Zp (math 1.0.0 API)

java.lang.Object
- org.cryptimeleon.math.structures.rings.zn.Zn
- - org.cryptimeleon.math.structures.rings.zn.Zp

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, Field, Ring, Structure
```
public class Zp
extends Zn
implements Field
```
A version of Zn where n is prime (making the ring a field).
This completely reuses the Zn implementation.

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

class Zp.ZpElement
The elements of Zp.
- Nested classes/interfaces inherited from class org.cryptimeleon.math.structures.rings.zn.Zn
  Zn.ZnElement

Nested Classes
Modifier and Type	Class and Description
`class`	`Zp.ZpElement` The elements of `Zp`.

Field Summary
- Fields inherited from class org.cryptimeleon.math.structures.rings.zn.Zn
  maxByteLength, n, nIsPrime, ONE, ZERO

Constructor Summary

Constructors
Constructor and Description

Zp(java.math.BigInteger p)
Construct the field Zp using a given prime p.

Zp(Representation repr)

Constructors
Constructor and Description
`Zp(java.math.BigInteger p)` Construct the field `Zp` using a given prime `p`.
`Zp(Representation repr)`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Zp.ZpElement`	`createZnElement(java.math.BigInteger v)` Creates an element from a `BigInteger` (formally, the projection of \(v\) from \(\mathbb{Z}\) to \(\mathbb{Z}_n\)).
`protected Zp.ZpElement`	`createZnElementUnsafe(java.math.BigInteger vBetween0andN)` Instantiates a `ZnElement` without checking that the given representative is within the proper range.
`Zp.ZpElement`	`getElement(java.math.BigInteger i)` Maps the integer i into this ring \(R\), such that this map is a ring homomorphism \(\mathbb{Z}_{\text{getCharacteristic()}} \rightarrow R\).
`Zp.ZpElement`	`getElement(long i)` Maps the integer i into this ring \(R\), such that this map is a ring homomorphism \(\mathbb{Z}_{\text{getCharacteristic()}} \rightarrow R\).
`Zp.ZpElement`	`getOneElement()` Returns the multiplicative neutral element of this ring.
`Zp.ZpElement`	`getPrimitiveElement()` If this is a finite field, returns a generator of the field's unit group.
`Zp.ZpElement`	`getUniformlyRandomElement()` Returns an element of this structure that is drawn uniformly at random using a cryptographically strong RNG.
`Zp.ZpElement`	`getUniformlyRandomNonzeroElement()` Generates a nonzero element from this ring uniformly at random using a cryptographically strong RNG.
`Zp.ZpElement`	`getUniformlyRandomUnit()` Generates an invertible element from this ring uniformly at random using a cryptographically strong RNG.
`Zp.ZpElement`	`getZeroElement()` Returns the additive neutral element of this ring.
`boolean`	`hasPrimeSize()` Checks if the structure has prime size.
`Zp.ZpElement`	`injectiveValueOf(byte[] bytes)` For all `k < floor((n.bitLength()-1)/8)`, this is an injective map `byte^k -> Zn`.
`Zp.ZpElement`	`restoreElement(Representation repr)` Creates an element of this structure from its representation.
`java.math.BigInteger`	`sizeUnitGroup()` Returns the number of units in this ring.
`Zp.ZpElement`	`valueOf(java.math.BigInteger representative)` Creates the corresponding element mod n.
`static Zp.ZpElement`	`valueOf(java.math.BigInteger representative, java.math.BigInteger modulus)` Create the element "representative mod modulus"
`Zp.ZpElement`	`valueOf(long representative)` Creates the corresponding element mod n.
`static Zp.ZpElement`	`valueOf(long representative, java.math.BigInteger modulus)` Create the element "representative mod modulus"
`static Zp.ZpElement`	`valueOf(long representative, long modulus)` Create the element "representative mod modulus"

Methods inherited from class org.cryptimeleon.math.structures.rings.zn.Zn
equals, getCharacteristic, getRepresentation, getUniqueByteLength, hashCode, isCommutative, size, toString, upperBoundForUniqueRepresentation

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.cryptimeleon.math.structures.rings.Field
isCommutative

Methods inherited from interface org.cryptimeleon.math.structures.rings.Ring
asAdditiveGroup, asUnitGroup, extendedEuclideanAlgorithm, extendedEuclideanAlgorithm, getCharacteristic, getUniformlyRandomElements, getUniformlyRandomNonzeroElements, getUniformlyRandomUnits, restoreFromRepresentation, restoreVector

Methods inherited from interface org.cryptimeleon.math.structures.Structure
getUniqueByteLength, size

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

- Constructor Detail
  - Zp
```
public Zp(java.math.BigInteger p)
```
    Construct the field Zp using a given prime p.
    
    Parameters:
    
    p - a prime number (is checked probabilistically)
    
    Throws:
    
    java.lang.IllegalArgumentException - if p is not prime
  - Zp
```
public Zp(Representation repr)
```
- Method Detail
  - sizeUnitGroup
```
public java.math.BigInteger sizeUnitGroup()
```
    Description copied from interface: Ring
    
    Returns the number of units in this ring.
    
    Specified by:
    
    sizeUnitGroup in interface Field
    
    Specified by:
    
    sizeUnitGroup in interface Ring
    
    Overrides:
    
    sizeUnitGroup in class Zn
    
    Returns:
    
    size of the unit group or null if infinite
  - hasPrimeSize
```
public boolean hasPrimeSize()
                     throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Structure
    
    Checks if the structure has prime size.
    
    Specified by:
    
    hasPrimeSize in interface Structure
    
    Overrides:
    
    hasPrimeSize in class Zn
    
    Returns:
    
    true if the structure has prime size, else false.
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the primality of the size cannot be determined
  - getUniformlyRandomUnit
```
public Zp.ZpElement getUniformlyRandomUnit()
                                    throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Ring
    
    Generates an invertible element from this ring uniformly at random using a cryptographically strong RNG.
    The default implementation generates random ring elements until it hits a unit. Implementors should override if this is not feasible or if there is a better way!
    
    Specified by:
    
    getUniformlyRandomUnit in interface Field
    
    Specified by:
    
    getUniformlyRandomUnit in interface Ring
    
    Overrides:
    
    getUniformlyRandomUnit in class Zn
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the ring does not support this method
  - getUniformlyRandomNonzeroElement
```
public Zp.ZpElement getUniformlyRandomNonzeroElement()
```
    Description copied from interface: Ring
    
    Generates a nonzero element from this ring uniformly at random using a cryptographically strong RNG.
    
    Specified by:
    
    getUniformlyRandomNonzeroElement in interface Ring
    
    Overrides:
    
    getUniformlyRandomNonzeroElement in class Zn
  - getUniformlyRandomElement
```
public Zp.ZpElement getUniformlyRandomElement()
                                       throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Structure
    
    Returns an element of this structure that is drawn uniformly at random using a cryptographically strong RNG.
    
    Specified by:
    
    getUniformlyRandomElement in interface Field
    
    Specified by:
    
    getUniformlyRandomElement in interface Ring
    
    Specified by:
    
    getUniformlyRandomElement in interface Structure
    
    Overrides:
    
    getUniformlyRandomElement in class Zn
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the operation is not supported
  - getOneElement
```
public Zp.ZpElement getOneElement()
```
    Description copied from interface: Ring
    
    Returns the multiplicative neutral element of this ring.
    
    Specified by:
    
    getOneElement in interface Field
    
    Specified by:
    
    getOneElement in interface Ring
    
    Overrides:
    
    getOneElement in class Zn
  - getZeroElement
```
public Zp.ZpElement getZeroElement()
```
    Description copied from interface: Ring
    
    Returns the additive neutral element of this ring.
    
    Specified by:
    
    getZeroElement in interface Field
    
    Specified by:
    
    getZeroElement in interface Ring
    
    Overrides:
    
    getZeroElement in class Zn
  - getPrimitiveElement
```
public Zp.ZpElement getPrimitiveElement()
                                 throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Field
    
    If this is a finite field, returns a generator of the field's unit group. Repeated calls may or may not always return the same element.
    
    Specified by:
    
    getPrimitiveElement in interface Field
    
    Throws:
    
    java.lang.UnsupportedOperationException - if operation is not feasible or undefined
  - restoreElement
```
public Zp.ZpElement restoreElement(Representation repr)
```
    Description copied from interface: Structure
    
    Creates an element of this structure from its representation.
    
    Specified by:
    
    restoreElement in interface Field
    
    Specified by:
    
    restoreElement in interface Ring
    
    Specified by:
    
    restoreElement in interface Structure
    
    Overrides:
    
    restoreElement in class Zn
    
    Parameters:
    
    repr - the Representation returned by Representable.getRepresentation()
    
    Returns:
    
    the decoded element corresponding to the representation
  - getElement
```
public Zp.ZpElement getElement(long i)
```
    Description copied from interface: Ring
    
    Maps the integer i into this ring \(R\), such that this map is a ring homomorphism \(\mathbb{Z}_{\text{getCharacteristic()}} \rightarrow R\).
    
    Specified by:
    
    getElement in interface Field
    
    Specified by:
    
    getElement in interface Ring
    
    Parameters:
    
    i - the integer to map
    
    Returns:
    
    an element of the ring
  - createZnElement
```
public Zp.ZpElement createZnElement(java.math.BigInteger v)
```
    Description copied from class: Zn
    
    Creates an element from a BigInteger (formally, the projection of \(v\) from \(\mathbb{Z}\) to \(\mathbb{Z}_n\)).
    Implementation detail: This factory method allows the subclass Zp to use its own kind of elements while reusing the Zn implementation.
    
    Overrides:
    
    createZnElement in class Zn
  - createZnElementUnsafe
```
protected Zp.ZpElement createZnElementUnsafe(java.math.BigInteger vBetween0andN)
```
    Description copied from class: Zn
    
    Instantiates a ZnElement without checking that the given representative is within the proper range.
    
    Overrides:
    
    createZnElementUnsafe in class Zn
    
    Parameters:
    
    vBetween0andN - the representative of the element to instantiate. Must be between 0 (inclusive) and n (exclusive).
  - getElement
```
public Zp.ZpElement getElement(java.math.BigInteger i)
```
    Description copied from interface: Ring
    
    Maps the integer i into this ring \(R\), such that this map is a ring homomorphism \(\mathbb{Z}_{\text{getCharacteristic()}} \rightarrow R\).
    
    Specified by:
    
    getElement in interface Field
    
    Specified by:
    
    getElement in interface Ring
    
    Overrides:
    
    getElement in class Zn
    
    Parameters:
    
    i - the integer to map
    
    Returns:
    
    an element of the ring
  - injectiveValueOf
```
public Zp.ZpElement injectiveValueOf(byte[] bytes)
                              throws java.lang.IllegalArgumentException
```
    Description copied from class: Zn
    
    For all k < floor((n.bitLength()-1)/8), this is an injective map byte^k -> Zn.
    Note that there may be collisions between injectiveValueOf(bytes1) and injectiveValueOf(bytes2) if bytes1.length != bytes2.length.
    
    Overrides:
    
    injectiveValueOf in class Zn
    
    Parameters:
    
    bytes - the bytes to map injectively into Zn.
    
    Returns:
    
    the resulting Zn element
    
    Throws:
    
    java.lang.IllegalArgumentException - if the byte array is too long
  - valueOf
```
public static Zp.ZpElement valueOf(java.math.BigInteger representative,
                                   java.math.BigInteger modulus)
```
    Create the element "representative mod modulus"
    
    Parameters:
    
    representative - the integer representative of the element
    
    modulus - the ring size
  - valueOf
```
public static Zp.ZpElement valueOf(long representative,
                                   java.math.BigInteger modulus)
```
    Create the element "representative mod modulus"
    
    Parameters:
    
    representative - the integer representative of the element
    
    modulus - the ring size
  - valueOf
```
public static Zp.ZpElement valueOf(long representative,
                                   long modulus)
```
    Create the element "representative mod modulus"
    
    Parameters:
    
    representative - the integer representative of the element
    
    modulus - the ring size
  - valueOf
```
public Zp.ZpElement valueOf(long representative)
```
    Description copied from class: Zn
    
    Creates the corresponding element mod n.
    
    Overrides:
    
    valueOf in class Zn
    
    Parameters:
    
    representative - the integer representative of the element
  - valueOf
```
public Zp.ZpElement valueOf(java.math.BigInteger representative)
```
    Description copied from class: Zn
    
    Creates the corresponding element mod n.
    
    Overrides:
    
    valueOf in class Zn
    
    Parameters:
    
    representative - the integer representative of the element

Class Zp

Nested Class Summary

Nested classes/interfaces inherited from class org.cryptimeleon.math.structures.rings.zn.Zn

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

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

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

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

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

Constructor Detail

Zp

Zp

Method Detail

sizeUnitGroup

hasPrimeSize

getUniformlyRandomUnit

getUniformlyRandomNonzeroElement

getUniformlyRandomElement

getOneElement

getZeroElement

getPrimitiveElement

restoreElement

getElement

createZnElement

createZnElementUnsafe

getElement

injectiveValueOf

valueOf

valueOf

valueOf

valueOf

valueOf