BarretoNaehrigBilinearGroupImpl (math 1.0.0 API)

java.lang.Object
- org.cryptimeleon.math.structures.groups.elliptic.type3.bn.BarretoNaehrigBilinearGroupImpl

All Implemented Interfaces:

Representable, StandaloneRepresentable, BilinearGroupImpl
```
public class BarretoNaehrigBilinearGroupImpl
extends java.lang.Object
implements BilinearGroupImpl
```
The implementation of our Barreto-Naehrig bilinear group.
For BN curves, \(\mathbb{G}_1\), \(\mathbb{G}_2\), and \(\mathbb{G}_T\) are defined based on:
- a finite field \(\mathbb{F}_p\) defined by a prime \(p\)
- a quadratic extension \(\mathbb{F}_2=\mathbb{F}_p(\alpha)\) defined by a quadratic non residue \(\alpha\) and the irreducible binomial \(x^2-\alpha\)
- a sextic extension \(\mathbb{F}_{12}=\mathbb{F}_2(\beta)\) defined by the irreducible binomial \(x^6-\beta\)
- an element \(b\) in \(\mathbb{F}_p\) with prime order in \(\mathbb{G}_1=E:y^2=x^3+b\)
- an element \(b'=b/\alpha\) in \(\mathbb{F}_2\) with \(\mathbb{G}_2\) a subgroup of size \(n\) in \(E':y^2=x^3+b'\)

Field Summary

Fields
Modifier and Type Field and Description

protected int[] minimumGroupBitSize

protected int[] securityLimits

Fields
Modifier and Type	Field and Description
`protected int[]`	`minimumGroupBitSize`
`protected int[]`	`securityLimits`

Constructor Summary

Constructors
Constructor and Description
`BarretoNaehrigBilinearGroupImpl(BarretoNaehrigParameterSpec spec)`
`BarretoNaehrigBilinearGroupImpl(int securityParameter)`
`BarretoNaehrigBilinearGroupImpl(Representation representation)`
`BarretoNaehrigBilinearGroupImpl(java.lang.String spec)`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`boolean`	`equals(java.lang.Object o)`
`BilinearMapImpl`	`getBilinearMap()` Returns the `BilinearMapImpl` (contains the pairing operation) belonging to this `BilinearGroupImpl`.
`GroupImpl`	`getG1()` Returns the source group G1 implementation associated with this bilinear group implementation.
`GroupImpl`	`getG2()` Returns the source group G2 implementation associated with this bilinear group implementation.
`GroupImpl`	`getGT()` Returns the target group G2 implementation associated with this bilinear group implementation.
`HashIntoGroupImpl`	`getHashIntoG1()` Retrieves a hash function implementation that maps byte arrays to G1.
`HashIntoGroupImpl`	`getHashIntoG2()` Retrieves a hash function implementation that maps byte arrays to G2.
`HashIntoGroupImpl`	`getHashIntoGT()` Retrieves a hash function implementation that maps byte arrays to GT.
`GroupHomomorphismImpl`	`getHomomorphismG2toG1()` This functions throws an exception because for type 3 pairings there is no efficient homomorphism `H : G2 -> G1`.
`BilinearGroup.Type`	`getPairingType()`
`Representation`	`getRepresentation()` The representation of this object.
`java.lang.Integer`	`getSecurityLevel()`
`int`	`hashCode()`
`protected void`	`init(int groupBitSize)` Construct all required objects based on a given group size.
`java.lang.String`	`toString()`

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

- Field Detail
  - securityLimits
```
protected final int[] securityLimits
```
  - minimumGroupBitSize
```
protected final int[] minimumGroupBitSize
```
- Constructor Detail
  - BarretoNaehrigBilinearGroupImpl
```
public BarretoNaehrigBilinearGroupImpl(int securityParameter)
```
  - BarretoNaehrigBilinearGroupImpl
```
public BarretoNaehrigBilinearGroupImpl(java.lang.String spec)
```
  - BarretoNaehrigBilinearGroupImpl
```
public BarretoNaehrigBilinearGroupImpl(BarretoNaehrigParameterSpec spec)
```
  - BarretoNaehrigBilinearGroupImpl
```
public BarretoNaehrigBilinearGroupImpl(Representation representation)
```
- 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
  - getG1
```
public GroupImpl getG1()
```
    Description copied from interface: BilinearGroupImpl
    
    Returns the source group G1 implementation associated with this bilinear group implementation.
    
    Specified by:
    
    getG1 in interface BilinearGroupImpl
  - getG2
```
public GroupImpl getG2()
```
    Description copied from interface: BilinearGroupImpl
    
    Returns the source group G2 implementation associated with this bilinear group implementation.
    
    Specified by:
    
    getG2 in interface BilinearGroupImpl
  - getGT
```
public GroupImpl getGT()
```
    Description copied from interface: BilinearGroupImpl
    
    Returns the target group G2 implementation associated with this bilinear group implementation.
    
    Specified by:
    
    getGT in interface BilinearGroupImpl
  - equals
```
public boolean equals(java.lang.Object o)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object
  - getBilinearMap
```
public BilinearMapImpl getBilinearMap()
```
    Description copied from interface: BilinearGroupImpl
    
    Returns the BilinearMapImpl (contains the pairing operation) belonging to this BilinearGroupImpl.
    
    Specified by:
    
    getBilinearMap in interface BilinearGroupImpl
  - getHashIntoG1
```
public HashIntoGroupImpl getHashIntoG1()
                                throws java.lang.UnsupportedOperationException
```
    Description copied from interface: BilinearGroupImpl
    
    Retrieves a hash function implementation that maps byte arrays to G1.
    
    Specified by:
    
    getHashIntoG1 in interface BilinearGroupImpl
    
    Throws:
    
    java.lang.UnsupportedOperationException - if no such hash function exists or the bilinear group is not configured to support such functionality
  - getHashIntoG2
```
public HashIntoGroupImpl getHashIntoG2()
```
    Description copied from interface: BilinearGroupImpl
    
    Retrieves a hash function implementation that maps byte arrays to G2.
    
    Specified by:
    
    getHashIntoG2 in interface BilinearGroupImpl
  - getHashIntoGT
```
public HashIntoGroupImpl getHashIntoGT()
```
    Description copied from interface: BilinearGroupImpl
    
    Retrieves a hash function implementation that maps byte arrays to GT.
    
    Specified by:
    
    getHashIntoGT in interface BilinearGroupImpl
  - getSecurityLevel
```
public java.lang.Integer getSecurityLevel()
```
    Specified by:
    
    getSecurityLevel in interface BilinearGroupImpl
  - getPairingType
```
public BilinearGroup.Type getPairingType()
```
    Specified by:
    
    getPairingType in interface BilinearGroupImpl
  - getHomomorphismG2toG1
```
public GroupHomomorphismImpl getHomomorphismG2toG1()
```
    This functions throws an exception because for type 3 pairings there is no efficient homomorphism H : G2 -> G1.
    
    Specified by:
    
    getHomomorphismG2toG1 in interface BilinearGroupImpl
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - init
```
protected void init(int groupBitSize)
```
    Construct all required objects based on a given group size.
    Basically implements Algorithm 2.1 of [1]

Class BarretoNaehrigBilinearGroupImpl

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

securityLimits

minimumGroupBitSize

Constructor Detail

BarretoNaehrigBilinearGroupImpl

BarretoNaehrigBilinearGroupImpl

BarretoNaehrigBilinearGroupImpl

BarretoNaehrigBilinearGroupImpl

Method Detail

getRepresentation

getG1

getG2

getGT

equals

hashCode

getBilinearMap

getHashIntoG1

getHashIntoG2

getHashIntoGT

getSecurityLevel

getPairingType

getHomomorphismG2toG1

toString

init