package org.bouncycastle.pqc.math.linearalgebra;
/**
* This class implements polynomials over GF2nElements.
*
* @see GF2nElement
*/
public class GF2nPolynomial
{
private GF2nElement[] coeff; // keeps the coefficients of this polynomial
private int size; // the size of this polynomial
/**
* Creates a new PolynomialGF2n of size <i>deg</i> and elem as
* coefficients.
*
* @param deg -
* the maximum degree + 1
* @param elem -
* a GF2nElement
*/
public GF2nPolynomial(int deg, GF2nElement elem)
{
size = deg;
coeff = new GF2nElement[size];
for (int i = 0; i < size; i++)
{
coeff[i] = (GF2nElement)elem.clone();
}
}
/**
* Creates a new PolynomialGF2n of size <i>deg</i>.
*
* @param deg the maximum degree + 1
*/
private GF2nPolynomial(int deg)
{
size = deg;
coeff = new GF2nElement[size];
}
/**
* Creates a new PolynomialGF2n by cloning the given PolynomialGF2n <i>a</i>.
*
* @param a the PolynomialGF2n to clone
*/
public GF2nPolynomial(GF2nPolynomial a)
{
int i;
coeff = new GF2nElement[a.size];
size = a.size;
for (i = 0; i < size; i++)
{
coeff[i] = (GF2nElement)a.coeff[i].clone();
}
}
/**
* Creates a new PolynomialGF2n from the given Bitstring <i>polynomial</i>
* over the GF2nField <i>B1</i>.
*
* @param polynomial the Bitstring to use
* @param B1 the field
*/
public GF2nPolynomial(GF2Polynomial polynomial, GF2nField B1)
{
size = B1.getDegree() + 1;
coeff = new GF2nElement[size];
int i;
if (B1 instanceof GF2nONBField)
{
for (i = 0; i < size; i++)
{
if (polynomial.testBit(i))
{
coeff[i] = GF2nONBElement.ONE((GF2nONBField)B1);
}
else
{
coeff[i] = GF2nONBElement.ZERO((GF2nONBField)B1);
}
}
}
else if (B1 instanceof GF2nPolynomialField)
{
for (i = 0; i < size; i++)
{
if (polynomial.testBit(i))
{
coeff[i] = GF2nPolynomialElement
.ONE((GF2nPolynomialField)B1);
}
else
{
coeff[i] = GF2nPolynomialElement
.ZERO((GF2nPolynomialField)B1);
}
}
}
else
{
throw new IllegalArgumentException(
"PolynomialGF2n(Bitstring, GF2nField): B1 must be "
+ "an instance of GF2nONBField or GF2nPolynomialField!");
}
}
public final void assignZeroToElements()
{
int i;
for (i = 0; i < size; i++)
{
coeff[i].assignZero();
}
}
/**
* Returns the size (=maximum degree + 1) of this PolynomialGF2n. This is
* not the degree, use getDegree instead.
*
* @return the size (=maximum degree + 1) of this PolynomialGF2n.
*/
public final int size()
{
return size;
}
/**
* Returns the degree of this PolynomialGF2n.
*
* @return the degree of this PolynomialGF2n.
*/
public final int getDegree()
{
int i;
for (i = size - 1; i >= 0; i--)
{
if (!coeff[i].isZero())
{
return i;
}
}
return -1;
}
/**
* Enlarges the size of this PolynomialGF2n to <i>k</i> + 1.
*
* @param k the new maximum degree
*/
public final void enlarge(int k)
{
if (k <= size)
{
return;
}
int i;
GF2nElement[] res = new GF2nElement[k];
System.arraycopy(coeff, 0, res, 0, size);
GF2nField f = coeff[0].getField();
if (coeff[0] instanceof GF2nPolynomialElement)
{
for (i = size; i < k; i++)
{
res[i] = GF2nPolynomialElement.ZERO((GF2nPolynomialField)f);
}
}
else if (coeff[0] instanceof GF2nONBElement)
{
for (i = size; i < k; i++)
{
res[i] = GF2nONBElement.ZERO((GF2nONBField)f);
}
}
size = k;
coeff = res;
}
public final void shrink()
{
int i = size - 1;
while (coeff[i].isZero() && (i > 0))
{
i--;
}
i++;
if (i < size)
{
GF2nElement[] res = new GF2nElement[i];
System.arraycopy(coeff, 0, res, 0, i);
coeff = res;
size = i;
}
}
/**
* Sets the coefficient at <i>index</i> to <i>elem</i>.
*
* @param index the index
* @param elem the GF2nElement to store as coefficient <i>index</i>
*/
public final void set(int index, GF2nElement elem)
{
if (!(elem instanceof GF2nPolynomialElement)
&& !(elem instanceof GF2nONBElement))
{
throw new IllegalArgumentException(
"PolynomialGF2n.set f must be an "
+ "instance of either GF2nPolynomialElement or GF2nONBElement!");
}
coeff[index] = (GF2nElement)elem.clone();
}
/**
* Returns the coefficient at <i>index</i>.
*
* @param index the index
* @return the GF2nElement stored as coefficient <i>index</i>
*/
public final GF2nElement at(int index)
{
return coeff[index];
}
/**
* Returns true if all coefficients equal zero.
*
* @return true if all coefficients equal zero.
*/
public final boolean isZero()
{
int i;
for (i = 0; i < size; i++)
{
if (coeff[i] != null)
{
if (!coeff[i].isZero())
{
return false;
}
}
}
return true;
}
public final boolean equals(Object other)
{
if (other == null || !(other instanceof GF2nPolynomial))
{
return false;
}
GF2nPolynomial otherPol = (GF2nPolynomial)other;
if (getDegree() != otherPol.getDegree())
{
return false;
}
int i;
for (i = 0; i < size; i++)
{
if (!coeff[i].equals(otherPol.coeff[i]))
{
return false;
}
}
return true;
}
/**
* @return the hash code of this polynomial
*/
public int hashCode()
{
return getDegree() + coeff.hashCode();
}
/**
* Adds the PolynomialGF2n <tt>b</tt> to <tt>this</tt> and returns the
* result in a new <tt>PolynomialGF2n</tt>.
*
* @param b -
* the <tt>PolynomialGF2n</tt> to add
* @return <tt>this + b</tt>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>b</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial add(GF2nPolynomial b)
throws RuntimeException
{
GF2nPolynomial result;
if (size() >= b.size())
{
result = new GF2nPolynomial(size());
int i;
for (i = 0; i < b.size(); i++)
{
result.coeff[i] = (GF2nElement)coeff[i].add(b.coeff[i]);
}
for (; i < size(); i++)
{
result.coeff[i] = coeff[i];
}
}
else
{
result = new GF2nPolynomial(b.size());
int i;
for (i = 0; i < size(); i++)
{
result.coeff[i] = (GF2nElement)coeff[i].add(b.coeff[i]);
}
for (; i < b.size(); i++)
{
result.coeff[i] = b.coeff[i];
}
}
return result;
}
/**
* Multiplies the scalar <i>s</i> to each coefficient of this
* PolynomialGF2n and returns the result in a new PolynomialGF2n.
*
* @param s the scalar to multiply
* @return <i>this</i> x <i>s</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>s</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial scalarMultiply(GF2nElement s)
throws RuntimeException
{
GF2nPolynomial result = new GF2nPolynomial(size());
int i;
for (i = 0; i < size(); i++)
{
result.coeff[i] = (GF2nElement)coeff[i].multiply(s); // result[i]
// =
// a[i]*s
}
return result;
}
/**
* Multiplies <i>this</i> by <i>b</i> and returns the result in a new
* PolynomialGF2n.
*
* @param b the PolynomialGF2n to multiply
* @return <i>this</i> * <i>b</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>b</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial multiply(GF2nPolynomial b)
throws RuntimeException
{
int i, j;
int aDegree = size();
int bDegree = b.size();
if (aDegree != bDegree)
{
throw new IllegalArgumentException(
"PolynomialGF2n.multiply: this and b must "
+ "have the same size!");
}
GF2nPolynomial result = new GF2nPolynomial((aDegree << 1) - 1);
for (i = 0; i < size(); i++)
{
for (j = 0; j < b.size(); j++)
{
if (result.coeff[i + j] == null)
{
result.coeff[i + j] = (GF2nElement)coeff[i]
.multiply(b.coeff[j]);
}
else
{
result.coeff[i + j] = (GF2nElement)result.coeff[i + j]
.add(coeff[i].multiply(b.coeff[j]));
}
}
}
return result;
}
/**
* Multiplies <i>this</i> by <i>b</i>, reduces the result by <i>g</i> and
* returns it in a new PolynomialGF2n.
*
* @param b the PolynomialGF2n to multiply
* @param g the modul
* @return <i>this</i> * <i>b</i> mod <i>g</i>
* @throws DifferentFieldsException if <tt>this</tt>, <tt>b</tt> and <tt>g</tt> are
* not all defined over the same field.
*/
public final GF2nPolynomial multiplyAndReduce(GF2nPolynomial b,
GF2nPolynomial g)
throws RuntimeException,
ArithmeticException
{
return multiply(b).reduce(g);
}
/**
* Reduces <i>this</i> by <i>g</i> and returns the result in a new
* PolynomialGF2n.
*
* @param g -
* the modulus
* @return <i>this</i> % <i>g</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>g</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial reduce(GF2nPolynomial g)
throws RuntimeException, ArithmeticException
{
return remainder(g); // return this % g
}
/**
* Shifts left <i>this</i> by <i>amount</i> and stores the result in
* <i>this</i> PolynomialGF2n.
*
* @param amount the amount to shift the coefficients
*/
public final void shiftThisLeft(int amount)
{
if (amount > 0)
{
int i;
int oldSize = size;
GF2nField f = coeff[0].getField();
enlarge(size + amount);
for (i = oldSize - 1; i >= 0; i--)
{
coeff[i + amount] = coeff[i];
}
if (coeff[0] instanceof GF2nPolynomialElement)
{
for (i = amount - 1; i >= 0; i--)
{
coeff[i] = GF2nPolynomialElement
.ZERO((GF2nPolynomialField)f);
}
}
else if (coeff[0] instanceof GF2nONBElement)
{
for (i = amount - 1; i >= 0; i--)
{
coeff[i] = GF2nONBElement.ZERO((GF2nONBField)f);
}
}
}
}
public final GF2nPolynomial shiftLeft(int amount)
{
if (amount <= 0)
{
return new GF2nPolynomial(this);
}
GF2nPolynomial result = new GF2nPolynomial(size + amount, coeff[0]);
result.assignZeroToElements();
for (int i = 0; i < size; i++)
{
result.coeff[i + amount] = coeff[i];
}
return result;
}
/**
* Divides <i>this</i> by <i>b</i> and stores the result in a new
* PolynomialGF2n[2], quotient in result[0] and remainder in result[1].
*
* @param b the divisor
* @return the quotient and remainder of <i>this</i> / <i>b</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>b</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial[] divide(GF2nPolynomial b)
throws RuntimeException, ArithmeticException
{
GF2nPolynomial[] result = new GF2nPolynomial[2];
GF2nPolynomial a = new GF2nPolynomial(this);
a.shrink();
GF2nPolynomial shift;
GF2nElement factor;
int bDegree = b.getDegree();
GF2nElement inv = (GF2nElement)b.coeff[bDegree].invert();
if (a.getDegree() < bDegree)
{
result[0] = new GF2nPolynomial(this);
result[0].assignZeroToElements();
result[0].shrink();
result[1] = new GF2nPolynomial(this);
result[1].shrink();
return result;
}
result[0] = new GF2nPolynomial(this);
result[0].assignZeroToElements();
int i = a.getDegree() - bDegree;
while (i >= 0)
{
factor = (GF2nElement)a.coeff[a.getDegree()].multiply(inv);
shift = b.scalarMultiply(factor);
shift.shiftThisLeft(i);
a = a.add(shift);
a.shrink();
result[0].coeff[i] = (GF2nElement)factor.clone();
i = a.getDegree() - bDegree;
}
result[1] = a;
result[0].shrink();
return result;
}
/**
* Divides <i>this</i> by <i>b</i> and stores the remainder in a new
* PolynomialGF2n.
*
* @param b the divisor
* @return the remainder <i>this</i> % <i>b</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>b</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial remainder(GF2nPolynomial b)
throws RuntimeException, ArithmeticException
{
GF2nPolynomial[] result = new GF2nPolynomial[2];
result = divide(b);
return result[1];
}
/**
* Divides <i>this</i> by <i>b</i> and stores the quotient in a new
* PolynomialGF2n.
*
* @param b the divisor
* @return the quotient <i>this</i> / <i>b</i>
* @throws DifferentFieldsException if <tt>this</tt> and <tt>b</tt> are not defined over
* the same field.
*/
public final GF2nPolynomial quotient(GF2nPolynomial b)
throws RuntimeException, ArithmeticException
{
GF2nPolynomial[] result = new GF2nPolynomial[2];
result = divide(b);
return result[0];
}
/**
* Computes the greatest common divisor of <i>this</i> and <i>g</i> and
* returns the result in a new PolynomialGF2n.
*
* @param g -
* a GF2nPolynomial
* @return gcd(<i>this</i>, <i>g</i>)
* @throws DifferentFieldsException if the coefficients of <i>this</i> and <i>g</i> use
* different fields
* @throws ArithmeticException if coefficients are zero.
*/
public final GF2nPolynomial gcd(GF2nPolynomial g)
throws RuntimeException, ArithmeticException
{
GF2nPolynomial a = new GF2nPolynomial(this);
GF2nPolynomial b = new GF2nPolynomial(g);
a.shrink();
b.shrink();
GF2nPolynomial c;
GF2nPolynomial result;
GF2nElement alpha;
while (!b.isZero())
{
c = a.remainder(b);
a = b;
b = c;
}
alpha = a.coeff[a.getDegree()];
result = a.scalarMultiply((GF2nElement)alpha.invert());
return result;
}
}