Point Class Reference

#include <pk.h>

Collaboration diagram for Point:

---

Detailed Description

Data type used to represent the elements of, and abstract the operations in, various Abelian groups, including elliptic curves.

As the class name indicates, operators are defined as if the underlying group operation is written additively, though obviously if the group is more commonly written multiplicatively, the operators should be interpreted that way. For example, operator*() is decribed below as scalar multiplication, but should be thought of as exponentiation in the multiplicative setting.

Public Member Functions
Constructors and Destructors
	Point ()
	Constructor used to create an empty Point object.
	Point (const Point &a)
	Copy constructor.
	Point (const GParms *p1)
	Constructor used to create an element of the specified Abelian group.
	Point (const Point &a, const str &b)
	Constructor used to create a Point in the same Abelian group as another Point.
virtual	~Point ()
	Destructor.
Object Reuse and Initialization
void	clear ()
	Clear this Point object.
int	setgen (const num &g)
	Specify a generator for the underlying Abelian group.
int	setcurve (const num &a, const num &b)
	Specify the coefficients in the equation of an elliptic curve:    in char p:  y 2 = x 3 + a x + b    in char 2:  y 2 + x y = x 3 + a x 2 + b.
void	power (const Point &x, const num &y)
	Assign an (unnormalized) multiple of a given Point to this one.
int	loadbin (int n, const char *b)
	Load an octet string into this Point.
void	add (int n, const char *b)
	Add; a void version of loadbin().
Assignment and Arithmetic Operators
void	operator= (int n)
	Assignment operator used to make this Point the identity element in the group.
void	operator= (const Point &x)
	Assignment operator used to copy Points.
Point	operator- () const
	Get the additive inverse of this Point.
Point	operator+ (const Point &y) const
	Add another Point to this one.
Point	operator- (const Point &y) const
	Subtract another Point from this one.
Point	operator * (const num &x) const
	Multiply this Point by an integer.
Predicate Operators
bool	operator== (int n) const
	Predicate used to test whether this Point is the identity element in the group.
bool	operator!= (int n) const
	Predicate used to test whether this Point differs from the identity element.
bool	operator== (const Point &x) const
	Predicate used to test the equality of this Point with another one.
bool	operator!= (const Point &x) const
	Predicate used to test the inequality of this Point with another one.
Predicate Functions
bool	isDef () const
	Predicate used to determine whether parameters are defined.
bool	isDH () const
	Predicate used to determine whether this point is an element of (a multiplicative subgroup of) the group of nonzero integers modulo a large prime.
bool	isEC () const
	Predicate used to determine whether this Point is on an elliptic curve.
bool	isChar2 () const
	Predicate used to determine whether this Point is on an elliptic curve in char 2.
bool	isValid () const
	Predicate used to test whether this Point lies on the underlying elliptic curve.
bool	hasOrder (const num &a) const
	Predicate used to test whether this group element has a specified order.
Inspectors
int	bits () const
	Get the number of bits required to represent this Point.
int	length () const
	Get the size in bytes of the largest integer that can be mapped into the current Abelian group.
num	modulus2 () const
	Get the order of the underlying finite field or order of the group.
Conversions
cdk::str	tostr (int n=0) const
	Convert this Point into a str.
template<class T>
T	to (int opt=0) const
	Convert Point into an object of type T.

---

Constructor & Destructor Documentation

Point

(

const Point &

a

)

[inline]

Copy constructor.

Parameters:

a

the Point to copy into this Point

Point

(

const GParms *

p1

)

[inline, explicit]

Constructor used to create an element of the specified Abelian group.

Parameters:

p1

a pointer to the group parameters (GParms) to use for this point.

Point	(	const Point &	a,
		const str &	b
	)			[explicit]

Constructor used to create a Point in the same Abelian group as another Point.

Parameters:

	a	a Point from which to copy group parameters
	b	a value indicating which group element this new Point is to represent

virtual ~Point

(

)

[inline, virtual]

Destructor.

Remarks:

Modifies: p (x, y, and z are zeroized by their destructors)

---

Member Function Documentation

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

Add; a void version of loadbin().

Parameters:

	n	length of the octet string in bytes
	b	pointer to the octet string

int bits

(

)

const

Get the number of bits required to represent this Point.

Returns:

the number of bits in the point

void clear

(

void

)

[inline]

Clear this Point object.

Remarks:

Modifies: x, y, z are zeroized; p (the parameters) is not cleared.

bool hasOrder

(

const num &

a

)

const

Predicate used to test whether this group element has a specified order.

Parameters:

a

suspected order of this group element

Returns:

true, if this element has order a
false, otherwise

bool isChar2

(

)

const [inline]

Predicate used to determine whether this Point is on an elliptic curve in char 2.

Returns:

true, if this Point's parameters are those for an elliptic curve over a finite field of char 2
false, otherwise

bool isDef

(

)

const [inline]

Predicate used to determine whether parameters are defined.

Returns:

true, if the parameters are defined
false, otherwise

bool isDH

(

)

const [inline]

Predicate used to determine whether this point is an element of (a multiplicative subgroup of) the group of nonzero integers modulo a large prime.

Returns:

true, if this Point's parameters are those for (a multiplicative subgroup of) Zp*
false, otherwise

bool isEC

(

)

const [inline]

Predicate used to determine whether this Point is on an elliptic curve.

Returns:

true, if this Point's parameters are those for an elliptic curve
false, otherwise

bool isValid

(

)

const

Predicate used to test whether this Point lies on the underlying elliptic curve.

Returns:

true, if this Point is on the underlying curve
false, otherwise

int length

(

)

const [inline]

Get the size in bytes of the largest integer that can be mapped into the current Abelian group.

Returns:

the maximum number of *bytes* that can be in a number as represented in the current field/group/curve

Remarks:

This function is useful when you want to know how large a random number to generate for certain cryptographic protocols (e.g., ECDSA signature generation).

int loadbin	(	int	n,
		const char *	b
	)

Load an octet string into this Point.

Parameters:

	n	length of the octet string in bytes
	b	pointer to the octet string

Returns:

the number of bytes used

num modulus2

(

)

const [inline]

Get the order of the underlying finite field or order of the group.

Returns:

the modulus of the underlying finite field or order of the group

Point operator *

(

const num &

x

)

const

Multiply this Point by an integer.

Parameters:

x

the multiple

Returns:

the specified multiple of this Point

bool operator!=

(

const Point &

x

)

const [inline]

Predicate used to test the inequality of this Point with another one.

Parameters:

x

the Point (i.e., group element) to which this one is to be compared

Returns:

true, if the two group elements disagree
false, if the two Points are equal

bool operator!=

(

int

n

)

const [inline]

Predicate used to test whether this Point differs from the identity element.

Parameters:

n

= must be 0 or method asserts

Returns:

true, if this Point is not the identify element
false, otherwise

Point operator+

(

const Point &

y

)

const

Add another Point to this one.

Parameters:

y

the Point to be added to this point

Returns:

the sum of this Point and y

Point operator-

(

const Point &

y

)

const

Subtract another Point from this one.

Parameters:

y

the Point to subtract from this point

Returns:

the difference of this Point and y

Point operator-

(

)

const

Get the additive inverse of this Point.

Returns:

the additive inverse of this Point

void operator=

(

const Point &

x

)

[inline]

Assignment operator used to copy Points.

Parameters:

x

the Point to copy into this one

void operator=

(

int

n

)

Assignment operator used to make this Point the identity element in the group.

Parameters:

n

must be 0 (any other value will trigger an exception)

bool operator==

(

const Point &

x

)

const [inline]

Predicate used to test the equality of this Point with another one.

Parameters:

x

the Point (i.e., group element) to which this one is to be compared

Returns:

true, if the two group elements are equal
false, if the two group elements disagree

bool operator==

(

int

n

)

const

Predicate used to test whether this Point is the identity element in the group.

Parameters:

n

must be 0 or method asserts

Returns:

true, if this Point is the identity element in its Abelian group
false, otherwise

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

Assign an (unnormalized) multiple of a given Point to this one.

Parameters:

	x	the base Point
	y	the multiple of x to be assigned to this Point

int setcurve	(	const num &	a,
		const num &	b
	)

Specify the coefficients in the equation of an elliptic curve:
   in char p:  y ² = x ³ + a x + b
   in char 2:  y ² + x y = x ³ + a x ² + b.

Parameters:

	a	the first coefficient
	b	the second coefficient

Returns:

0

int setgen

(

const num &

g

)

Specify a generator for the underlying Abelian group.

Parameters:

g

a new generator for the underlying group

Returns:

0

T to

(

int

opt = 0

)

const

Convert Point into an object of type T.

Parameters:

opt

compression indicator: 0 = compressed, 1 = uncompressed

Returns:

an object of type T representing this Point

cdk::str tostr

(

int

n = 0

)

const

Convert this Point into a str.

Parameters:

n

a compression indicator: 0 = compressed, 1 = uncompressed

Returns:

a str representation of this Point

---

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

• pk.h

---

ISC Cryptographic Development Kit - User's Guide
Questions? E-mail ISC technical support
Copyright© 2002-2006 Information Security Corp. All rights reserved.