Field (ECCelerate 6.2 API)

All Superinterfaces:

ECField, GenericField

All Known Implementing Classes:

AbstractPrimeField, BinaryField
```
public interface Field
extends GenericField
```
This interface specifies important (arithmetical) methods that all (base) fields have in common. This interface is used to describe binary and prime fields.

Author:

Christian Hanser

See Also:

FieldElement, BinaryField, PrimeField

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`FieldElement`	`add(GenericFieldElement a, GenericFieldElement b)` Adds `b` to `a`, i.e.
`FieldElement`	`divide(GenericFieldElement a, GenericFieldElement b)` Divides `a` by `b`, i.e.
`FieldElement`	`exponentiate(GenericFieldElement a, BigInteger n)` Raises `a` to the power `n`, i.e.
`FieldElement`	`exponentiateByPowerOf2(GenericFieldElement a, int n)` Raises `a` to the power `2ⁿ`.
`FieldElement`	`getOne()` Returns the one element.
`FieldElement`	`getZero()` Returns the zero element.
`FieldElement`	`invert(GenericFieldElement a)` Inverts `a`, i.e.
`FieldElement`	`multiply(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`FieldElement`	`multiply(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`FieldElement`	`multiplyOutOfPlace(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`FieldElement`	`multiplyOutOfPlace(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`FieldElement`	`negate(GenericFieldElement a)` Negates `a`, i.e.
`FieldElement`	`negateOutOfPlace(GenericFieldElement a)` Negates `a`, i.e.
`FieldElement`	`newElement(BigInteger b)` Creates a new field element from its `BigInteger` representation.
`FieldElement`	`newElement(byte[] b)` Creates a new field element from a `byte[]`.
`FieldElement`	`square(GenericFieldElement a)` Squares `a`, i.e.
`FieldElement`	`squareOutOfPlace(GenericFieldElement a)` Squares `a`, i.e.
`FieldElement`	`squareRoot(FieldElement a)` Computes the square root of a field element.
`FieldElement`	`subtract(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `a`, i.e.
`iaik.asn1.SEQUENCE`	`toASN1Object()` Returns the ASN.1 representation of this field.
`byte[]`	`toByteArray(FieldElement a)` Converts a field element to its raw `byte[]` representation.

Methods inherited from interface iaik.security.ec.math.field.GenericField
equals, exponentiate, getBaseField, getCardinality, getFieldType, hashCode, invertElements, toElement

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

- Method Detail
  - negate
```
FieldElement negate(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Negates a, i.e. performs the operation b = -b.
    
    Specified by:
    
    negate in interface GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - negateOutOfPlace
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the negative of a
  - add
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the first addend
    
    b - the second addend
    
    Returns:
    
    the sum of a and b
  - subtract
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the minuend
    
    b - the subtrahend
    
    Returns:
    
    the difference of a and b
  - multiply
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiplyOutOfPlace
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the first factor
    
    b - the second factor
    
    Returns:
    
    the product of a and b
  - multiply
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - multiplyOutOfPlace
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the first factor
    
    n - the second factor
    
    Returns:
    
    the product of a and n
  - divide
```
FieldElement divide(GenericFieldElement a,
                    GenericFieldElement b)
```
    Description copied from interface: GenericField
    
    Divides a by b, i.e. performs the operation a /= b.
    
    Specified by:
    
    divide in interface GenericField
    
    Parameters:
    
    a - the dividend
    
    b - the divisor
    
    Returns:
    
    the quotient of a and b
  - invert
```
FieldElement invert(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Inverts a, i.e. performs the operation a = a^(-1).
    
    Specified by:
    
    invert in interface GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    the inverse of a
  - square
```
FieldElement square(GenericFieldElement a)
```
    Description copied from interface: GenericField
    
    Squares a, i.e. performs the operation a *= a.
    
    Specified by:
    
    square in interface GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - squareOutOfPlace
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square of a
  - exponentiate
```
FieldElement 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 GenericField
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    a field element representing the nth power of a
  - exponentiateByPowerOf2
```
FieldElement exponentiateByPowerOf2(GenericFieldElement a,
                                    int n)
```
    Description copied from interface: GenericField
    
    Raises a to the power 2ⁿ.
    
    Specified by:
    
    exponentiateByPowerOf2 in interface GenericField
    
    Parameters:
    
    a - the field element
    
    n - the exponent
    
    Returns:
    
    the resulting field element
  - getOne
```
FieldElement getOne()
```
    Description copied from interface: GenericField
    
    Returns the one element.
    
    Specified by:
    
    getOne in interface GenericField
    
    Returns:
    
    an object holding the one element
  - getZero
```
FieldElement getZero()
```
    Description copied from interface: GenericField
    
    Returns the zero element.
    
    Specified by:
    
    getZero in interface GenericField
    
    Returns:
    
    an object holding the zero element
  - squareRoot
```
FieldElement squareRoot(FieldElement a)
```
    Computes the square root of a field element.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a field element representing the square root of a
  - newElement
```
FieldElement newElement(BigInteger b)
```
    Creates a new field element from its BigInteger representation.
    
    Parameters:
    
    b - the BigInteger
    
    Returns:
    
    the field element
  - newElement
```
FieldElement newElement(byte[] b)
```
    Creates a new field element from a byte[].
    
    Specified by:
    
    newElement in interface GenericField
    
    Parameters:
    
    b - the element encoded as byte[] in little-endian order
    
    Returns:
    
    the field element
  - toASN1Object
```
iaik.asn1.SEQUENCE toASN1Object()
```
    Returns the ASN.1 representation of this field.
    
    Returns:
    
    an ASN.1 object representing this field
  - toByteArray
```
byte[] toByteArray(FieldElement a)
```
    Converts a field element to its raw byte[] representation.
    
    Parameters:
    
    a - the field element
    
    Returns:
    
    a byte[]

Interface Field

Method Summary

Methods inherited from interface iaik.security.ec.math.field.GenericField

Methods inherited from interface java.security.spec.ECField

Method Detail

negate

negateOutOfPlace

add

subtract

multiply

multiplyOutOfPlace

multiply

multiplyOutOfPlace

divide

invert

square

squareOutOfPlace

exponentiate

exponentiateByPowerOf2

getOne

getZero

squareRoot

newElement

newElement

toASN1Object

toByteArray