net.i2p.crypto.eddsa.math

Class FieldElement

java.lang.Object

net.i2p.crypto.eddsa.math.FieldElement

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

BigIntegerFieldElement, Ed25519FieldElement

public abstract class FieldElement
extends Object
implements Serializable

Represents an element in a finite field of order $2^{b}-3$. Note: concrete subclasses must implement hashCode() and equals()

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected Field	f The field this element belongs to

Constructor Summary

Constructors

Constructor and Description
FieldElement(Field f) Creates a new field element in the specified field.

Method Summary

Modifier and Type	Method and Description
abstract FieldElement	add(FieldElement val) Adds another field element to this one.
FieldElement	addOne() Adds one to this field element.
abstract FieldElement	cmov(FieldElement val, int b) Conditional move - sets this element to val if b is 1, otherwise leaves it unchanged.
FieldElement	divide(FieldElement val) Divides this field element by another one.
abstract FieldElement	invert() Computes the multiplicative inverse of this field element.
boolean	isNegative() Checks if this field element is negative.
abstract boolean	isNonZero() Checks if this field element is non-zero.
abstract FieldElement	multiply(FieldElement val) Multiplies this field element by another one.
abstract FieldElement	negate() Negates this field element.
abstract FieldElement	pow22523() Raises this field element to the power of $2^{252} - 3$.
abstract FieldElement	square() Squares this field element.
abstract FieldElement	squareAndDouble() Squares this field element and doubles the result.
abstract FieldElement	subtract(FieldElement val) Subtracts another field element from this one.
FieldElement	subtractOne() Subtracts one from this field element.
byte[]	toByteArray() Encode a FieldElement in its $(b-1)$-bit encoding.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

f

protected final Field f

The field this element belongs to

Constructor Detail

FieldElement

public FieldElement(Field f)

Creates a new field element in the specified field.

Parameters:

f - the field this element belongs to

Throws:

IllegalArgumentException - if f is null

Method Detail

add

public abstract FieldElement add(FieldElement val)

Adds another field element to this one.

Parameters:

val - the field element to add

Returns:

the sum of this element and val

addOne

public FieldElement addOne()

Adds one to this field element.

Returns:

this element plus one

cmov

public abstract FieldElement cmov(FieldElement val,
                                  int b)

Conditional move - sets this element to val if b is 1, otherwise leaves it unchanged.

Parameters:

val - the field element to potentially assign

b - the condition: 1 means assign val, 0 means keep this element

Returns:

this element, potentially modified

divide

public FieldElement divide(FieldElement val)

Divides this field element by another one.

Parameters:

val - the divisor

Returns:

this element divided by val

invert

public abstract FieldElement invert()

Computes the multiplicative inverse of this field element.

Returns:

the multiplicative inverse of this element

Throws:

ArithmeticException - if this element is zero

isNegative

public boolean isNegative()

Checks if this field element is negative. Negative is defined as the least significant bit being 1.

Returns:

true if this element is negative, false otherwise

isNonZero

public abstract boolean isNonZero()

Checks if this field element is non-zero.

Returns:

true if this element is not equal to zero, false otherwise

multiply

public abstract FieldElement multiply(FieldElement val)

Multiplies this field element by another one.

Parameters:

val - the multiplier

Returns:

the product of this element and val

negate

public abstract FieldElement negate()

Negates this field element.

Returns:

the negation of this element

pow22523

public abstract FieldElement pow22523()

Raises this field element to the power of $2^{252} - 3$.

Returns:

this element raised to the power of $2^{252} - 3$

square

public abstract FieldElement square()

Squares this field element.

Returns:

this element squared

squareAndDouble

public abstract FieldElement squareAndDouble()

Squares this field element and doubles the result.

Returns:

(this element squared) * 2

subtract

public abstract FieldElement subtract(FieldElement val)

Subtracts another field element from this one.

Parameters:

val - the field element to subtract

Returns:

the difference of this element and val

subtractOne

public FieldElement subtractOne()

Subtracts one from this field element.

Returns:

this element minus one

toByteArray

public byte[] toByteArray()

Encode a FieldElement in its $(b-1)$-bit encoding.

Returns:

the $(b-1)$-bit encoding of this FieldElement