num Struct Reference

#include <pk.h>

Collaboration diagram for num:

---

Detailed Description

Implementation of the arithmetic in various groups, rings, and fields.

Public Member Functions
Constructors and Destructors
	num ()
	Constructor.
	num (const num &x)
	Constructor used to duplicate a given num object.
	num (const num &x, const str &y)
	Constructor used to convert a str into a num object with specified parameters.
	num (int x)
	Constructor used to instantiate a new num object based on an integer.
	num (const FParms *p1)
	Constructor used to create new num with specified parameters.
	num (const str &x)
	Constructor used to convert a str into a num object.
	num (int type1, int len)
	Constructor used to created a new num object of specified type and size.
	~num ()
	Destructor. Calls clear1().
Initializers
void	setlen (int n)
	Set the length of this object in nwords.
void	add (int n, const char *x)
	Load octet string into this object.
void	mod2to (int n)
	Assign a power of 2 to this object.
Assignment and Arithmetic Operators
void	operator= (const FParms *p1)
	Assign parameters to this object.
void	operator= (const num &x)
	Assignment operator for num objects.
num	operator & (const FParms *p1) const
	Change this object's parameters, but not its value.
num &	operator= (nword x)
	Assignment operator for nword.
num &	operator= (int x)
	Assignment operator for int.
num &	operator-= (int x)
	Decrement this object by a specified integer.
num	operator- () const
	Negate this object.
num	operator- (int x)
	Subtract an integer from this object.
num	operator+ (const num &y) const
	Add a num object to this one.
num	operator- (const num &y) const
	Subtract a num object from this one.
num	operator * (int y) const
	Multiply this object by an integer.
num	operator * (const num &y) const
	Multiply this num by another one.
num	operator/ (int y) const
	Divide this num by an integer.
num	operator/ (const num &x) const
	Divide this num by another num.
num &	operator+= (const num &x)
	Increment this object by a specified value.
num &	operator-= (const num &x)
	Decrement this object by a specified value.
int	operator% (int k) const
	Compute this num's residue modulo a specified integer.
num	operator^ (int n) const
	Raise this object's value to an integer exponent.
num &	operator *= (int n)
	Multiply this num by an integer.
num &	operator/= (int n)
	Divide this object by an integer.
Arithmetic Predicates
bool	isNeg () const
	Predicate used to determine if this object is negative.
bool	isNat () const
	Predicate used to determine if this object represents a natural number.
bool	isMod () const
	Predicate used to determine if this object is a ring or field element.
bool	isChar2 () const
	Predicate used to determine if this object is an element of a field of char 2.
bool	isEven () const
	Predicate used to determine if this object is even.
bool	isZero () const
	Predicate used to determine if this object is the zero element.
bool	isPrime (int rounds=8) const
	Predicate used to test primality.
bool	isIrred () const
	Predicate used to test irreducibility.
bool	isMontg () const
	Predicate used to determine if this object is in its Montgomery representation.
int	isSquare () const
	Predicate to test quadratic residuosity.
Operator Predicates
bool	operator| (const num &y) const
	Predicate used to test whether a given num divides this one.
bool	operator== (const num &y) const
	Predicate to test equality of two nums.
bool	operator!= (const num &y) const
	Predicate to test inequality of two nums.
bool	operator== (int n) const
	Predicate to test equality of this oject with an int.
bool	operator!= (int n) const
	Predicate to test inequality of this oject with an int.
bool	operator< (const num &y) const
	Predicate to test "less than" relation between two nums.
bool	operator<= (const num &y) const
	Predicate to test "less than or equal to" relation between two nums.
bool	operator> (const num &y) const
	Predicate to test "greater than" relation between two nums.
bool	operator>= (const num &y) const
	Predicate to test "greater than or equal to" relation between two nums.
bool	operator> (int n) const
	Predicate to test "greater than" relation with an int.
bool	operator< (int n) const
	Predicate to test "less than" relation with an int.
bool	operator<= (int n) const
	Predicate to test "less than or equal to" relation with an int.
bool	operator>= (int n) const
	Predicate to test "greater than or equal to" relation with an int.
Arithmetic Functions
num	abs () const
	Absolute value of this object.
num	sqrt () const
	Calculate square root.
void	mmult (const num &x, const num &y)
	Assign the product of two num objects to this one.
void	divide (const num &y, num &quot, num &rem) const
	Divide this num by another.
num	mod1 (const num &y, int deg=0) const
	Modular reduction.
num	mod (const num &y, int deg=0) const
	Modular reduction. Alias for mod1().
num	mod2 (const num &y) const
	Modular reduction.
num	inverse () const
	Compute the inverse of this object (uses Euclidean Algorithm).
void	power (const num &x, const num &y)
	Assign x^y to this object.
num	reciprocal () const
	Invert this object.
void	square ()
	Square this object.
void	square (int k)
	Square this object a specified number of times.
void	square (const num &x)
	Assign the square of another num to this object.
void	mpower (const num &x, const num &y)
	Exponentiation: assign x^y to this object.
Inspectors
int	bytes () const
	Get the length of this object's value in bytes.
int	l () const
	Get the length of this object in nwords.
int	bits () const
	Get the number of bits in this object's representation.
int	bit (int k) const
	Get the kth bit of this object's value.
int	byte (int k) const
	Get the kth element in the array of bytes representing this object's value.
nword &	wd (int k)
	Get reference to kth nword in the representation of this object as an array of nwords.
nword	w (int k) const
	Get kth nword in the representation of this object as an array of nwords.
const nword *	words () const
	Get a pointer to the array of nwords representing this object.
int	degree () const
	Get object's degree.
int	degf () const
	Get the degree of the underlying field extension in characteristic 2.
num	modulus () const
	Get the characteristic of the underlying field.
num	modulus2 () const
	Get the degree of the field extension in char 2.
const FParms *	parms () const
	Get the parameters of the underlying group, ring, or field.
int	checkModulus () const
	Test object's parameters.
Conversions
num	toint () const
	Map this object to a natural number.
template<class T>
T	to (int n=0) const
	Convert this object to type T.
cdk::str	tostr (int n=0) const
	Get a str representation of this object.

---

Constructor & Destructor Documentation

num

(

const num &

x

)

[inline]

Constructor used to duplicate a given num object.

Parameters:

x

num to duplicate in this object

num	(	const num &	x,
		const str &	y
	)			[inline]

Constructor used to convert a str into a num object with specified parameters.

Parameters:

	x	num whose parameters are to be copied
	y	str to convert into this num object

num

(

int

x

)

[inline]

Constructor used to instantiate a new num object based on an integer.

Parameters:

x

int to be assigned to this new num object.

num

(

const FParms *

p1

)

[inline]

Constructor used to create new num with specified parameters.

Parameters:

p1

parameters to use for this new num object.

num

(

const str &

x

)

[explicit]

Constructor used to convert a str into a num object.

Parameters:

x

str to be converted into this num.

num	(	int	type1,
		int	len
	)			[inline]

Constructor used to created a new num object of specified type and size.

Parameters:

	type1	one of FParms::Types
	len	size of num object to be created

~num

(

)

[inline]

Destructor. Calls clear1().

Remarks:

Modifies: v (zeroized as v may have held a key), p

---

Member Function Documentation

num abs

(

)

const

Absolute value of this object.

Returns:

a positive representation of this num with the same absolute value

void add	(	int	n,
		const char *	x
	)			[inline]

Load octet string into this object.

Parameters:

	n	length of input array in nwords
	x	pointer to an octet string (base 256) to assign to this object.

int bit

(

int

k

)

const [inline]

Get the k^th bit of this object's value.

Parameters:

k

the index of the bit to be returned

Returns:

the k^th bit of this object's value

int bits

(

)

const [inline]

Get the number of bits in this object's representation.

Returns:

1 plus the object's degree

int byte

(

int

k

)

const [inline]

Get the k^th element in the array of bytes representing this object's value.

Parameters:

k

index of byte to return

Returns:

the k^th byte of the num

int bytes

(

)

const [inline]

Get the length of this object's value in bytes.

Returns:

the size of the num in bytes

int checkModulus

(

)

const

Test object's parameters.

Returns:

0, if the object's parameters are prime/irreducible
non-zero, otherwise

int degf

(

)

const [inline]

Get the degree of the underlying field extension in characteristic 2.

Returns:

the degree of the field extension containing this object

int degree

(

)

const [inline]

Get object's degree.

Returns:

the degree of this object

void divide	(	const num &	y,
		num &	quot,
		num &	rem
	)			const

Divide this num by another.

Parameters:

	y	num by which to divide this object
	quot	buffer which is to receive quotient
	rem	buffer which is to receive remainder

num inverse

(

)

const

Compute the inverse of this object (uses Euclidean Algorithm).

Returns:

a num containing the inverse of this object

bool isChar2

(

)

const [inline]

Predicate used to determine if this object is an element of a field of char 2.

Returns:

true, if type is Char2
false, otherwise

bool isEven

(

)

const [inline]

Predicate used to determine if this object is even.

Returns:

true, if object is even
false, otherwise

bool isIrred

(

)

const

Predicate used to test irreducibility.

Returns:

true, if this object is irreducible
false, otherwise

bool isMod

(

)

const [inline]

Predicate used to determine if this object is a ring or field element.

Returns:

true, if type is Modular
false, otherwise

bool isMontg

(

)

const [inline]

Predicate used to determine if this object is in its Montgomery representation.

Returns:

true, if this object is in its Montgomery representation
false, otherwise

bool isNat

(

)

const [inline]

Predicate used to determine if this object represents a natural number.

Returns:

true, if type is Natural
false, otherwise

bool isNeg

(

)

const [inline]

Predicate used to determine if this object is negative.

Returns:

true, if type is Negative
false, otherwise

bool isPrime

(

int

rounds = 8

)

const

Predicate used to test primality.

Parameters:

rounds

number of Miller-Rabin rounds to run

Returns:

true, if this object passes the test (i.e., is a probable prime)
false, if this object is composite

int isSquare

(

)

const

Predicate to test quadratic residuosity.

Returns:

+1 if this is a square mod p

bool isZero

(

)

const [inline]

Predicate used to determine if this object is the zero element.

Returns:

true, if object is the additive identity
false otherwise

int l

(

)

const [inline]

Get the length of this object in nwords.

Returns:

the length of this object in nwords

void mmult	(	const num &	x,
		const num &	y
	)

Assign the product of two num objects to this one.

Parameters:

	x	multiplicand
	y	multiplier

Remarks:

This object receives the value x * y.

num mod	(	const num &	y,
		int	deg = 0
	)			const [inline]

Modular reduction. Alias for mod1().

Parameters:

	y	modulus
	deg	0 for char p; degree of the field extension in char 2

Returns:

this object reduced modulo y

num mod1	(	const num &	y,
		int	deg = 0
	)			const

Modular reduction.

Parameters:

	y	modulus
	deg	0 for char p; degree of the field extension in char 2

Returns:

this reduced mod y

num mod2

(

const num &

y

)

const [inline]

Modular reduction.

Parameters:

y

modulus

Returns:

this object reduced modulo y

void mod2to

(

int

n

)

Assign a power of 2 to this object.

Parameters:

n

exponent to which 2 is to be raised before storing in this object.

num modulus

(

)

const

Get the characteristic of the underlying field.

Returns:

the characteristic of the underlying field (a large prime)

num modulus2

(

)

const

Get the degree of the field extension in char 2.

Returns:

the degree of the field extension in char 2

void mpower	(	const num &	x,
		const num &	y
	)

Exponentiation: assign x^y to this object.

Parameters:

	x	base
	y	exponent

num operator &

(

const FParms *

p1

)

const

Change this object's parameters, but not its value.

Parameters:

p1

pointer to new parameters to use this num object.

num operator *

(

const num &

y

)

const

Multiply this num by another one.

Parameters:

y

num by which to multiply this num

Returns:

a num representing this object's value * y's value

num operator *

(

int

y

)

const

Multiply this object by an integer.

Parameters:

y

int by which this object is to be multiplied

Returns:

a num representing this object's value times y

num& operator *=

(

int

n

)

Multiply this num by an integer.

Parameters:

n

integer multiplier

Returns:

a reference to this object

bool operator!=

(

int

n

)

const [inline]

Predicate to test inequality of this oject with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is not equal to n
false, otherwise

bool operator!=

(

const num &

y

)

const [inline]

Predicate to test inequality of two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is not equal to y
false, otherwise

int operator%

(

int

k

)

const

Compute this num's residue modulo a specified integer.

Parameters:

k

modulus

Returns:

remainder obtained by dividing this object by k

num operator+

(

const num &

y

)

const

Add a num object to this one.

Parameters:

y

the num to added to this object.

Returns:

a num representing this object's value plus y's value

num& operator+=

(

const num &

x

)

Increment this object by a specified value.

Parameters:

x

num to add to this one

Returns:

a reference to this object

num operator-

(

const num &

y

)

const

Subtract a num object from this one.

Parameters:

y

the num to subtracted from this object.

Returns:

a num representing this object's value minus y's value

num operator-

(

int

x

)

[inline]

Subtract an integer from this object.

Parameters:

x

int to be subtracted from this object.

Returns:

a num representing this object's value minus x

num operator-

(

)

const

Negate this object.

Returns:

a negated copy of this object

Remarks:

If this object represents A, then a num representing -A is returned.

num& operator-=

(

const num &

x

)

Decrement this object by a specified value.

Parameters:

x

num to subtract from this one

Returns:

a reference to this object

num& operator-=

(

int

x

)

[inline]

Decrement this object by a specified integer.

Parameters:

x

int to be subtracted from this object.

Returns:

a reference to this object

num operator/

(

const num &

x

)

const [inline]

Divide this num by another num.

Parameters:

x

divisor

Returns:

a num representing this object's value divided by x's value

num operator/

(

int

y

)

const

Divide this num by an integer.

Parameters:

y

the integer divisor

Returns:

a num representing this object's value divided by y

num& operator/=

(

int

n

)

Divide this object by an integer.

Parameters:

n

int divisor

Returns:

a reference to this object

bool operator<

(

int

n

)

const [inline]

Predicate to test "less than" relation with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is less than n
false, otherwise

bool operator<

(

const num &

y

)

const

Predicate to test "less than" relation between two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is less than y
false, otherwise

bool operator<=

(

int

n

)

const [inline]

Predicate to test "less than or equal to" relation with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is less than or equal to n
false, otherwise

bool operator<=

(

const num &

y

)

const

Predicate to test "less than or equal to" relation between two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is less than or equal to y
false, otherwise

num& operator=

(

int

x

)

Assignment operator for int.

Parameters:

x

int to be assigned to this object.

Returns:

a reference to this object

num& operator=

(

nword

x

)

Assignment operator for nword.

Parameters:

x

nword to to be assigned to this object.

Returns:

a reference to this object

void operator=

(

const num &

x

)

[inline]

Assignment operator for num objects.

Parameters:

x

num to copy into this num object.

void operator=

(

const FParms *

p1

)

[inline]

Assign parameters to this object.

Parameters:

p1

new parameters to use for this object.

bool operator==

(

int

n

)

const

Predicate to test equality of this oject with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is equal to n
false, otherwise

bool operator==

(

const num &

y

)

const

Predicate to test equality of two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is equal to y
false, otherwise

bool operator>

(

int

n

)

const [inline]

Predicate to test "greater than" relation with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is greater than n
false, otherwise

bool operator>

(

const num &

y

)

const [inline]

Predicate to test "greater than" relation between two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is greater than y
false, otherwise

bool operator>=

(

int

n

)

const

Predicate to test "greater than or equal to" relation with an int.

Parameters:

n

int to which this object is to be compared

Returns:

true, if this object is greater than or equal to n
false, otherwise

bool operator>=

(

const num &

y

)

const [inline]

Predicate to test "greater than or equal to" relation between two nums.

Parameters:

y

num to which this object is to be compared

Returns:

true, if this object is greater than or equal to y
false, otherwise

num operator^

(

int

n

)

const

Raise this object's value to an integer exponent.

Parameters:

n

exponent

Returns:

a num = this ^ n if n < 1000 (if n >= 1000 an assertion occurs)

bool operator|

(

const num &

y

)

const [inline]

Predicate used to test whether a given num divides this one.

Parameters:

y

divisor

Returns:

true, if y divides this object
false, otherwise

const FParms* parms

(

)

const [inline]

Get the parameters of the underlying group, ring, or field.

Returns:

a pointer to this object's parameters

void power	(	const num &	x,
		const num &	y
	)

Assign x^y to this object.

Parameters:

	x	the base
	y	the exponent

num reciprocal

(

)

const

Invert this object.

Returns:

a num containing the reciprocal of this object

void setlen

(

int

n

)

[inline]

Set the length of this object in nwords.

Parameters:

n

the number of nwords to use for this num.

Remarks:

WARNING: This call is dangerous!

num sqrt

(

)

const

Calculate square root.

Returns:

the square root of this object

void square

(

const num &

x

)

[inline]

Assign the square of another num to this object.

Parameters:

x

the num to be squared

void square

(

int

k

)

Square this object a specified number of times.

Parameters:

k

number of times to square this object

T to

(

int

n = 0

)

const

Convert this object to type T.

Parameters:

n

minimum size of output in bytes

Returns:

a type T represenation of this object (typically a str representation with leading 0's removed)

num toint

(

)

const

Map this object to a natural number.

Returns:

a num containing this object's value but without parameter information

cdk::str tostr

(

int

n = 0

)

const

Get a str representation of this object.

Parameters:

n

the minimum length of the str to be created

Returns:

a (binary) str representation of the value of this num

nword w

(

int

k

)

const [inline]

Get k^th nword in the representation of this object as an array of nwords.

Parameters:

k

index of nword to return

Returns:

the k^th nword

nword& wd

(

int

k

)

[inline]

Get reference to k^th nword in the representation of this object as an array of nwords.

Parameters:

k

index of nword to return

Returns:

a reference to the k^th nword

const nword* words

(

)

const [inline]

Get a pointer to the array of nwords representing this object.

Returns:

a reference to the array of nwords stored in this Nat object

---

The documentation for this struct was generated from the following file:

• pk.h

---

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