org.cryptimeleon.math.structures.rings.integers

Class IntegerElement

java.lang.Object

org.cryptimeleon.math.structures.rings.integers.IntegerElement

All Implemented Interfaces:

UniqueByteRepresentable, Representable, Element, RingElement

public class IntegerElement
extends java.lang.Object
implements RingElement

An Integer (as an Element of IntegerRing).

Constructor Summary

Constructors

Constructor and Description
IntegerElement(java.math.BigInteger v)
IntegerElement(long v)

Method Summary

Modifier and Type	Method and Description
IntegerElement	add(Element e) Computes \(\text{this} + e\).
java.math.BigInteger	asInteger() Interprets this element as an integer.
boolean	divides(RingElement e) Returns true iff there exists an \(x\) in the ring such that \(\text{this} \cdot x = e\).
IntegerElement[]	divideWithRemainder(RingElement e) Divides this by e with remainder, returning both quotient and remainder.
boolean	equals(java.lang.Object o)
java.math.BigInteger	getBigInt() Returns the BigInteger underlying this element.
java.math.BigInteger	getRank() Implements the euclidean function of a euclidean domain.
Representation	getRepresentation() The representation of this object.
Ring	getStructure() Returns the Structure that this Element belongs to.
int	hashCode()
IntegerElement	inv() Computes the multiplicative inverse of this element.
IntegerElement	mul(java.math.BigInteger k) Computes \(\text{this} \cdot k\) (equivalent to \(\text{this} + \text{this} + \cdots\) k-times).
IntegerElement	mul(Element e) Computes \(\text{this} \cdot e\).
IntegerElement	neg() Computes the additive inverse of this element.
java.lang.String	toString()
ByteAccumulator	updateAccumulator(ByteAccumulator accumulator) Updates the ByteAccumulator with the unique byte representation of this object.

Methods inherited from class java.lang.Object

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

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

div, isOne, isUnit, isZero, mul, pow, pow, square, sub, toAdditiveGroupElement, toUnitGroupElement

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

getUniqueByteRepresentation

Constructor Detail

IntegerElement

public IntegerElement(java.math.BigInteger v)

IntegerElement

public IntegerElement(long v)

Method Detail

getRepresentation

public Representation getRepresentation()

Description copied from interface: Representable

The representation of this object. Used for serialization. A convenient way to implement this is using @link ReprUtil

Specified by:

getRepresentation in interface Representable

Returns:

a Representation or null if an equal object can be recreated without any information.

See Also:

Representation

getBigInt

public java.math.BigInteger getBigInt()

Returns the BigInteger underlying this element.

getStructure

public Ring 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 RingElement

add

public IntegerElement add(Element e)

Description copied from interface: RingElement

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

Specified by:

add in interface RingElement

Parameters:

e - the addend

Returns:

the result

neg

public IntegerElement neg()

Description copied from interface: RingElement

Computes the additive inverse of this element.

Specified by:

neg in interface RingElement

Returns:

the result

mul

public IntegerElement mul(Element e)

Description copied from interface: RingElement

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

Specified by:

mul in interface RingElement

Parameters:

e - the factor

Returns:

the result

mul

public IntegerElement 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 RingElement

Parameters:

k - the factor

Returns:

the result

inv

public IntegerElement inv()
                   throws java.lang.UnsupportedOperationException

Description copied from interface: RingElement

Computes the multiplicative inverse of this element.

Specified by:

inv in interface RingElement

Returns:

the result

Throws:

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

divides

public boolean divides(RingElement e)
                throws java.lang.UnsupportedOperationException

Description copied from interface: RingElement

Returns true iff there exists an \(x\) in the ring such that \(\text{this} \cdot x = e\).

Specified by:

divides in interface RingElement

Throws:

java.lang.UnsupportedOperationException - if this cannot be decided (efficiently)

divideWithRemainder

public IntegerElement[] divideWithRemainder(RingElement e)
                                     throws java.lang.UnsupportedOperationException,
                                            java.lang.IllegalArgumentException

Description copied from interface: RingElement

Divides this by e with remainder, returning both quotient and remainder.

Specifically, returns an array result such that the first entry contains the quotient and the second entry the remainder. Furthermore, result[1].getRank() < e.getRank() or result[1] = 0.

This definition implies that the remainder is zero if and only if e divides this element.

Specified by:

divideWithRemainder in interface RingElement

Throws:

java.lang.UnsupportedOperationException - if the ring is not a euclidean domain

java.lang.IllegalArgumentException - if e is zero

getRank

public java.math.BigInteger getRank()
                             throws java.lang.UnsupportedOperationException

Description copied from interface: RingElement

Implements the euclidean function of a euclidean domain.

The euclidean function is a function from \(R \setminus \{0\}\) to \(\mathbb{N}_0\) such that

• a.getRank() >= 0 for any a in the ring
• a.mul(b).getRank() >= a.getRank() for any a, b != 0
• the remainder rank after divideWithRemainder is less than the divisor's rank

For example, for a polynomial ring this corresponds to the degree of the polynomial.

The rank of the zero element is undefined (no guarantee as to what this method returns in that case).

Specified by:

getRank in interface RingElement

Throws:

java.lang.UnsupportedOperationException - if the ring is not a euclidean domain

equals

public boolean equals(java.lang.Object o)

Specified by:

equals in interface Element

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Specified by:

hashCode in interface Element

Overrides:

hashCode in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

updateAccumulator

public ByteAccumulator updateAccumulator(ByteAccumulator accumulator)

Description copied from interface: UniqueByteRepresentable

Updates the ByteAccumulator with the unique byte representation of this object.

The input to the accumulators update function is an injective (with respect to a given domain) byte encoding of this object.

For many use-cases, the AnnotatedUbrUtil can be used to quickly implement this method.

Specified by:

updateAccumulator in interface UniqueByteRepresentable

Returns:

the same accumulator as was input

asInteger

public java.math.BigInteger asInteger()
                               throws java.lang.UnsupportedOperationException

Description copied from interface: RingElement

Interprets this element as an integer.

Result will be between 0 and the ring's characteristic.

Formally, this method shall return the inverse of Ring.getElement(BigInteger), i.e. x.getStructure().getElement(x.asInteger()).equals(x) (if asInteger() doesn't throw an exception).

Specified by:

asInteger in interface RingElement

Returns:

the integer corresponding to this element

Throws:

java.lang.UnsupportedOperationException - if no such element exists or cannot be efficiently computed