Element (JPBC - API 2.0.0 API)

All Superinterfaces:

ElementPow

All Known Subinterfaces:

Point<E>, Polynomial<E>, Vector<E>
```
public interface Element
extends ElementPow
```
Elements of groups, rings and fields are accessible using the Element interface. You can obtain an instance of an Element starting from an algebraic structure, such as a particular finite field or elliptic curve group, represented by the Field interface.

Since:

1.0.0

Author:

Angelo De Caro (jpbclib@gmail.com)

See Also:
Field, Field, ElementPowPreProcessing

Method Summary

Methods
Modifier and Type	Method and Description
`Element`	`add(Element element)` Sets this = this + element.
`Element`	`div(Element element)` Sets this = this / element
`Element`	`duplicate()` Returns a copy of this element.
`ElementPowPreProcessing`	`getElementPowPreProcessing()` Prepare to exponentiate this element and returns pre-processing information.
`Field`	`getField()` Returns the field to which this element lie.
`Element`	`getImmutable()` Returns an immutable copy of this element if the element is not already immutable.
`int`	`getLengthInBytes()` Returns the length in bytes necessary to represent this element.
`Element`	`halve()` Sets this = this / 2.
`Element`	`invert()` Sets this to the inverse of itself.
`boolean`	`isEqual(Element value)` Returns `true` if this and value have the same value, `false` otherwise.
`boolean`	`isImmutable()` Returns `true` if this element is immutable, `false` otherwise.
`boolean`	`isOne()` Returns true if n is one, false otherwise.
`boolean`	`isSqr()` Returns true if this element is a perfect square (quadratic residue), false otherwise.
`boolean`	`isZero()` Returns true if n is zero, false otherwise.
`Element`	`mul(BigInteger n)` Sets this = this * n, that is this + this + ...
`Element`	`mul(Element element)` Sets this = this * element.
`Element`	`mul(int z)` Sets this = this * z, that is this + this + ...
`Element`	`mulZn(Element z)` Sets this = this * z, that is this + this + … + this where there are z this's and z is an element of a ring Z_N for some N.
`Element`	`negate()` Set this = -this.
`Element`	`pow(BigInteger n)` Sets this = this^n.
`Element`	`powZn(Element n)` Sets this = this^n, where n is an element of a ring Z_N for some N (typically the order of the algebraic structure n lies in).
`Element`	`set(BigInteger value)` Sets this element to value.
`Element`	`set(Element value)` Sets this element to value.
`Element`	`set(int value)` Sets this element to value.
`int`	`setFromBytes(byte[] source)` Reads this element from the buffer source.
`int`	`setFromBytes(byte[] source, int offset)` Reads this element from the buffer source starting from offset.
`Element`	`setFromHash(byte[] source, int offset, int length)` Sets this element deterministically from the length bytes stored in the source parameter starting from the passed offset.
`Element`	`setToOne()` Sets this element to one.
`Element`	`setToRandom()` If this element lies in a finite algebraic structure, assigns a uniformly random element to it.
`Element`	`setToZero()` Sets this element to zero.
`int`	`sign()` If this element is zero, returns 0.
`Element`	`sqrt()` Sets this = sqrt(this).
`Element`	`square()` Se this = this^2.
`Element`	`sub(Element element)` Sets this = this - element.
`BigInteger`	`toBigInteger()` Converts this to a BigInteger if such operation makes sense.
`byte[]`	`toBytes()` Converts this element to bytes.
`byte[]`	`toCanonicalRepresentation()` Returns the canonical representation of this element.
`Element`	`twice()` Sets this = this + this.

- Method Detail
  - getField
```
Field getField()
```
    Returns the field to which this element lie.
    
    Returns:
    the field to which this element lie.
    Since:
    
    1.0.0
  - getLengthInBytes
```
int getLengthInBytes()
```
    Returns the length in bytes necessary to represent this element.
    
    Returns:
    the length in bytes necessary to represent this element.
    Since:
    
    1.0.0
    
    See Also:
    Field.getLengthInBytes()
  - isImmutable
```
boolean isImmutable()
```
    Returns true if this element is immutable, false otherwise.
    
    Returns:
    true if this element is immutable, false otherwise.
    See Also:
    getImmutable()
  - getImmutable
```
Element getImmutable()
```
    Returns an immutable copy of this element if the element is not already immutable.
    For immutable elements the internal value cannot be modified after it is created, any method designed to modify the internal state of the element will return a new element whose internal value represents the computation executed.
    
    Returns:
    an immutable copy of this element if the element is not already immutable.
    See Also:
    isImmutable()
  - duplicate
```
Element duplicate()
```
    Returns a copy of this element. If this element is immutable then the copy is mutable.
    
    Returns:
    a copy of this element.
    Since:
    
    1.0.0
  - set
```
Element set(Element value)
```
    Sets this element to value.
    
    Parameters:
    value - the new value of this element.
    
    Returns:
    this element set to value.
    Since:
    
    1.0.0
  - set
```
Element set(int value)
```
    Sets this element to value.
    
    Parameters:
    value - the new value of this element.
    
    Returns:
    this element set to value.
    Since:
    
    1.0.0
  - set
```
Element set(BigInteger value)
```
    Sets this element to value.
    
    Parameters:
    value - the new value of this element.
    
    Returns:
    this element set to value.
    Since:
    
    1.0.0
  - toBigInteger
```
BigInteger toBigInteger()
```
    Converts this to a BigInteger if such operation makes sense.
    
    Returns:
    a BigInteger which represents this element.
    Since:
    
    1.0.0
  - setToRandom
```
Element setToRandom()
```
    If this element lies in a finite algebraic structure, assigns a uniformly random element to it.
    
    Returns:
    this.
    Since:
    
    1.0.0
  - setFromHash
```
Element setFromHash(byte[] source,
                  int offset,
                  int length)
```
    Sets this element deterministically from the length bytes stored in the source parameter starting from the passed offset.
    
    Parameters:
    source - the buffer data.
    offset - the starting offset.
    length - the number of bytes to be used.
    
    Returns:
    this element modified.
    Since:
    
    1.0.0
  - setFromBytes
```
int setFromBytes(byte[] source)
```
    Reads this element from the buffer source.
    
    Parameters:
    source - the source of bytes.
    
    Returns:
    the number of bytes read.
    Since:
    
    1.0.0
  - setFromBytes
```
int setFromBytes(byte[] source,
               int offset)
```
    Reads this element from the buffer source starting from offset.
    
    Parameters:
    source - the source of bytes.
    offset - the starting offset.
    
    Returns:
    the number of bytes read.
    Since:
    
    1.0.0
  - toBytes
```
byte[] toBytes()
```
    Converts this element to bytes. The number of bytes it will write can be determined calling getLengthInBytes().
    
    Returns:
    the bytes written.
    Since:
    
    1.0.0
  - toCanonicalRepresentation
```
byte[] toCanonicalRepresentation()
```
    Returns the canonical representation of this element. In most of the cases the output of this method is the same as that of the #toBytes method.
    
    Returns:
    the canonical representation of this element.
    Since:
    
    2.0.0
  - setToZero
```
Element setToZero()
```
    Sets this element to zero.
    
    Returns:
    this element set to zero.
    Since:
    
    1.0.0
  - isZero
```
boolean isZero()
```
    Returns true if n is zero, false otherwise.
    
    Returns:
    true if n is zero, false otherwise.
    Since:
    
    1.0.0
  - setToOne
```
Element setToOne()
```
    Sets this element to one.
    
    Returns:
    this element set to one.
    Since:
    
    1.0.0
  - isEqual
```
boolean isEqual(Element value)
```
    Returns true if this and value have the same value, false otherwise.
    
    Parameters:
    value - the element to be compared.
    
    Returns:
    true if this and value have the same value, false otherwise.
  - isOne
```
boolean isOne()
```
    Returns true if n is one, false otherwise.
    
    Returns:
    true if n is one, false otherwise.
    Since:
    
    1.0.0
  - twice
```
Element twice()
```
    Sets this = this + this.
    
    Returns:
    this + this.
    Since:
    
    1.0.0
  - square
```
Element square()
```
    Se this = this^2.
    
    Returns:
    this^2.
    Since:
    
    1.0.0
  - invert
```
Element invert()
```
    Sets this to the inverse of itself.
    
    Returns:
    the inverse of itself.
    Since:
    
    1.0.0
  - halve
```
Element halve()
```
    Sets this = this / 2.
    
    Returns:
    this / 2.
    Since:
    
    1.0.0
  - negate
```
Element negate()
```
    Set this = -this.
    
    Returns:
    -this.
    Since:
    
    1.0.0
  - add
```
Element add(Element element)
```
    Sets this = this + element.
    
    Parameters:
    element - the value to be added.
    
    Returns:
    this + element.
    Since:
    
    1.0.0
  - sub
```
Element sub(Element element)
```
    Sets this = this - element.
    
    Parameters:
    element - the value to be subtracted.
    
    Returns:
    this - element.
    Since:
    
    1.0.0
  - mul
```
Element mul(Element element)
```
    Sets this = this * element.
    
    Parameters:
    element - the value to be multiplied
    
    Returns:
    this * element.
    Since:
    
    1.0.0
  - mul
```
Element mul(int z)
```
    Sets this = this * z, that is this + this + ... + this where there are z this's.
    
    Parameters:
    z - the value to be multiplied
    
    Returns:
    this * z
    Since:
    
    1.0.0
  - mul
```
Element mul(BigInteger n)
```
    Sets this = this * n, that is this + this + ... + this where there are n this's.
    
    Parameters:
    n - the value to be multiplied
    
    Returns:
    this * n
    Since:
    
    1.0.0
  - mulZn
```
Element mulZn(Element z)
```
    Sets this = this * z, that is this + this + … + this where there are z this's and z is an element of a ring Z_N for some N.
    
    Parameters:
    z - the value to be multiplied
    
    Returns:
    this * z
    Since:
    
    1.0.0
  - div
```
Element div(Element element)
```
    Sets this = this / element
    
    Parameters:
    element - is the divisor.
    
    Returns:
    this / element
    Since:
    
    1.0.0
  - pow
```
Element pow(BigInteger n)
```
    Sets this = this^n.
    
    Specified by:
    
    pow in interface ElementPow
    
    Parameters:
    n - the exponent of the power.
    
    Returns:
    this^n.
    Since:
    
    1.0.0
  - powZn
```
Element powZn(Element n)
```
    Sets this = this^n, where n is an element of a ring Z_N for some N (typically the order of the algebraic structure n lies in).
    
    Specified by:
    
    powZn in interface ElementPow
    
    Parameters:
    n - the exponent of the power.
    
    Returns:
    this^n
    Since:
    
    1.0.0
  - getElementPowPreProcessing
```
ElementPowPreProcessing getElementPowPreProcessing()
```
    Prepare to exponentiate this element and returns pre-processing information.
    
    Returns:
    the pre-processing information used to execute the exponentation of this element.
    See Also:
    ElementPowPreProcessing
  - sqrt
```
Element sqrt()
```
    Sets this = sqrt(this).
    
    Returns:
    the square radix of this element.
    Since:
    
    1.0.0
  - isSqr
```
boolean isSqr()
```
    Returns true if this element is a perfect square (quadratic residue), false otherwise.
    
    Returns:
    true if this element is a perfect square (quadratic residue), false otherwise.
    Since:
    
    1.0.0
  - sign
```
int sign()
```
    If this element is zero, returns 0. For a non zero value the behaviour depends on the algebraic structure.
    
    Returns:
    0 is this element is zero, otherwise the behaviour depends on the algebraic structure.
    Since:
    
    1.0.0

Interface Element

Method Summary

Method Detail

getField

getLengthInBytes

isImmutable

getImmutable

duplicate

set

set

set

toBigInteger

setToRandom

setFromHash

setFromBytes

setFromBytes

toBytes

toCanonicalRepresentation

setToZero

isZero

setToOne

isEqual

isOne

twice

square

invert

halve

negate

add

sub

mul

mul

mul

mulZn

div

pow

powZn

getElementPowPreProcessing

sqrt

isSqr

sign