ ( int )

inline

Post-increment.

Definition at line 548 of file integer.h.

◆ operator+=()

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

Addition Assignment.

Parameters

t	the other Integer

Returns: the result of *this + t

Definition at line 4009 of file integer.cpp.

◆ operator-()

Integer Integer::operator- ( ) const

Subtraction.

Definition at line 3159 of file integer.cpp.

◆ operator--() [1/2]

Integer & Integer::operator-- ( )

Pre-decrement.

Definition at line 3780 of file integer.cpp.

◆ operator--() [2/2]

Integer Integer::operator-- ( int )

inline

Post-decrement.

Definition at line 550 of file integer.h.

◆ operator-=()

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

Subtraction Assignment.

Parameters

t	the other Integer

Returns: the result of *this - t

Definition at line 4055 of file integer.cpp.

◆ operator/=() [1/2]

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

inline

Division Assignment.

Parameters

t	the other Integer

Returns: the result of *this / t

Definition at line 381 of file integer.h.

◆ operator/=() [2/2]

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

inline

Division Assignment.

Parameters

t	the other word

Returns: the result of *this / t

Definition at line 390 of file integer.h.

◆ operator<<()

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

inline

Left-shift.

Definition at line 622 of file integer.h.

◆ operator<<=()

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

Left-shift Assignment.

Parameters

n	number of bits to shift

Returns: reference to this Integer

Definition at line 4078 of file integer.cpp.

◆ operator=()

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

Assignment.

Parameters

t	the other Integer

Returns: the result of assignment

Definition at line 3099 of file integer.cpp.

◆ operator>>()

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

inline

Right-shift.

Definition at line 620 of file integer.h.

◆ operator>>=()

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

Right-shift Assignment.

Parameters

n	number of bits to shift

Returns: reference to this Integer

Definition at line 4090 of file integer.cpp.

◆ operator^=()

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++ 6.0

Definition at line 4137 of file integer.cpp.

◆ operator|=()

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++ 6.0

Definition at line 4116 of file integer.cpp.

◆ Or()

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++ 6.0

Definition at line 3838 of file integer.cpp.

◆ Plus()

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

Addition.

Definition at line 3986 of file integer.cpp.

◆ Power2()

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 3087 of file integer.cpp.

◆ Randomize() [1/3]

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 3530 of file integer.cpp.

◆ Randomize() [2/3]

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 3547 of file integer.cpp.

◆ Randomize() [3/3]

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 3520 of file integer.cpp.

◆ SetBit()

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

Set the n-th bit to value.

0-based numbering.

Definition at line 3120 of file integer.cpp.

◆ SetByte()

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

Set the n-th byte to value.

0-based numbering.

Definition at line 3143 of file integer.cpp.

◆ SetNegative()

void Integer::SetNegative ( )

inline

Sets the Integer to negative.

Definition at line 529 of file integer.h.

◆ SetPositive()

void Integer::SetPositive ( )

inline

Sets the Integer to positive.

Definition at line 526 of file integer.h.

◆ Squared()

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 633 of file integer.h.

◆ SquareRoot()

Integer Integer::SquareRoot ( ) const

Extract square root.

if negative return 0, else return floor of square root

Definition at line 4415 of file integer.cpp.

◆ swap()

void Integer::swap ( Integer & a )

Swaps this Integer with another Integer.

Definition at line 3173 of file integer.cpp.

◆ Times()

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

Multiplication.

See also: a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4182 of file integer.cpp.

◆ Two()

const Integer & Integer::Two ( )

static

Integer representing 2.

Returns: an Integer representing 2

Two() avoids calling constructors for frequently used integers

Definition at line 4932 of file integer.cpp.

◆ WordCount()

unsigned int Integer::WordCount ( ) const

Determines the number of words required to represent the Integer.

Returns: number of significant words

WordCount is calculated as ceiling(ByteCount()/sizeof(word)).

Definition at line 3350 of file integer.cpp.

◆ Xor()

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++ 6.0

Definition at line 3876 of file integer.cpp.

◆ Zero()

const Integer & Integer::Zero ( )

static

Integer representing 0.

Returns: an Integer representing 0

Zero() avoids calling constructors for frequently used integers

Definition at line 4908 of file integer.cpp.

Friends And Related Symbol Documentation

◆ a_exp_b_mod_c

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

friend

Modular exponentiation.

Parameters

x	reference to the base
e	reference to the exponent
m	reference to the modulus

Returns: an Integer (a ^ b) % m.

Definition at line 4458 of file integer.cpp.

◆ a_times_b_mod_c

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

friend

Modular multiplication.

Parameters

x	reference to the first term
y	reference to the second term
m	reference to the modulus

Returns: an Integer (a * b) % m.

Definition at line 4449 of file integer.cpp.

◆ HalfMontgomeryRepresentation

friend class HalfMontgomeryRepresentation

friend

Definition at line 747 of file integer.h.

◆ ModularArithmetic

friend class ModularArithmetic

friend

Definition at line 745 of file integer.h.

◆ MontgomeryRepresentation

friend class MontgomeryRepresentation

friend

Definition at line 746 of file integer.h.

◆ operator<<

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

friend

Insertion operator.

Parameters

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

Returns: 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 3712 of file integer.cpp.

◆ operator>>

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

friend

Extraction operator.

Parameters

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

Returns: reference to a std::istream reference

Definition at line 3677 of file integer.cpp.

◆ PositiveAdd

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

friend

Definition at line 3912 of file integer.cpp.

◆ PositiveDivide

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

friend

Definition at line 4211 of file integer.cpp.

◆ PositiveMultiply

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

friend

Definition at line 4162 of file integer.cpp.

◆ PositiveSubtract

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

friend

Definition at line 3941 of file integer.cpp.

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

G:/work/subversion/scol-technologies/trunk/scol/plugins/security/cryptopp/integer.h
G:/work/subversion/scol-technologies/trunk/scol/plugins/security/cryptopp/integer.cpp

Classes

ENUMS, EXCEPTIONS, and TYPEDEFS

INPUT/OUTPUT

CREATORS

ENCODE/DECODE

ACCESSORS

MANIPULATORS

UNARY OPERATORS

BINARY OPERATORS

OTHER ARITHMETIC FUNCTIONS

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ RandomNumberType

◆ Sign

◆ Signedness

Constructor & Destructor Documentation

◆ Integer() [1/12]

◆ Integer() [2/12]

◆ Integer() [3/12]

◆ Integer() [4/12]

◆ Integer() [5/12]

◆ Integer() [6/12]

◆ Integer() [7/12]

◆ Integer() [8/12]

◆ Integer() [9/12]

◆ Integer() [10/12]

◆ Integer() [11/12]

◆ Integer() [12/12]

Member Function Documentation

◆ AbsoluteValue()

◆ And()

◆ BERDecode() [1/2]

◆ BERDecode() [2/2]

◆ BERDecodeAsOctetString()

◆ BitCount()

◆ ByteCount()

◆ Compare()

◆ ConvertToLong()

◆ Decode() [1/2]

◆ Decode() [2/2]

◆ DEREncode()

◆ DEREncodeAsOctetString()

◆ Divide() [1/2]

◆ Divide() [2/2]

◆ DivideByPowerOf2()

◆ DividedBy() [1/2]

◆ DividedBy() [2/2]

◆ Doubled()

◆ Encode() [1/2]

◆ Encode() [2/2]

◆ Gcd()

◆ GenerateRandom()

◆ GenerateRandomNoThrow()

◆ GetBit()

◆ GetBits()

◆ GetByte()

◆ InverseMod() [1/2]

◆ InverseMod() [2/2]

◆ InverseModNext()

◆ IsConvertableToLong()

◆ IsEven()

◆ IsNegative()

◆ IsOdd()

◆ IsPositive()

◆ IsSquare()

◆ IsUnit()

◆ IsZero()

◆ MinEncodedSize()

◆ Minus()

◆ Modulo() [1/2]

◆ Modulo() [2/2]

◆ MultiplicativeInverse()

◆ Negate()

◆ NotNegative()

◆ NotPositive()

◆ NotZero()

◆ One()

◆ OpenPGPDecode() [1/2]

◆ OpenPGPDecode() [2/2]