package org.bouncycastle.pqc.math.linearalgebra;


This abstract class implements an element of the finite field GF(2)n
 in either optimal normal basis representation (ONB)
or in polynomial representation. It is extended by the classes  GF2nONBElement and  GF2nPolynomialElement .
See Also:
GF2nPolynomialElement
GF2nONBElement
GF2nONBField/**
 * This abstract class implements an element of the finite field <i>GF(2)<sup>n
 * </sup></i> in either <i>optimal normal basis</i> representation (<i>ONB</i>)
 * or in <i>polynomial</i> representation. It is extended by the classes <a
 * href = GF2nONBElement.html><tt> GF2nONBElement</tt></a> and <a href =
 * GF2nPolynomialElement.html> <tt>GF2nPolynomialElement</tt> </a>.
 *
 * @see GF2nPolynomialElement
 * @see GF2nONBElement
 * @see GF2nONBField
 */
public abstract class GF2nElement
    implements GFElement
{

    // /////////////////////////////////////////////////////////////////////
    // member variables
    // /////////////////////////////////////////////////////////////////////

    
holds a pointer to this element's corresponding field.
/**
     * holds a pointer to this element's corresponding field.
     */
    protected GF2nField mField;

    
holds the extension degree n of this element's corresponding
field.
/**
     * holds the extension degree <i>n</i> of this element's corresponding
     * field.
     */
    protected int mDegree;

    // /////////////////////////////////////////////////////////////////////
    // pseudo-constructors
    // /////////////////////////////////////////////////////////////////////

    
Returns:
a copy of this GF2nElement/**
     * @return a copy of this GF2nElement
     */
    public abstract Object clone();

    // /////////////////////////////////////////////////////////////////////
    // assignments
    // /////////////////////////////////////////////////////////////////////

    
Assign the value 0 to this element.
/**
     * Assign the value 0 to this element.
     */
    abstract void assignZero();

    
Assigns the value 1 to this element.
/**
     * Assigns the value 1 to this element.
     */
    abstract void assignOne();

    // /////////////////////////////////////////////////////////////////////
    // access
    // /////////////////////////////////////////////////////////////////////

    
Returns whether the rightmost bit of the bit representation is set. This
is needed for data conversion according to 1363.
Returns:
true if the rightmost bit of this element is set/**
     * Returns whether the rightmost bit of the bit representation is set. This
     * is needed for data conversion according to 1363.
     *
     * @return true if the rightmost bit of this element is set
     */
    public abstract boolean testRightmostBit();

    
Checks whether the indexed bit of the bit representation is set
Params:
index – the index of the bit to test
Returns:
true if the indexed bit is set/**
     * Checks whether the indexed bit of the bit representation is set
     *
     * @param index the index of the bit to test
     * @return <tt>true</tt> if the indexed bit is set
     */
    abstract boolean testBit(int index);

    
Returns the field of this element.
Returns:
the field of this element/**
     * Returns the field of this element.
     *
     * @return the field of this element
     */
    public final GF2nField getField()
    {
        return mField;
    }

    // /////////////////////////////////////////////////////////////////////
    // arithmetic
    // /////////////////////////////////////////////////////////////////////

    
Returns this element + 1.
Returns:
this + 1/**
     * Returns <tt>this</tt> element + 1.
     *
     * @return <tt>this</tt> + 1
     */
    public abstract GF2nElement increase();

    
Increases this element by one.
/**
     * Increases this element by one.
     */
    public abstract void increaseThis();

    
Compute the difference of this element and minuend.
Params:
minuend – the minuend
Returns:
this - minuend (newly created)/**
     * Compute the difference of this element and <tt>minuend</tt>.
     *
     * @param minuend the minuend
     * @return <tt>this - minuend</tt> (newly created)
     */
    public final GFElement subtract(GFElement minuend)
    {
        return add(minuend);
    }

    
Compute the difference of this element and minuend,
overwriting this element.
Params:
minuend – the minuend/**
     * Compute the difference of this element and <tt>minuend</tt>,
     * overwriting this element.
     *
     * @param minuend the minuend
     */
    public final void subtractFromThis(GFElement minuend)
    {
        addToThis(minuend);
    }

    
Returns this element to the power of 2.
Returns:
this2/**
     * Returns <tt>this</tt> element to the power of 2.
     *
     * @return <tt>this</tt><sup>2</sup>
     */
    public abstract GF2nElement square();

    
Squares this element.
/**
     * Squares <tt>this</tt> element.
     */
    public abstract void squareThis();

    
Compute the square root of this element and return the result in a new GF2nElement. 
Returns:
this1/2 (newly created)/**
     * Compute the square root of this element and return the result in a new
     * {@link GF2nElement}.
     *
     * @return <tt>this<sup>1/2</sup></tt> (newly created)
     */
    public abstract GF2nElement squareRoot();

    
Compute the square root of this element.
/**
     * Compute the square root of this element.
     */
    public abstract void squareRootThis();

    
Performs a basis transformation of this element to the given GF2nField
basis.
Params:
basis – the GF2nField representation to transform this element to
Returns:
this element in the representation of basis/**
     * Performs a basis transformation of this element to the given GF2nField
     * <tt>basis</tt>.
     *
     * @param basis the GF2nField representation to transform this element to
     * @return this element in the representation of <tt>basis</tt>
     */
    public final GF2nElement convert(GF2nField basis)
    {
        return mField.convert(this, basis);
    }

    
Returns the trace of this element.
Returns:
the trace of this element/**
     * Returns the trace of this element.
     *
     * @return the trace of this element
     */
    public abstract int trace();

    
Solves a quadratic equation.

Let z2 + z = this. Then this method returns z.
Returns:
z with z2 + z = this/**
     * Solves a quadratic equation.<br>
     * Let z<sup>2</sup> + z = <tt>this</tt>. Then this method returns z.
     *
     * @return z with z<sup>2</sup> + z = <tt>this</tt>
     */
    public abstract GF2nElement solveQuadraticEquation()
        throws RuntimeException;

}