AbstractPrimeField (ECCelerate 6.2 API)

java.lang.Object
- java.security.spec.ECFieldFp
- - iaik.security.ec.math.field.AbstractPrimeField

All Implemented Interfaces:

Field, GenericField, PrimeCharacteristicField, ECField
```
public abstract class AbstractPrimeField
extends ECFieldFp
implements Field, PrimeCharacteristicField
```
This class implements arbitrary finite fields F_p of odd characteristic. Although it has been optimized for speed there are still more specific (i.e. faster) classes, which are part of the addon.
Note that due to reasons of performance the arithmetical methods of this class do not check, whether the inputs are valid elements of this field.
Also note that (almost) all methods in this class work in-place. So, there is no guarantee that values input to methods in this class will not be overridden. In case of doubt and if values need to be reused, always clone the value, before inputting it to a method.
References:
[1] Darrel Hankerson, Alfred J. Menezes and Scott Vanstone. Guide to Elliptic Curve Cryptography. Springer-Verlag New York, Inc. (2003)
[2] Henri Cohen and Gerhard Frey. Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall/CRC (2005)

Author:

Christian Hanser, Sebastian Ramacher

See Also:

BinaryField, PrimeFieldElement, PrimeFieldByBitLengthFactory, PrimeFieldByPrimeFactory

Field Summary

Fields
Modifier and Type Field and Description

static String PRIME_FIELD_OID
Object Identifier for a prime field for ASN.1 encoding.

Fields
Modifier and Type	Field and Description
`static String`	`PRIME_FIELD_OID` Object Identifier for a prime field for ASN.1 encoding.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`PrimeFieldElement`	`add(GenericFieldElement a, GenericFieldElement b)` Adds `b` to `a`, i.e.
`PrimeFieldElement`	`addOutOfPlace(PrimeCharacteristicFieldElement a, PrimeCharacteristicFieldElement b)` Adds two elements and returns a new object holding the result.
`PrimeFieldElement`	`divide(GenericFieldElement a, GenericFieldElement b)` Divides `a` by `b`, i.e.
`PrimeFieldElement`	`divideBy2(PrimeCharacteristicFieldElement a)` Divides `a` by 2.
`boolean`	`equals(Object obj)`
`PrimeFieldElement`	`exponentiate(GenericFieldElement a, BigInteger n)` Raises `a` to the power `n`, i.e.
`PrimeFieldElement`	`exponentiate(GenericFieldElement a, int n)` Raises `a` to the power `n`, i.e.
`PrimeFieldElement`	`exponentiateByPowerOf2(GenericFieldElement a, int n)` Raises `a` to the power `2ⁿ`.
`AbstractPrimeField`	`getBaseField()` Returns the base field of this field.
`BigInteger`	`getCardinality()` Returns the cardinality of this field.
`FieldTypes`	`getFieldType()` Returns the field type of the underlying implementation.
`PrimeFieldElement`	`getOne()` Returns the one element.
`int`	`getQuadraticCharacter(PrimeCharacteristicFieldElement a)` Implements a quadratic character, which returns -1,0,1 depending on whether the given value `a`is a quadratic non-residue modulo the prime `p`, a multiple of `p`, or a quadratic residue.
`PrimeFieldElement`	`getUniformlyRandomElement()` Get a uniformly random prime field element.
`PrimeFieldElement`	`getUniformlyRandomNonZeroElement()` Get a uniformly random, non-zero prime field element.
`PrimeFieldElement`	`getZero()` Returns the zero element.
`int`	`hashCode()`
`PrimeFieldElement`	`invert(GenericFieldElement a)` Inverts `a`, i.e.
`GenericFieldElement[]`	`invertElements(GenericFieldElement[] elements)` Simultaneously inverts an an array of field elements.
`boolean`	`isQthResidue(PrimeFieldElement element, int q)` Check if prime field element is a `q`-th residue.
`PrimeFieldElement`	`multiply(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`PrimeFieldElement`	`multiply(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`PrimeFieldElement`	`multiplyBy2(PrimeCharacteristicFieldElement a)` Multiplies `a` by `2`, which is a left-shift.
`PrimeFieldElement`	`multiplyBy2OutOfPlace(PrimeCharacteristicFieldElement a)` Multiplies `a` by `2`, which is a left-shift and returns a new object holding the result.
`PrimeFieldElement`	`multiplyBy3(PrimeCharacteristicFieldElement a)` Multiplies `a` by `3`, which is a left-shift plus an addition.
`PrimeFieldElement`	`multiplyBy3OutOfPlace(PrimeCharacteristicFieldElement a)` Multiplies `a` by `3`, which is a left-shift plus an addition and returns a new object holding the result.
`PrimeFieldElement`	`multiplyByPowerOf2(PrimeCharacteristicFieldElement a, int exponent)` Multiplies `a` by a power of `2`, which is a left-shift.
`PrimeFieldElement`	`multiplyByPowerOf2OutOfPlace(PrimeCharacteristicFieldElement a, int exponent)` Multiplies `a` by a power of `2`, which is a left-shift and returns a new object holding the result.
`PrimeFieldElement`	`multiplyOutOfPlace(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`PrimeFieldElement`	`multiplyOutOfPlace(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`PrimeFieldElement`	`negate(GenericFieldElement a)` Negates `a`, i.e.
`PrimeFieldElement`	`negateOutOfPlace(GenericFieldElement a)` Negates `a`, i.e.
`PrimeFieldElement`	`newElement(BigInteger b)` Creates a new field element from its `BigInteger` representation.
`PrimeFieldElement`	`newElement(byte[] b)` Creates a new field element from a `byte[]`.
`PrimeFieldElement`	`square(GenericFieldElement a)` Squares `a`, i.e.
`PrimeFieldElement`	`squareOutOfPlace(GenericFieldElement a)` Squares `a`, i.e.
`PrimeFieldElement`	`squareRoot(FieldElement a)` Computes the square root of a field element.
`PrimeFieldElement`	`subtract(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `a`, i.e.
`PrimeFieldElement`	`subtractOutOfPlace(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `this` and returns a new object holding the result.
`iaik.asn1.SEQUENCE`	`toASN1Object()` Compiles and returns the ASN.1 representation of this prime field, which is:
`byte[]`	`toByteArray(FieldElement a)` Converts a field element to its raw `byte[]` representation.
`PrimeFieldElement`	`toElement(byte[] bytes)` Create new field element from a `byte`-array.
`byte[]`	`toLEByteArray(FieldElement a)` Converts a field element to its raw `byte[]` representation in little endian.
`String`	`toString()`

Methods inherited from class java.security.spec.ECFieldFp
getFieldSize, getP

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

Methods inherited from interface java.security.spec.ECField
getFieldSize

- Field Detail
  - PRIME_FIELD_OID
```
public static final String PRIME_FIELD_OID
```
    Object Identifier for a prime field for ASN.1 encoding.
    
    See Also:
    
    Constant Field Values
- Method Detail
  - add
```
public final PrimeFieldElement add(GenericFieldElement a,
                                   GenericFieldElement b)
```
    Description copied from interface: GenericField
    
    Adds b to a, i.e. performs the operation a += b.
    
    Specified by:
    
    add in interface Field
    
    Specified by:
    
    add in interface GenericField
    
    Specified by:
    
    add in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the first addend
    
    b - the second addend
    
    Returns:
    
    the sum of a and b
  - addOutOfPlace
```
public final PrimeFieldElement addOutOfPlace(PrimeCharacteristicFieldElement a,
                                             PrimeCharacteristicFieldElement b)
```
    Description copied from interface: PrimeCharacteristicField
    
    Adds two elements and returns a new object holding the result.
    
    Specified by:
    
    addOutOfPlace in interface PrimeCharacteristicField
    
    Parameters:
    
    a - first summand
    
    b - second summand
    
    Returns:
    
    the sum
  - subtract
```
public final PrimeFieldElement subtract(GenericFieldElement a,
                                        GenericFieldElement b)
```
    Description copied from interface: GenericField
    
    Subtracts b from a, i.e. performs the operation a -= b.
    
    Specified by:
    
    subtract in interface Field
    
    Specified by:
    
    subtract in interface GenericField
    
    Specified by:
    
    subtract in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the minuend
    
    b - the subtrahend
    
    Returns:
    
    the difference of a and b
  - subtractOutOfPlace
```
public final PrimeFieldElement subtractOutOfPlace(GenericFieldElement a,
                                                  GenericFieldElement b)
```
    Description copied from interface: PrimeCharacteristicField
    
    Subtracts b from this and returns a new object holding the result.
    
    Specified by:
    
    subtractOutOfPlace in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the minuend
    
    b - the subtrahend
    
    Returns:
    
    the difference of a and b
  - negate
```
public final PrimeFieldElement negate(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Negates a, i.e. performs the operation b = -b.
    
    Specified by:
    
    negate in interface Field
    
    Specified by:
    
    negate in interface GenericField
    
    Specified by:
    
    negate in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - negateOutOfPlace
```
public PrimeFieldElement negateOutOfPlace(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Negates a, i.e. performs the operation b = -b, where a new object holding the result is created.
    
    Specified by:
    
    negateOutOfPlace in interface Field
    
    Specified by:
    
    negateOutOfPlace in interface GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - divide
```
public final PrimeFieldElement divide(GenericFieldElement a,
                                      GenericFieldElement b)
```
    Divides a by b, i.e. performs the operation a /= b.
    You have no guarantee that the input arguments remain unchanged.
    
    Specified by:
    
    divide in interface Field
    
    Specified by:
    
    divide in interface GenericField
    
    Specified by:
    
    divide in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the dividend
    
    b - the divisor
    
    Returns:
    
    the quotient of a and b
  - divideBy2
```
public final PrimeFieldElement divideBy2(PrimeCharacteristicFieldElement a)
```
    Description copied from interface: PrimeCharacteristicField
    
    Divides a by 2.
    
    Specified by:
    
    divideBy2 in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the dividend
    
    Returns:
    
    the quotient of a and 2.
  - invert
```
public PrimeFieldElement invert(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Inverts a, i.e. performs the operation a = a^(-1).
    
    Specified by:
    
    invert in interface Field
    
    Specified by:
    
    invert in interface GenericField
    
    Specified by:
    
    invert in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the inverse of a
  - invertElements
```
public final GenericFieldElement[] invertElements(GenericFieldElement[] elements)
```
    Description copied from interface: GenericField
    
    Simultaneously inverts an an array of field elements.
    
    Specified by:
    
    invertElements in interface GenericField
    
    Parameters:
    
    elements - the array of field elements
    
    Returns:
    
    the array holding the inverted elements (in the same order as the input elements)
  - multiply
```
public PrimeFieldElement multiply(GenericFieldElement a,
                                  GenericFieldElement b)
```
    Description copied from interface: GenericField
    
    Multiplies a by b, i.e. performs the operation a *= b.
    
    Specified by:
    
    multiply in interface Field
    
    Specified by:
    
    multiply in interface GenericField
    
    Specified by:
    
    multiply in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiplyOutOfPlace
```
public PrimeFieldElement multiplyOutOfPlace(GenericFieldElement a,
                                            GenericFieldElement b)
```
    Description copied from interface: GenericField
    
    Multiplies a by b, i.e. performs the operation a *= b, where a new object holding the result is created.
    
    Specified by:
    
    multiplyOutOfPlace in interface Field
    
    Specified by:
    
    multiplyOutOfPlace in interface GenericField
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiply
```
public PrimeFieldElement multiply(GenericFieldElement a,
                                  BigInteger n)
```
    Description copied from interface: GenericField
    
    Multiplies a by n, i.e. performs the operation a *= n.
    
    Specified by:
    
    multiply in interface Field
    
    Specified by:
    
    multiply in interface GenericField
    
    Specified by:
    
    multiply in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - multiplyOutOfPlace
```
public PrimeFieldElement multiplyOutOfPlace(GenericFieldElement a,
                                            BigInteger n)
```
    Description copied from interface: GenericField
    
    Multiplies a by n, i.e. performs the operation a *= n, where a new object holding the result is created.
    
    Specified by:
    
    multiplyOutOfPlace in interface Field
    
    Specified by:
    
    multiplyOutOfPlace in interface GenericField
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - multiplyBy2
```
public final PrimeFieldElement multiplyBy2(PrimeCharacteristicFieldElement a)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by 2, which is a left-shift. Works in-place.
    
    Specified by:
    
    multiplyBy2 in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to be shifted
    
    Returns:
    
    a holding the result
  - multiplyBy2OutOfPlace
```
public final PrimeFieldElement multiplyBy2OutOfPlace(PrimeCharacteristicFieldElement a)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by 2, which is a left-shift and returns a new object holding the result.
    
    Specified by:
    
    multiplyBy2OutOfPlace in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to be shifted
    
    Returns:
    
    a holding the result
  - multiplyBy3
```
public final PrimeFieldElement multiplyBy3(PrimeCharacteristicFieldElement a)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by 3, which is a left-shift plus an addition. Works in-place.
    
    Specified by:
    
    multiplyBy3 in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to multiplied
    
    Returns:
    
    a holding the result
  - multiplyBy3OutOfPlace
```
public final PrimeFieldElement multiplyBy3OutOfPlace(PrimeCharacteristicFieldElement a)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by 3, which is a left-shift plus an addition and returns a new object holding the result.
    
    Specified by:
    
    multiplyBy3OutOfPlace in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to multiplied
    
    Returns:
    
    a holding the result
  - multiplyByPowerOf2
```
public PrimeFieldElement multiplyByPowerOf2(PrimeCharacteristicFieldElement a,
                                            int exponent)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by a power of 2, which is a left-shift. Works in-place.
    
    Specified by:
    
    multiplyByPowerOf2 in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to be shifted
    
    exponent - the power of 2
    
    Returns:
    
    a holding the result
  - multiplyByPowerOf2OutOfPlace
```
public PrimeFieldElement multiplyByPowerOf2OutOfPlace(PrimeCharacteristicFieldElement a,
                                                      int exponent)
```
    Description copied from interface: PrimeCharacteristicField
    
    Multiplies a by a power of 2, which is a left-shift and returns a new object holding the result.
    
    Specified by:
    
    multiplyByPowerOf2OutOfPlace in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the element to be shifted
    
    exponent - the power of 2
    
    Returns:
    
    a holding the result
  - square
```
public PrimeFieldElement square(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Squares a, i.e. performs the operation a *= a.
    
    Specified by:
    
    square in interface Field
    
    Specified by:
    
    square in interface GenericField
    
    Specified by:
    
    square in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - squareOutOfPlace
```
public PrimeFieldElement squareOutOfPlace(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Squares a, i.e. performs the operation a*a, where a new object holding the result is created.
    
    Specified by:
    
    squareOutOfPlace in interface Field
    
    Specified by:
    
    squareOutOfPlace in interface GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - squareRoot
```
public final PrimeFieldElement squareRoot(FieldElement a)
```
    Description copied from interface: Field
    
    Computes the square root of a field element.
    
    Specified by:
    
    squareRoot in interface Field
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square root of a
  - getQuadraticCharacter
```
public final int getQuadraticCharacter(PrimeCharacteristicFieldElement a)
```
    Implements a quadratic character, which returns -1,0,1 depending on whether the given value ais a quadratic non-residue modulo the prime p, a multiple of p, or a quadratic residue. In this case this is the Legendre symbol according to [2, Algorithm 11.19].
    
    Specified by:
    
    getQuadraticCharacter in interface PrimeCharacteristicField
    
    Parameters:
    
    a - a prime field element
    
    Returns:
    
    the Legendre symbol (a/p)
  - getOne
```
public PrimeFieldElement getOne()
```
    Description copied from interface: GenericField
    
    Returns the one element.
    
    Specified by:
    
    getOne in interface Field
    
    Specified by:
    
    getOne in interface GenericField
    
    Specified by:
    
    getOne in interface PrimeCharacteristicField
    
    Returns:
    
    an object holding the one element
  - getZero
```
public PrimeFieldElement getZero()
```
    Description copied from interface: GenericField
    
    Returns the zero element.
    
    Specified by:
    
    getZero in interface Field
    
    Specified by:
    
    getZero in interface GenericField
    
    Specified by:
    
    getZero in interface PrimeCharacteristicField
    
    Returns:
    
    an object holding the zero element
  - getCardinality
```
public final BigInteger getCardinality()
```
    Description copied from interface: GenericField
    
    Returns the cardinality of this field.
    
    Specified by:
    
    getCardinality in interface GenericField
    
    Returns:
    
    a BigInteger holding the cardinality
  - newElement
```
public final PrimeFieldElement newElement(BigInteger b)
```
    Description copied from interface: Field
    
    Creates a new field element from its BigInteger representation.
    
    Specified by:
    
    newElement in interface Field
    
    Parameters:
    
    b - the BigInteger
    
    Returns:
    
    the field element
  - newElement
```
public final PrimeFieldElement newElement(byte[] b)
```
    Description copied from interface: Field
    
    Creates a new field element from a byte[].
    
    Specified by:
    
    newElement in interface Field
    
    Specified by:
    
    newElement in interface GenericField
    
    Specified by:
    
    newElement in interface PrimeCharacteristicField
    
    Parameters:
    
    b - the element encoded as byte[] in little-endian order
    
    Returns:
    
    the field element
  - toElement
```
public PrimeFieldElement toElement(byte[] bytes)
```
    Description copied from interface: GenericField
    
    Create new field element from a byte-array. Unlike GenericField.newElement(byte[]), this method does not assume the input to be a valid encoding of a field element.
    
    Specified by:
    
    toElement in interface GenericField
    
    Specified by:
    
    toElement in interface PrimeCharacteristicField
    
    Parameters:
    
    bytes - a byte[] in little-endian order
    
    Returns:
    
    an object holding the new field element
  - exponentiate
```
public PrimeFieldElement exponentiate(GenericFieldElement a,
                                      BigInteger n)
```
    Description copied from interface: GenericField
    
    Raises a to the power n, i.e. performs the operation a = a^n.
    
    Specified by:
    
    exponentiate in interface Field
    
    Specified by:
    
    exponentiate in interface GenericField
    
    Specified by:
    
    exponentiate in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    a field element representing the nth power of a
  - exponentiate
```
public PrimeFieldElement exponentiate(GenericFieldElement a,
                                      int n)
```
    Description copied from interface: GenericField
    
    Raises a to the power n, i.e. performs the operation a = a^n.
    
    Specified by:
    
    exponentiate in interface GenericField
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    a field element representing the nth power of a
  - exponentiateByPowerOf2
```
public final PrimeFieldElement exponentiateByPowerOf2(GenericFieldElement a,
                                                      int n)
```
    Description copied from interface: GenericField
    
    Raises a to the power 2ⁿ.
    
    Specified by:
    
    exponentiateByPowerOf2 in interface Field
    
    Specified by:
    
    exponentiateByPowerOf2 in interface GenericField
    
    Specified by:
    
    exponentiateByPowerOf2 in interface PrimeCharacteristicField
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    the resulting field element
  - toByteArray
```
public byte[] toByteArray(FieldElement a)
```
    Description copied from interface: Field
    
    Converts a field element to its raw byte[] representation.
    
    Specified by:
    
    toByteArray in interface Field
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a byte[]
  - toLEByteArray
```
public byte[] toLEByteArray(FieldElement a)
```
    Converts a field element to its raw byte[] representation in little endian.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a byte[]
  - getFieldType
```
public final FieldTypes getFieldType()
```
    Description copied from interface: GenericField
    
    Returns the field type of the underlying implementation.
    
    Specified by:
    
    getFieldType in interface GenericField
    
    Returns:
    
    the field type
  - getBaseField
```
public final AbstractPrimeField getBaseField()
```
    Description copied from interface: GenericField
    
    Returns the base field of this field.
    
    Specified by:
    
    getBaseField in interface GenericField
    
    Returns:
    
    the base field
  - toASN1Object
```
public final iaik.asn1.SEQUENCE toASN1Object()
```
    Compiles and returns the ASN.1 representation of this prime field, which is:
```
  FieldID ::= SEQUENCE {
    fieldType   OBJECT IDENTIFIER,
    parameters  ANY DEFINED BY fieldType
  }
 
```
    Specified by:
    
    toASN1Object in interface Field
    
    Returns:
    
    the ASN.1 representation of this prime field
  - equals
```
public final boolean equals(Object obj)
```
    Specified by:
    
    equals in interface GenericField
    
    Overrides:
    
    equals in class ECFieldFp
  - hashCode
```
public final int hashCode()
```
    Specified by:
    
    hashCode in interface GenericField
    
    Overrides:
    
    hashCode in class ECFieldFp
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - isQthResidue
```
public final boolean isQthResidue(PrimeFieldElement element,
                                  int q)
```
    Check if prime field element is a q-th residue.
    
    Parameters:
    
    element - prime field element
    
    q - an integer
    
    Returns:
    
    whether element is a q-th residue
  - getUniformlyRandomElement
```
public final PrimeFieldElement getUniformlyRandomElement()
```
    Get a uniformly random prime field element.
    
    Specified by:
    
    getUniformlyRandomElement in interface PrimeCharacteristicField
    
    Returns:
    
    element of the field.
  - getUniformlyRandomNonZeroElement
```
public final PrimeFieldElement getUniformlyRandomNonZeroElement()
```
    Get a uniformly random, non-zero prime field element.
    
    Specified by:
    
    getUniformlyRandomNonZeroElement in interface PrimeCharacteristicField
    
    Returns:
    
    element of the field.

Class AbstractPrimeField

Field Summary

Method Summary

Methods inherited from class java.security.spec.ECFieldFp

Methods inherited from class java.lang.Object

Methods inherited from interface java.security.spec.ECField

Field Detail

PRIME_FIELD_OID

Method Detail

add

addOutOfPlace

subtract

subtractOutOfPlace

negate

negateOutOfPlace

divide

divideBy2

invert

invertElements

multiply

multiplyOutOfPlace

multiply

multiplyOutOfPlace

multiplyBy2

multiplyBy2OutOfPlace

multiplyBy3

multiplyBy3OutOfPlace

multiplyByPowerOf2

multiplyByPowerOf2OutOfPlace

square

squareOutOfPlace

squareRoot

getQuadraticCharacter

getOne

getZero

getCardinality

newElement

newElement

toElement

exponentiate

exponentiate

exponentiateByPowerOf2

toByteArray

toLEByteArray

getFieldType

getBaseField

toASN1Object

equals

hashCode

toString

isQthResidue

getUniformlyRandomElement

getUniformlyRandomNonZeroElement