PolynomialRing (math 3.1.0 API)

java.lang.Object
- org.cryptimeleon.math.structures.rings.polynomial.PolynomialRing

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, Ring, Structure
```
public class PolynomialRing
extends java.lang.Object
implements Ring
```
A polynomial ring over a given base commutative Ring.

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

class PolynomialRing.Polynomial
An element of PolynomialRing.

Nested Classes
Modifier and Type	Class and Description
`class`	`PolynomialRing.Polynomial` An element of `PolynomialRing`.

Field Summary

Fields
Modifier and Type Field and Description

protected Ring baseRing
The ring over which the polynomials are defined.

Fields
Modifier and Type	Field and Description
`protected Ring`	`baseRing` The ring over which the polynomials are defined.

Constructor Summary

Constructors
Constructor and Description

PolynomialRing(Representation arg)

PolynomialRing(Ring base)
Creates the polynomial ring over the given base.

Constructors
Constructor and Description
`PolynomialRing(Representation arg)`
`PolynomialRing(Ring base)` Creates the polynomial ring over the given base.

Method Summary

All Methods Static 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.
`double`	`estimateCostNegPerOp()` Estimates the number of negations (additive inversions) that can be done per group operation for the same cost.
`Ring`	`getBaseRing()` Returns the base ring.
`java.math.BigInteger`	`getCharacteristic()` Returns the characteristic of the ring.
`PolynomialRing.Polynomial`	`getElement(java.math.BigInteger i)` Maps the integer i into this ring \(R\), such that this map is a ring homomorphism \(\mathbb{Z}_{\text{getCharacteristic()}} \rightarrow R\).
`PolynomialRing.Polynomial`	`getOneElement()` Returns the multiplicative neutral element of this ring.
`static PolynomialRing.Polynomial`	`getPoly(java.util.Map<? extends RingElement,? extends RingElement> dataPoints)` Creates a new polynomial using interpolation.
`static PolynomialRing.Polynomial`	`getPoly(java.util.Map<? extends RingElement,? extends RingElement> dataPoints, int degreeOfPolynomial)` Creates a new polynomial using interpolation.
`static PolynomialRing.Polynomial`	`getPoly(RingElement... coefficients)` Shorthand to create a polynomial from given coefficients in order from lowest exponent to highest.
`Representation`	`getRepresentation()` The representation of this object.
`PolynomialRing.Polynomial`	`getUniformlyRandomElement()` Returns an element of this structure that is drawn uniformly at random using a cryptographically strong RNG.
`PolynomialRing.Polynomial`	`getUniformlyRandomUnit()` Generates an invertible element from this ring uniformly at random using a cryptographically strong RNG.
`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.
`PolynomialRing.Polynomial`	`getX()` Returns the Polynomial 1*x + 0
`PolynomialRing.Polynomial`	`getZeroElement()` Returns the additive neutral element of this ring.
`int`	`hashCode()`
`boolean`	`isCommutative()` Returns true if this ring is known to be commutative.
`PolynomialRing.Polynomial`	`restoreElement(Representation arg)` Creates an element of this structure from its representation.
`java.math.BigInteger`	`size()` Returns the number of elements in this structure (the size).
`java.math.BigInteger`	`sizeUnitGroup()` Returns the number of units in this ring.
`PolynomialRing.Polynomial`	`valueOf(RingElement... coefficients)` Returns \(\sum \mathit{coefficient}_i \cdot X^i \).

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

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

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

- Field Detail
  - baseRing
```
protected Ring baseRing
```
    The ring over which the polynomials are defined.
- Constructor Detail
  - PolynomialRing
```
public PolynomialRing(Ring base)
```
    Creates the polynomial ring over the given base.
  - PolynomialRing
```
public PolynomialRing(Representation arg)
```
- Method Detail
  - size
```
public java.math.BigInteger size()
                          throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Structure
    
    Returns the number of elements in this structure (the size).
    
    Specified by:
    
    size in interface Structure
    
    Returns:
    
    the number of elements contained in this structure or null if infinite
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the number of elements is unknown or too expensive to compute
  - 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
  - sizeUnitGroup
```
public java.math.BigInteger sizeUnitGroup()
                                   throws java.lang.UnsupportedOperationException
```
    Description copied from interface: Ring
    
    Returns the number of units in this ring.
    
    Specified by:
    
    sizeUnitGroup in interface Ring
    
    Returns:
    
    size of the unit group or null if infinite
    
    Throws:
    
    java.lang.UnsupportedOperationException - if size is unknown or is computationally too expensive to compute
  - getZeroElement
```
public PolynomialRing.Polynomial getZeroElement()
```
    Description copied from interface: Ring
    
    Returns the additive neutral element of this ring.
    
    Specified by:
    
    getZeroElement in interface Ring
  - getOneElement
```
public PolynomialRing.Polynomial getOneElement()
```
    Description copied from interface: Ring
    
    Returns the multiplicative neutral element of this ring.
    
    Specified by:
    
    getOneElement in interface Ring
  - getX
```
public PolynomialRing.Polynomial getX()
```
    Returns the Polynomial 1*x + 0
  - getElement
```
public PolynomialRing.Polynomial 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 Ring
    
    Parameters:
    
    i - the integer to map
    
    Returns:
    
    an element of the ring
  - estimateCostInvPerOp
```
public double estimateCostInvPerOp()
```
    Description copied from interface: Ring
    
    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 Ring
    
    Returns:
    
    estimated number of inversions that can be done per group operation for the same cost
  - estimateCostNegPerOp
```
public double estimateCostNegPerOp()
```
    Description copied from interface: Ring
    
    Estimates the number of negations (additive inversions) that can be done per group operation for the same cost. For example, 2 would mean that a negation costs half as much as a group operation, on average.
    
    Specified by:
    
    estimateCostNegPerOp in interface Ring
    
    Returns:
    
    estimated number of inversions that can be done per group operation for the same cost
  - getBaseRing
```
public Ring getBaseRing()
```
    Returns the base ring.
  - restoreElement
```
public PolynomialRing.Polynomial restoreElement(Representation arg)
```
    Description copied from interface: Structure
    
    Creates an element of this structure from its representation.
    
    Specified by:
    
    restoreElement in interface Ring
    
    Specified by:
    
    restoreElement in interface Structure
    
    Parameters:
    
    arg - the Representation returned by Representable.getRepresentation()
    
    Returns:
    
    the decoded element corresponding to the representation
  - getUniformlyRandomElement
```
public PolynomialRing.Polynomial 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 Ring
    
    Specified by:
    
    getUniformlyRandomElement in interface Structure
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the operation is not supported
  - getUniformlyRandomUnit
```
public PolynomialRing.Polynomial 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 Ring
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the ring does not support this method
  - 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
  - getCharacteristic
```
public java.math.BigInteger getCharacteristic()
```
    Description copied from interface: Ring
    
    Returns the characteristic of the ring.
    The characteristic of a ring is defined to be the number n such that there is a ring homomorphism from Zn to the ring.
    
    Specified by:
    
    getCharacteristic in interface Ring
  - valueOf
```
public PolynomialRing.Polynomial valueOf(RingElement... coefficients)
```
    Returns \(\sum \mathit{coefficient}_i \cdot X^i \).
  - getPoly
```
public static PolynomialRing.Polynomial getPoly(RingElement... coefficients)
```
    Shorthand to create a polynomial from given coefficients in order from lowest exponent to highest.
    For example, getPoly(1,2,3) returns \(1 + 2 \cdot X + 3 \cdot X^2\).
    
    Parameters:
    
    coefficients - the polynomial's coefficients in orderfrom lowest exponent to highest
  - getPoly
```
public static PolynomialRing.Polynomial getPoly(java.util.Map<? extends RingElement,? extends RingElement> dataPoints,
                                                int degreeOfPolynomial)
```
    Creates a new polynomial using interpolation. One must provide at least d+1 data points to interpolate a polynomial of degree d.
    The interpolation implements Neville's Algorithm (see http://mathworld.wolfram.com/NevillesAlgorithm.html). Beware that this operation has complexity \(O(n^2)\), where \(n\) is the number of dataPoints needed to interpolate the polynomial (degree + 1). Only to be used if the actual coefficients of the polynomial are unknown.
    Note: This implementation is based on Apache's commons math library (org.apache.commons.math3.analysis.polynomials.PolynomialFunctionLagrangeForm#computeCoefficients).
    
    Parameters:
    
    dataPoints - known points \((x_i, y_i)\) on the resulting polynomial \(P\) used for interpolation.
    
    degreeOfPolynomial - the desired degree of the interpolated polynomial
    
    Returns:
    
    interpolated polynomial \(P\) where \(P(x_i) = y_i\) for every given data point.
  - getPoly
```
public static PolynomialRing.Polynomial getPoly(java.util.Map<? extends RingElement,? extends RingElement> dataPoints)
```
    Creates a new polynomial using interpolation. The resulting polynomial will have the largest possible degree (number of supplied data points - 1).
    The interpolation implements Neville's Algorithm (see http://mathworld.wolfram.com/NevillesAlgorithm.html). Beware that this operation has complexity \(O(n^2)\), where \(n\) is the number of dataPoints needed to interpolate the polynomial (degree + 1). Only to be used if the actual coefficients of the polynomial are unknown.
    Note: This implementation is based on Apache's commons math library (org.apache.commons.math3.analysis.polynomials.PolynomialFunctionLagrangeForm#computeCoefficients).
    
    Parameters:
    
    dataPoints - known points \((x_i, y_i)\) on the resulting polynomial \(P\) used for interpolation.
    
    Returns:
    
    interpolated polynomial \(P\) where \(P(x_i) = y_i\) for every given data point.
  - getUniqueByteLength
```
public java.util.Optional<java.lang.Integer> getUniqueByteLength()
```
    Description copied from interface: Structure
    
    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 Structure
    
    Returns:
    
    the guaranteed fixed length of getUniqueByteRepresentation(), or an empty Optional, if no guarantee
  - isCommutative
```
public boolean isCommutative()
```
    Description copied from interface: Ring
    
    Returns true if this ring is known to be commutative.
    
    Specified by:
    
    isCommutative in interface Ring

Class PolynomialRing

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

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

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

Field Detail

baseRing

Constructor Detail

PolynomialRing

PolynomialRing

Method Detail

size

getRepresentation

sizeUnitGroup

getZeroElement

getOneElement

getX

getElement

estimateCostInvPerOp

estimateCostNegPerOp

getBaseRing

restoreElement

getUniformlyRandomElement

getUniformlyRandomUnit

equals

hashCode

getCharacteristic

valueOf

getPoly

getPoly

getPoly

getUniqueByteLength

isCommutative