PrimeCharacteristicField (ECCelerate 6.2 API)

All Superinterfaces:

ECField, GenericField

All Known Subinterfaces:

ExtensionField

All Known Implementing Classes:

AbstractPrimeField, QuadraticExtensionField, SexticOverQuadraticTowerExtensionField
```
public interface PrimeCharacteristicField
extends GenericField
```
This interface specifies important (arithmetical) methods that all fields of prime characteristic have in common.

Author:

Christian Hanser

See Also:

PrimeCharacteristicFieldElement, PrimeField

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`PrimeCharacteristicFieldElement`	`add(GenericFieldElement a, GenericFieldElement b)` Adds `b` to `a`, i.e.
`PrimeCharacteristicFieldElement`	`addOutOfPlace(PrimeCharacteristicFieldElement a, PrimeCharacteristicFieldElement b)` Adds two elements and returns a new object holding the result.
`PrimeCharacteristicFieldElement`	`divide(GenericFieldElement a, GenericFieldElement b)` Divides `a` by `b`, i.e.
`PrimeCharacteristicFieldElement`	`divideBy2(PrimeCharacteristicFieldElement a)` Divides `a` by 2.
`PrimeCharacteristicFieldElement`	`exponentiate(GenericFieldElement a, BigInteger n)` Raises `a` to the power `n`, i.e.
`PrimeCharacteristicFieldElement`	`exponentiateByPowerOf2(GenericFieldElement a, int n)` Raises `a` to the power `2ⁿ`.
`PrimeCharacteristicFieldElement`	`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, a multiple of the modulus, or a quadratic residue.
`PrimeCharacteristicFieldElement`	`getUniformlyRandomElement()` Get a uniformly random prime field element.
`PrimeCharacteristicFieldElement`	`getUniformlyRandomNonZeroElement()` Get a uniformly random, non-zero prime field element.
`PrimeCharacteristicFieldElement`	`getZero()` Returns the zero element.
`PrimeCharacteristicFieldElement`	`invert(GenericFieldElement a)` Inverts `a`, i.e.
`PrimeCharacteristicFieldElement`	`multiply(GenericFieldElement a, BigInteger n)` Multiplies `a` by `n`, i.e.
`PrimeCharacteristicFieldElement`	`multiply(GenericFieldElement a, GenericFieldElement b)` Multiplies `a` by `b`, i.e.
`PrimeCharacteristicFieldElement`	`multiplyBy2(PrimeCharacteristicFieldElement a)` Multiplies `a` by `2`, which is a left-shift.
`PrimeCharacteristicFieldElement`	`multiplyBy2OutOfPlace(PrimeCharacteristicFieldElement a)` Multiplies `a` by `2`, which is a left-shift and returns a new object holding the result.
`PrimeCharacteristicFieldElement`	`multiplyBy3(PrimeCharacteristicFieldElement a)` Multiplies `a` by `3`, which is a left-shift plus an addition.
`PrimeCharacteristicFieldElement`	`multiplyBy3OutOfPlace(PrimeCharacteristicFieldElement a)` Multiplies `a` by `3`, which is a left-shift plus an addition and returns a new object holding the result.
`PrimeCharacteristicFieldElement`	`multiplyByPowerOf2(PrimeCharacteristicFieldElement a, int exponent)` Multiplies `a` by a power of `2`, which is a left-shift.
`PrimeCharacteristicFieldElement`	`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.
`PrimeCharacteristicFieldElement`	`negate(GenericFieldElement a)` Negates `a`, i.e.
`PrimeCharacteristicFieldElement`	`newElement(byte[] bytes)` Create new field element from `byte`-array representation.
`PrimeCharacteristicFieldElement`	`square(GenericFieldElement a)` Squares `a`, i.e.
`PrimeCharacteristicFieldElement`	`subtract(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `a`, i.e.
`PrimeCharacteristicFieldElement`	`subtractOutOfPlace(GenericFieldElement a, GenericFieldElement b)` Subtracts `b` from `this` and returns a new object holding the result.
`PrimeCharacteristicFieldElement`	`toElement(byte[] bytes)` Create new field element from a `byte`-array.

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

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

- Method Detail
  - divideBy2
```
PrimeCharacteristicFieldElement divideBy2(PrimeCharacteristicFieldElement a)
```
    Divides a by 2.
    
    Parameters:
    
    a - the dividend
    
    Returns:
    
    the quotient of a and 2.
  - multiplyBy2
```
PrimeCharacteristicFieldElement multiplyBy2(PrimeCharacteristicFieldElement a)
```
    Multiplies a by 2, which is a left-shift. Works in-place.
    
    Parameters:
    
    a - the element to be shifted
    
    Returns:
    
    a holding the result
  - multiplyBy2OutOfPlace
```
PrimeCharacteristicFieldElement multiplyBy2OutOfPlace(PrimeCharacteristicFieldElement a)
```
    Multiplies a by 2, which is a left-shift and returns a new object holding the result.
    
    Parameters:
    
    a - the element to be shifted
    
    Returns:
    
    a holding the result
  - multiplyBy3
```
PrimeCharacteristicFieldElement multiplyBy3(PrimeCharacteristicFieldElement a)
```
    Multiplies a by 3, which is a left-shift plus an addition. Works in-place.
    
    Parameters:
    
    a - the element to multiplied
    
    Returns:
    
    a holding the result
  - multiplyBy3OutOfPlace
```
PrimeCharacteristicFieldElement multiplyBy3OutOfPlace(PrimeCharacteristicFieldElement a)
```
    Multiplies a by 3, which is a left-shift plus an addition and returns a new object holding the result.
    
    Parameters:
    
    a - the element to multiplied
    
    Returns:
    
    a holding the result
  - multiplyByPowerOf2
```
PrimeCharacteristicFieldElement multiplyByPowerOf2(PrimeCharacteristicFieldElement a,
                                                   int exponent)
```
    Multiplies a by a power of 2, which is a left-shift. Works in-place.
    
    Parameters:
    
    a - the element to be shifted
    
    exponent - the power of 2
    
    Returns:
    
    a holding the result
  - multiplyByPowerOf2OutOfPlace
```
PrimeCharacteristicFieldElement 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.
    
    Parameters:
    
    a - the element to be shifted
    
    exponent - the power of 2
    
    Returns:
    
    a holding the result
  - getZero
```
PrimeCharacteristicFieldElement getZero()
```
    Description copied from interface: GenericField
    
    Returns the zero element.
    
    Specified by:
    
    getZero in interface GenericField
    
    Returns:
    
    an object holding the zero element
  - getOne
```
PrimeCharacteristicFieldElement getOne()
```
    Description copied from interface: GenericField
    
    Returns the one element.
    
    Specified by:
    
    getOne in interface GenericField
    
    Returns:
    
    an object holding the one element
  - add
```
PrimeCharacteristicFieldElement 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
  - addOutOfPlace
```
PrimeCharacteristicFieldElement addOutOfPlace(PrimeCharacteristicFieldElement a,
                                              PrimeCharacteristicFieldElement b)
```
    Adds two elements and returns a new object holding the result.
    
    Parameters:
    
    a - first summand
    
    b - second summand
    
    Returns:
    
    the sum
  - subtract
```
PrimeCharacteristicFieldElement 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
  - subtractOutOfPlace
```
PrimeCharacteristicFieldElement subtractOutOfPlace(GenericFieldElement a,
                                                   GenericFieldElement b)
```
    Subtracts b from this and returns a new object holding the result.
    
    Parameters:
    
    a - the minuend
    
    b - the subtrahend
    
    Returns:
    
    the difference of a and b
  - negate
```
PrimeCharacteristicFieldElement 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
  - multiply
```
PrimeCharacteristicFieldElement 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
  - multiply
```
PrimeCharacteristicFieldElement 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
  - square
```
PrimeCharacteristicFieldElement 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
  - exponentiate
```
PrimeCharacteristicFieldElement 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
  - divide
```
PrimeCharacteristicFieldElement 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
  - exponentiateByPowerOf2
```
PrimeCharacteristicFieldElement 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
  - invert
```
PrimeCharacteristicFieldElement 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
  - newElement
```
PrimeCharacteristicFieldElement newElement(byte[] bytes)
```
    Description copied from interface: GenericField
    
    Create new field element from byte-array representation.
    
    Specified by:
    
    newElement in interface GenericField
    
    Parameters:
    
    bytes - the byte[] in little-endian order
    
    Returns:
    
    an object holding the new field element
  - toElement
```
PrimeCharacteristicFieldElement 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
    
    Parameters:
    
    bytes - a byte[] in little-endian order
    
    Returns:
    
    an object holding the new field element
  - getQuadraticCharacter
```
int getQuadraticCharacter(PrimeCharacteristicFieldElement a)
```
    Implements a quadratic character, which returns -1,0,1 depending on whether the given value ais a quadratic non-residue, a multiple of the modulus, or a quadratic residue.
    
    Parameters:
    
    a - a field element
    
    Returns:
    
    the quadratic character (a/p)
  - getUniformlyRandomElement
```
PrimeCharacteristicFieldElement getUniformlyRandomElement()
```
    Get a uniformly random prime field element.
    
    Returns:
    
    element of the field.
  - getUniformlyRandomNonZeroElement
```
PrimeCharacteristicFieldElement getUniformlyRandomNonZeroElement()
```
    Get a uniformly random, non-zero prime field element.
    
    Returns:
    
    element of the field.

Interface PrimeCharacteristicField

Method Summary

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

Methods inherited from interface java.security.spec.ECField

Method Detail

divideBy2

multiplyBy2

multiplyBy2OutOfPlace

multiplyBy3

multiplyBy3OutOfPlace

multiplyByPowerOf2

multiplyByPowerOf2OutOfPlace

getZero

getOne

add

addOutOfPlace

subtract

subtractOutOfPlace

negate

multiply

multiply

square

exponentiate

divide

exponentiateByPowerOf2

invert

newElement

toElement

getQuadraticCharacter

getUniformlyRandomElement

getUniformlyRandomNonZeroElement