GenericField (ECCelerate 6.2 API)

All Superinterfaces:

ECField

All Known Subinterfaces:

ExtensionField, Field, PrimeCharacteristicField

All Known Implementing Classes:

AbstractPrimeField, BinaryField, QuadraticExtensionField, SexticOverQuadraticTowerExtensionField
```
public interface GenericField
extends ECField
```
This interface specifies important (arithmetical) methods that all fields have in common.

Author:

Christian Hanser

See Also:

GenericFieldElement, BinaryField, PrimeField

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`GenericFieldElement`	`add(GenericFieldElement a, GenericFieldElement b)` Adds `b` to `a`, i.e.
`GenericFieldElement`	`divide(GenericFieldElement a, GenericFieldElement b)` Divides `a` by `b`, i.e.
`boolean`	`equals(Object obj)`
`GenericFieldElement`	`exponentiate(GenericFieldElement a, BigInteger n)` Raises `a` to the power `n`, i.e.
`GenericFieldElement`	`exponentiate(GenericFieldElement a, int n)` Raises `a` to the power `n`, i.e.
`GenericFieldElement`	`exponentiateByPowerOf2(GenericFieldElement a, int n)` Raises `a` to the power `2ⁿ`.
`Field`	`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.
`GenericFieldElement`	`getOne()` Returns the one element.
`GenericFieldElement`	`getZero()` Returns the zero element.
`int`	`hashCode()`
`GenericFieldElement`	`invert(GenericFieldElement a)` Inverts `a`, i.e.
`GenericFieldElement[]`	`invertElements(GenericFieldElement[] elements)` Simultaneously inverts an an array of field elements.
`GenericFieldElement`	`multiply(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`GenericFieldElement`	`multiply(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`GenericFieldElement`	`multiplyOutOfPlace(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`GenericFieldElement`	`multiplyOutOfPlace(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`GenericFieldElement`	`negate(GenericFieldElement a)` Negates `a`, i.e.
`GenericFieldElement`	`negateOutOfPlace(GenericFieldElement a)` Negates `a`, i.e.
`GenericFieldElement`	`newElement(byte[] bytes)` Create new field element from `byte`-array representation.
`GenericFieldElement`	`square(GenericFieldElement a)` Squares `a`, i.e.
`GenericFieldElement`	`squareOutOfPlace(GenericFieldElement a)` Squares `a`, i.e.
`GenericFieldElement`	`subtract(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `a`, i.e.
`GenericFieldElement`	`toElement(byte[] bytes)` Create new field element from a `byte`-array.

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

- Method Detail
  - negate
```
GenericFieldElement negate(GenericFieldElement a)
```
    Negates a, i.e. performs the operation b = -b.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - negateOutOfPlace
```
GenericFieldElement negateOutOfPlace(GenericFieldElement a)
```
    Negates a, i.e. performs the operation b = -b, where a new object holding the result is created.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - add
```
GenericFieldElement add(GenericFieldElement a,
                        GenericFieldElement b)
```
    Adds b to a, i.e. performs the operation a += b.
    
    Parameters:
    
    a - the first addend
    
    b - the second addend
    
    Returns:
    
    the sum of a and b
  - subtract
```
GenericFieldElement subtract(GenericFieldElement a,
                             GenericFieldElement b)
```
    Subtracts b from a, i.e. performs the operation a -= b.
    
    Parameters:
    
    a - the minuend
    
    b - the subtrahend
    
    Returns:
    
    the difference of a and b
  - multiply
```
GenericFieldElement multiply(GenericFieldElement a,
                             GenericFieldElement b)
```
    Multiplies a by b, i.e. performs the operation a *= b.
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiplyOutOfPlace
```
GenericFieldElement multiplyOutOfPlace(GenericFieldElement a,
                                       GenericFieldElement b)
```
    Multiplies a by b, i.e. performs the operation a *= b, where a new object holding the result is created.
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiply
```
GenericFieldElement multiply(GenericFieldElement a,
                             BigInteger n)
```
    Multiplies a by n, i.e. performs the operation a *= n.
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - multiplyOutOfPlace
```
GenericFieldElement multiplyOutOfPlace(GenericFieldElement a,
                                       BigInteger n)
```
    Multiplies a by n, i.e. performs the operation a *= n, where a new object holding the result is created.
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - divide
```
GenericFieldElement divide(GenericFieldElement a,
                           GenericFieldElement b)
```
    Divides a by b, i.e. performs the operation a /= b.
    
    Parameters:
    
    a - the dividend
    
    b - the divisor
    
    Returns:
    
    the quotient of a and b
  - invert
```
GenericFieldElement invert(GenericFieldElement a)
```
    Inverts a, i.e. performs the operation a = a^(-1).
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the inverse of a
  - invertElements
```
GenericFieldElement[] invertElements(GenericFieldElement[] elements)
```
    Simultaneously inverts an an array of field elements.
    
    Parameters:
    
    elements - the array of field elements
    
    Returns:
    
    the array holding the inverted elements (in the same order as the input elements)
  - square
```
GenericFieldElement square(GenericFieldElement a)
```
    Squares a, i.e. performs the operation a *= a.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - squareOutOfPlace
```
GenericFieldElement squareOutOfPlace(GenericFieldElement a)
```
    Squares a, i.e. performs the operation a*a, where a new object holding the result is created.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - exponentiate
```
GenericFieldElement exponentiate(GenericFieldElement a,
                                 BigInteger n)
```
    Raises a to the power n, i.e. performs the operation a = a^n.
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    a field element representing the nth power of a
  - exponentiate
```
GenericFieldElement exponentiate(GenericFieldElement a,
                                 int n)
```
    Raises a to the power n, i.e. performs the operation a = a^n.
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    a field element representing the nth power of a
  - exponentiateByPowerOf2
```
GenericFieldElement exponentiateByPowerOf2(GenericFieldElement a,
                                           int n)
```
    Raises a to the power 2ⁿ.
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    the resulting field element
  - getOne
```
GenericFieldElement getOne()
```
    Returns the one element.
    
    Returns:
    
    an object holding the one element
  - getZero
```
GenericFieldElement getZero()
```
    Returns the zero element.
    
    Returns:
    
    an object holding the zero element
  - newElement
```
GenericFieldElement newElement(byte[] bytes)
```
    Create new field element from byte-array representation.
    
    Parameters:
    
    bytes - the byte[] in little-endian order
    
    Returns:
    
    an object holding the new field element
  - toElement
```
GenericFieldElement toElement(byte[] bytes)
```
    Create new field element from a byte-array. Unlike newElement(byte[]), this method does not assume the input to be a valid encoding of a field element.
    
    Parameters:
    
    bytes - a byte[] in little-endian order
    
    Returns:
    
    an object holding the new field element
  - getCardinality
```
BigInteger getCardinality()
```
    Returns the cardinality of this field.
    
    Returns:
    
    a BigInteger holding the cardinality
  - getBaseField
```
Field getBaseField()
```
    Returns the base field of this field.
    
    Returns:
    
    the base field
  - getFieldType
```
FieldTypes getFieldType()
```
    Returns the field type of the underlying implementation.
    
    Returns:
    
    the field type
  - equals
```
boolean equals(Object obj)
```
    Overrides:
    
    equals in class Object
  - hashCode
```
int hashCode()
```
    Overrides:
    
    hashCode in class Object

Interface GenericField

Method Summary

Methods inherited from interface java.security.spec.ECField

Method Detail

negate

negateOutOfPlace

add

subtract

multiply

multiplyOutOfPlace

multiply

multiplyOutOfPlace

divide

invert

invertElements

square

squareOutOfPlace

exponentiate

exponentiate

exponentiateByPowerOf2

getOne

getZero

newElement

toElement

getCardinality

getBaseField

getFieldType

equals

hashCode