Secp256k1 (math 1.0.0 API)

java.lang.Object
- org.cryptimeleon.math.structures.groups.elliptic.nopairing.Secp256k1

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, EllipticCurve, WeierstrassCurve, GroupImpl
```
public class Secp256k1
extends java.lang.Object
implements WeierstrassCurve
```
An implementation of the secp256k1 curve.
The curve is defined in Weierstrass short form \(y^2 = x^3 + b\) over a field \(\mathbb{F}_p\). Specific parameters are taken from here.

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class Secp256k1.HashIntoSecp256k1
A hash function mapping bit strings into the group such that

Nested Classes
Modifier and Type	Class and Description
`static class`	`Secp256k1.HashIntoSecp256k1` A hash function mapping bit strings into the group such that

Field Summary

Fields
Modifier and Type	Field and Description
`static Zp.ZpElement`	`b` Parameter for the weierstrass equation \(y^2 = x^3 + b\).
`static Zp.ZpElement`	`generatorX` x-coordinate of generator element.
`static Zp.ZpElement`	`generatorY` y-coordinate of generator element.
`static java.math.BigInteger`	`n` The number of elements on the curve.
`static java.math.BigInteger`	`p` The prime used to instantiate the field \(\mathbb{F}_p\).
`static Zp`	`zp` The field \(\mathbb{F}_p\) over which the curve is defined.

Constructor Summary

Constructors
Constructor and Description
`Secp256k1()` Initialize the curve.
`Secp256k1(Representation repr)` Initialize the curve from a representation (not used since all parameters are fixed).

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`boolean`	`equals(java.lang.Object obj)`
`double`	`estimateCostInvPerOp()` Estimates the number of inversions that can be done per group operation for the same cost.
`FieldElement`	`getA1()` Returns \(A1\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
`FieldElement`	`getA2()` Returns \(A2\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
`FieldElement`	`getA3()` Returns \(A3\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
`FieldElement`	`getA4()` Returns \(A4\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
`FieldElement`	`getA6()` Returns \(A6\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
`EllipticCurvePoint`	`getElement(FieldElement x, FieldElement y)` Construct an point on this curve given the x- and y-coordinates.
`Field`	`getFieldOfDefinition()` Returns the base field over which the elliptic curve is defined.
`GroupElementImpl`	`getGenerator()` Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.
`GroupElementImpl`	`getNeutralElement()` Returns the neutral element of this group.
`Representation`	`getRepresentation()` The representation of this object.
`GroupElementImpl`	`getUniformlyRandomElement()` Generates a uniformly random element of this group.
`java.util.Optional<java.lang.Integer>`	`getUniqueByteLength()` Returns the number of bytes returned by this structure's `UniqueByteRepresentable.getUniqueByteRepresentation()`, or an empty `Optional` if this structure's elements do not guarantee a fixed length.
`int`	`hashCode()`
`boolean`	`hasPrimeSize()` Returns true if the size of this structure is known and prime.
`GroupElementImpl`	`restoreElement(Representation repr)` Restores a group element from its representation.
`java.math.BigInteger`	`size()` Retrieves number of elements in the group if possible.

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

Methods inherited from interface org.cryptimeleon.math.structures.groups.elliptic.WeierstrassCurve
isShortForm

Methods inherited from interface org.cryptimeleon.math.structures.groups.elliptic.EllipticCurve
isCommutative

Methods inherited from interface org.cryptimeleon.math.structures.groups.GroupImpl
exp, getUniformlyRandomNonNeutral, implementsOwnExp, implementsOwnMultiExp, multiexp, restoreFromRepresentation

- Field Detail
  - p
```
public static final java.math.BigInteger p
```
    The prime used to instantiate the field \(\mathbb{F}_p\).
  - n
```
public static final java.math.BigInteger n
```
    The number of elements on the curve.
  - zp
```
public static final Zp zp
```
    The field \(\mathbb{F}_p\) over which the curve is defined.
  - b
```
public static final Zp.ZpElement b
```
    Parameter for the weierstrass equation \(y^2 = x^3 + b\).
  - generatorX
```
public static final Zp.ZpElement generatorX
```
    x-coordinate of generator element.
  - generatorY
```
public static final Zp.ZpElement generatorY
```
    y-coordinate of generator element.
- Constructor Detail
  - Secp256k1
```
public Secp256k1()
```
    Initialize the curve.
  - Secp256k1
```
public Secp256k1(Representation repr)
```
    Initialize the curve from a representation (not used since all parameters are fixed).
    The representation is not used, as all parameters are fixed. Hence, it can be any value.
    
    Parameters:
    
    repr - the representation to use for restoration. Not used
- Method Detail
  - getA6
```
public FieldElement getA6()
```
    Description copied from interface: WeierstrassCurve
    
    Returns \(A6\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
    
    Specified by:
    
    getA6 in interface WeierstrassCurve
  - getA4
```
public FieldElement getA4()
```
    Description copied from interface: WeierstrassCurve
    
    Returns \(A4\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
    
    Specified by:
    
    getA4 in interface WeierstrassCurve
  - getA3
```
public FieldElement getA3()
```
    Description copied from interface: WeierstrassCurve
    
    Returns \(A3\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
    Is zero if the curve is given by a weierstrass equation in short form.
    
    Specified by:
    
    getA3 in interface WeierstrassCurve
  - getA2
```
public FieldElement getA2()
```
    Description copied from interface: WeierstrassCurve
    
    Returns \(A2\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
    Is zero if the curve is given by a weierstrass equation in short form.
    
    Specified by:
    
    getA2 in interface WeierstrassCurve
  - getA1
```
public FieldElement getA1()
```
    Description copied from interface: WeierstrassCurve
    
    Returns \(A1\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
    Is zero if the curve is given by a weierstrass equation in short form.
    
    Specified by:
    
    getA1 in interface WeierstrassCurve
  - getElement
```
public EllipticCurvePoint getElement(FieldElement x,
                                     FieldElement y)
```
    Description copied from interface: WeierstrassCurve
    
    Construct an point on this curve given the x- and y-coordinates.
    
    Specified by:
    
    getElement in interface WeierstrassCurve
    
    Parameters:
    
    x - the x-coordinate
    
    y - the y-coordinate
    
    Returns:
    
    the corresponding elliptic curve point
  - getFieldOfDefinition
```
public Field getFieldOfDefinition()
```
    Description copied from interface: EllipticCurve
    
    Returns the base field over which the elliptic curve is defined.
    
    Specified by:
    
    getFieldOfDefinition in interface EllipticCurve
  - getNeutralElement
```
public GroupElementImpl getNeutralElement()
```
    Description copied from interface: GroupImpl
    
    Returns the neutral element of this group.
    
    Specified by:
    
    getNeutralElement in interface GroupImpl
  - getUniformlyRandomElement
```
public GroupElementImpl getUniformlyRandomElement()
                                           throws java.lang.UnsupportedOperationException
```
    Description copied from interface: GroupImpl
    
    Generates a uniformly random element of this group.
    
    Specified by:
    
    getUniformlyRandomElement in interface GroupImpl
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the random generation cannot be done
  - restoreElement
```
public GroupElementImpl restoreElement(Representation repr)
```
    Description copied from interface: GroupImpl
    
    Restores a group element from its representation.
    
    Specified by:
    
    restoreElement in interface GroupImpl
  - getGenerator
```
public GroupElementImpl getGenerator()
                              throws java.lang.UnsupportedOperationException
```
    Description copied from interface: GroupImpl
    
    Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.
    Repeated calls may or may not always supply the same generator again (i.e. the output is not guaranteed to be random)!
    
    Specified by:
    
    getGenerator in interface GroupImpl
    
    Throws:
    
    java.lang.UnsupportedOperationException - if group is not cyclic or it's too hard to compute a generator
  - size
```
public java.math.BigInteger size()
                          throws java.lang.UnsupportedOperationException
```
    Description copied from interface: GroupImpl
    
    Retrieves number of elements in the group if possible.
    
    Specified by:
    
    size in interface GroupImpl
    
    Returns:
    
    size of this group (number of group elements in it) or null if infinite
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the number of elements is unknown or is too expensive to compute
  - hasPrimeSize
```
public boolean hasPrimeSize()
```
    Description copied from interface: GroupImpl
    
    Returns true if the size of this structure is known and prime.
    
    Specified by:
    
    hasPrimeSize in interface GroupImpl
  - estimateCostInvPerOp
```
public double estimateCostInvPerOp()
```
    Description copied from interface: GroupImpl
    
    Estimates the number of inversions that can be done per group operation for the same cost. For example, 2 would mean that an inversion costs half as much as a group operation, on average.
    
    Specified by:
    
    estimateCostInvPerOp in interface GroupImpl
    
    Returns:
    
    Estimated number of inversions that can be done per group operation for the same cost
  - getUniqueByteLength
```
public java.util.Optional<java.lang.Integer> getUniqueByteLength()
```
    Description copied from interface: GroupImpl
    
    Returns the number of bytes returned by this structure's UniqueByteRepresentable.getUniqueByteRepresentation(), or an empty Optional if this structure's elements do not guarantee a fixed length.
    For example, elements of Zp will always be represented by ceil(ceil(log(p))/8) bytes, hence getUniqueByteLength() would return ceil(ceil(log(p))/8).
    A polynomial ring would return an empty Optional since a polynomial's unique byte representation length depends on its degree.
    
    Specified by:
    
    getUniqueByteLength in interface GroupImpl
    
    Returns:
    
    the guaranteed fixed length of getUniqueByteRepresentation(), or an empty Optional, if no guarantee
  - 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
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object

Class Secp256k1

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.cryptimeleon.math.structures.groups.elliptic.WeierstrassCurve

Methods inherited from interface org.cryptimeleon.math.structures.groups.elliptic.EllipticCurve

Methods inherited from interface org.cryptimeleon.math.structures.groups.GroupImpl

Field Detail

p

n

zp

b

generatorX

generatorY

Constructor Detail

Secp256k1

Secp256k1

Method Detail

getA6

getA4

getA3

getA2

getA1

getElement

getFieldOfDefinition

getNeutralElement

getUniformlyRandomElement

restoreElement

getGenerator

size

hasPrimeSize

estimateCostInvPerOp

getUniqueByteLength

getRepresentation

equals

hashCode