## Introduction

A point represents a element of public-key cryptographic group. For example, A point can be a number modulo the prime P in a DSA-style Schnorr group, or an (x, y) point on elliptic curve. A point can contain a Diffie-Hellman public key, an Elgamal ciphertext, etc.

In here a point is implemented by the use of an interface by the name Point.

``````type Point interface {
Marshaling

Equal(s2 Point) bool
Null() Point
Base() Point
Pick(rand cipher.Stream) Point
Set(p Point) Point
Clone() Point
EmbedLen() int
Embed(data []byte, r cipher.Stream) Point
Data() ([]byte, error)
Sub(a, b Point) Point
Neg(a Point) Point
Mul(s Scalar, p Point) Point
}
``````

## Data Members

### Marshaling

Marshaling is a basic interface representing fixed-length (or known-length) cryptographic objects or structures having a built-in binary encoding. Implementors must ensure that calls to these methods do not modify the underlying object so that other users of the object can access it concurrently.

## Functions

### Equal()

Function `Point.Equal(Point) bool`
Parameters - `Point` : The Point with which the equality has to be checked with
Output - `Boolean` : Answer to the equality of the points

This function is used to check the equality of two Points derived from the same group. It returns a `true/false` indicating wether the Points are equal or not.

### Null()

Function `Point.Null() Point`
Parameters - `None`
Output - `Point` : Caller Point with value equal to the neutral identity element

This function sets the receiver object to a neutral identity element, depending upon the suite taken into consideration.

### Base()

Function `Point.Base() Point`
Parameters - `None`
Output - `Point` : Caller Point with value equal to the group's standard base

This function sets the receiver object to the parent group's standard base.

### Pick()

Function `Point.Pick(cipher.Stream) Point`
Parameters - `cipher.Stream` : Source from which random / pseudo-random values are picked
Output - `Point` : Caller Point with a random / pseudo-random value

This functions sets the receiver object to a random or pseudo-random Point, which is extracted with the help of the cipher.Stream which is passed as a parameter to the function.

### Set()

Function `Point.Set(Point) Point`
Parameters - `Point` : Point whose value has to be set to the current Point
Output - `Point` : Caller Point with the same value as the parametric Point

This function sets the receiver object's value to the Point specified by another object passed as a parameter to the function.

### Clone()

Function `Point.Clone() Point`
Parameters - `None`
Output - `Point` : A new point which is a clone of the caller object

This functions clones the underlying object.

Function `Point.Add(Point, Point) Point`
Parameters - `Point, Point` : The two points which have to be added
Output - `Point` : Caller Point with value equal to the sum of the above two Points

This function sets the receiving object to the sum of two Points passed to the function as parameters. This addition is achieved such the scalars of those two Points add homomorphically.

### Sub()

Function `Point.Sub(Point, Point) Point`
Parameters - `Point, Point` : The two Points which have to subtracted
Output - `Point` : Caller Point with value equal to the difference of the above two Points

This function sets the receiving object to the difference of the two Points passed as parameters to the function. This substraction is achieved such that the scalars of those two Points are substracted homorphically.

### Neg()

Function `Point.Neg(Point) Point`
Parameters - `Point` : Point whose value has to be negated
Output - `Point` : Caller Point with value equal to the negation of the value of the parametric Point

This function sets the receiving object to the negation of the Point passed to the function as the parameter.

### Mul()

Function `Point.Mul(Scalar, Point) Point`
Parameters - `Scalar, Point` : The Scalar and the Point which have to the multiplied
Output - `Point` : Caller Point with value equal to the product of the parametric Scalar and Point

This function sets the receiving object to the product of the Point and the Scalar, passed to the function as parameters. If the Point is equal to the null value then the Scalar is multiplied with the standard base, which depends upon the suite being used.

### EmbedLen()

Function `Point.EmbedLen() int`
Parameters - `None`
Output - `int` : Maximum number of bytes which can be embedded in a single group element

The EmbedLen function returns the maximum number of bytes that can be embedded in a single group element via the Pick() function.

### Embeded()

Function `Point.Embed(data []byte, r cipher.Stream) Point`
Parameters - `[]byte` : Byte encoding of the message to be embedded
- `cipher.Stream` - Source from where random values for the Point are picked
Output - `Point` : Caller Point with a random new value and the given message embedded to it

Embed encodes a limited amount of specified data in the Point, using r as a source of cryptographically secure random data. Implementations only embed the first EmbedLen bytes of the given data.

### Data()

Function `Point.Data() ([]byte, error)`
Parameters - `None`
Output - `[]byte` : Byte encoding of the embedded message in the caller Point
- `error` : Contains an error if something unexpected happened, otherwise is nil

This function extracts the data embedded in a Point chosen via Embed(). It returns an error if the Point doesn't represent valid embedded data.