org.cryptimeleon.math.structures.rings.zn

Class Zp.ZpElement

java.lang.Object

org.cryptimeleon.math.structures.rings.zn.Zn.ZnElement

org.cryptimeleon.math.structures.rings.zn.Zp.ZpElement

All Implemented Interfaces:

UniqueByteRepresentable, Representable, Element, FieldElement, RingElement

Enclosing class:

Zp

public class Zp.ZpElement
extends Zn.ZnElement
implements FieldElement

The elements of Zp.

See Also:

ZnElement

Field Summary

Fields inherited from class org.cryptimeleon.math.structures.rings.zn.Zn.ZnElement

v

Constructor Summary

Constructors

Constructor and Description
ZpElement(java.math.BigInteger v)

Method Summary

Modifier and Type	Method and Description
Zp.ZpElement	add(Element e) Computes \(\text{this} + e\).
FieldElement	applyFrobenius() Computes this^characteristic.
Zp.ZpElement	div(Element e) Computes \(\text{this} / e = \text{this} \cdot e^{-1}\).
Zp	getStructure() Returns the Structure that this Element belongs to.
Zp.ZpElement	inv() Computes the multiplicative inverse of this element.
boolean	isSquare() Returns true if there is a \(y \in \mathbb{Z}_p\) such that \(y^2 = \text{this}\)
Zp.ZpElement	mul(java.math.BigInteger k) Computes \(\text{this} \cdot k\) (equivalent to \(\text{this} + \text{this} + \cdots\) k-times).
Zp.ZpElement	mul(Element e) Computes \(\text{this} \cdot e\).
Zp.ZpElement	mul(long k) Computes \(\text{this} \cdot k\) (equivalent to \(\text{this} + \text{this} + \cdots\) k-times).
Zp.ZpElement	neg() Computes the additive inverse of this element.
Zp.ZpElement	pow(java.math.BigInteger k) Calculates \(\text{this}^k\).
Zp.ZpElement	pow(long k) Calculates \(\text{this}^k\).
Zp.ZpElement	sqrt() Computes a square root of this element if it exists.
Zp.ZpElement	square() Computes \(\text{this}^2\).
Zp.ZpElement	sub(Element e) Computes \(\text{this} - e\).

Methods inherited from class org.cryptimeleon.math.structures.rings.zn.Zn.ZnElement

add, asExponentExpression, asInteger, checkSameModulus, divides, divideWithRemainder, equals, getRank, getRepresentation, hashCode, isEqualTo, isEqualTo, isEqualTo, isEqualTo, mul, pow, sub, toString, updateAccumulator

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.cryptimeleon.math.structures.rings.FieldElement

applyFrobenius, divides, divideWithRemainder, getRank

Methods inherited from interface org.cryptimeleon.math.structures.rings.RingElement

asInteger, isOne, isUnit, isZero, toAdditiveGroupElement, toUnitGroupElement

Methods inherited from interface org.cryptimeleon.math.structures.Element

equals, hashCode

Methods inherited from interface org.cryptimeleon.math.serialization.Representable

getRepresentation

Methods inherited from interface org.cryptimeleon.math.hash.UniqueByteRepresentable

getUniqueByteRepresentation, updateAccumulator

Constructor Detail

ZpElement

public ZpElement(java.math.BigInteger v)

Method Detail

getStructure

public Zp getStructure()

Description copied from interface: Element

Returns the Structure that this Element belongs to.

Specified by:

getStructure in interface Element

Specified by:

getStructure in interface FieldElement

Specified by:

getStructure in interface RingElement

Overrides:

getStructure in class Zn.ZnElement

add

public Zp.ZpElement add(Element e)

Description copied from interface: RingElement

Computes \(\text{this} + e\).

Specified by:

add in interface FieldElement

Specified by:

add in interface RingElement

Overrides:

add in class Zn.ZnElement

Parameters:

e - the addend

Returns:

the result

sub

public Zp.ZpElement sub(Element e)

Description copied from interface: RingElement

Computes \(\text{this} - e\).

Specified by:

sub in interface FieldElement

Specified by:

sub in interface RingElement

Overrides:

sub in class Zn.ZnElement

Parameters:

e - the subtrahend

Returns:

the result

neg

public Zp.ZpElement neg()

Description copied from interface: RingElement

Computes the additive inverse of this element.

Specified by:

neg in interface FieldElement

Specified by:

neg in interface RingElement

Overrides:

neg in class Zn.ZnElement

Returns:

the result

mul

public Zp.ZpElement mul(Element e)

Description copied from interface: RingElement

Computes \(\text{this} \cdot e\).

Specified by:

mul in interface FieldElement

Specified by:

mul in interface RingElement

Overrides:

mul in class Zn.ZnElement

Parameters:

e - the factor

Returns:

the result

mul

public Zp.ZpElement mul(java.math.BigInteger k)

Description copied from interface: RingElement

Computes \(\text{this} \cdot k\) (equivalent to \(\text{this} + \text{this} + \cdots\) k-times).

Specified by:

mul in interface FieldElement

Specified by:

mul in interface RingElement

Overrides:

mul in class Zn.ZnElement

Parameters:

k - the factor

Returns:

the result

mul

public Zp.ZpElement mul(long k)

Description copied from interface: RingElement

Computes \(\text{this} \cdot k\) (equivalent to \(\text{this} + \text{this} + \cdots\) k-times).

Specified by:

mul in interface FieldElement

Specified by:

mul in interface RingElement

Overrides:

mul in class Zn.ZnElement

Parameters:

k - the factor

Returns:

the result

inv

public Zp.ZpElement inv()
                 throws java.lang.UnsupportedOperationException

Description copied from interface: RingElement

Computes the multiplicative inverse of this element.

Specified by:

inv in interface FieldElement

Specified by:

inv in interface RingElement

Overrides:

inv in class Zn.ZnElement

Returns:

the result

Throws:

java.lang.UnsupportedOperationException - if this is not a unit

square

public Zp.ZpElement square()

Description copied from interface: RingElement

Computes \(\text{this}^2\).

Useful if the ring allows squaring to be more efficiently implemented than general exponentiation.

Specified by:

square in interface FieldElement

Specified by:

square in interface RingElement

Overrides:

square in class Zn.ZnElement

div

public Zp.ZpElement div(Element e)
                 throws java.lang.IllegalArgumentException

Description copied from interface: RingElement

Computes \(\text{this} / e = \text{this} \cdot e^{-1}\).

Specified by:

div in interface FieldElement

Specified by:

div in interface RingElement

Overrides:

div in class Zn.ZnElement

Parameters:

e - the divisor

Returns:

the result

Throws:

java.lang.IllegalArgumentException - if e is not a unit

pow

public Zp.ZpElement pow(java.math.BigInteger k)

Description copied from interface: RingElement

Calculates \(\text{this}^k\).

Note that \(a^0 = 1\) for any \(a\) in the ring, particularly \(0^0 = 1\).

Specified by:

pow in interface FieldElement

Specified by:

pow in interface RingElement

Overrides:

pow in class Zn.ZnElement

pow

public Zp.ZpElement pow(long k)

Description copied from interface: RingElement

Calculates \(\text{this}^k\).

Note that \(a^0 = 1\) for any \(a\) in the ring, particularly \(0^0 = 1\).

Specified by:

pow in interface FieldElement

Specified by:

pow in interface RingElement

Overrides:

pow in class Zn.ZnElement

isSquare

public boolean isSquare()

Returns true if there is a \(y \in \mathbb{Z}_p\) such that \(y^2 = \text{this}\)

sqrt

public Zp.ZpElement sqrt()
                  throws java.lang.ArithmeticException

Computes a square root of this element if it exists.

Returns:

an element \(x\) with \(x^2 = \text{this}\)

Throws:

java.lang.ArithmeticException - if element is not a quadratic residue

applyFrobenius

public FieldElement applyFrobenius()

Description copied from interface: FieldElement

Computes this^characteristic.

Specified by:

applyFrobenius in interface FieldElement