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package java.security.spec;
import java.math.BigInteger;
import java.util.Arrays;
This immutable class defines an elliptic curve (EC)
characteristic 2 finite field.
Author: Valerie Peng See Also: - ECField
Since: 1.5
/**
* This immutable class defines an elliptic curve (EC)
* characteristic 2 finite field.
*
* @see ECField
*
* @author Valerie Peng
*
* @since 1.5
*/
public class ECFieldF2m implements ECField {
private int m;
private int[] ks;
private BigInteger rp;
Creates an elliptic curve characteristic 2 finite field which has 2^m elements with normal basis. Params: - m – with 2^
m being the number of elements.
Throws: - IllegalArgumentException – if
m is not positive.
/**
* Creates an elliptic curve characteristic 2 finite
* field which has 2^{@code m} elements with normal basis.
* @param m with 2^{@code m} being the number of elements.
* @exception IllegalArgumentException if {@code m}
* is not positive.
*/
public ECFieldF2m(int m) {
if (m <= 0) {
throw new IllegalArgumentException("m is not positive");
}
this.m = m;
this.ks = null;
this.rp = null;
}
Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis. The reduction polynomial for this field is based on rp whose i-th bit corresponds to the i-th coefficient of the reduction polynomial. Note: A valid reduction polynomial is either a trinomial (X^m + X^k + 1 with m > k >= 1) or a pentanomial (X^m + X^k3 + X^k2 + X^k1 + 1 with m > k3 > k2 > k1 >= 1).
Params: - m – with 2^
m being the number of elements. - rp – the BigInteger whose i-th bit corresponds to
the i-th coefficient of the reduction polynomial.
Throws: - NullPointerException – if
rp is null. - IllegalArgumentException – if
m is not positive, or rp does not represent a valid reduction polynomial.
/**
* Creates an elliptic curve characteristic 2 finite
* field which has 2^{@code m} elements with
* polynomial basis.
* The reduction polynomial for this field is based
* on {@code rp} whose i-th bit corresponds to
* the i-th coefficient of the reduction polynomial.<p>
* Note: A valid reduction polynomial is either a
* trinomial (X^{@code m} + X^{@code k} + 1
* with {@code m} > {@code k} >= 1) or a
* pentanomial (X^{@code m} + X^{@code k3}
* + X^{@code k2} + X^{@code k1} + 1 with
* {@code m} > {@code k3} > {@code k2}
* > {@code k1} >= 1).
* @param m with 2^{@code m} being the number of elements.
* @param rp the BigInteger whose i-th bit corresponds to
* the i-th coefficient of the reduction polynomial.
* @exception NullPointerException if {@code rp} is null.
* @exception IllegalArgumentException if {@code m}
* is not positive, or {@code rp} does not represent
* a valid reduction polynomial.
*/
public ECFieldF2m(int m, BigInteger rp) {
// check m and rp
this.m = m;
this.rp = rp;
if (m <= 0) {
throw new IllegalArgumentException("m is not positive");
}
int bitCount = this.rp.bitCount();
if (!this.rp.testBit(0) || !this.rp.testBit(m) ||
((bitCount != 3) && (bitCount != 5))) {
throw new IllegalArgumentException
("rp does not represent a valid reduction polynomial");
}
// convert rp into ks
BigInteger temp = this.rp.clearBit(0).clearBit(m);
this.ks = new int[bitCount-2];
for (int i = this.ks.length-1; i >= 0; i--) {
int index = temp.getLowestSetBit();
this.ks[i] = index;
temp = temp.clearBit(index);
}
}
Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis. The reduction polynomial for this field is based on ks whose content contains the order of the middle term(s) of the reduction polynomial. Note: A valid reduction polynomial is either a trinomial (X^m + X^k + 1 with m > k >= 1) or a pentanomial (X^m + X^k3 + X^k2 + X^k1 + 1 with m > k3 > k2 > k1 >= 1), so ks should have length 1 or 3. Params: - m – with 2^
m being the number of elements. - ks – the order of the middle term(s) of the
reduction polynomial. Contents of this array are copied
to protect against subsequent modification.
Throws: - NullPointerException – if
ks is null. - IllegalArgumentException – if
m is not positive, or the length of ks is neither 1 nor 3, or values in ks are not between m-1 and 1 (inclusive) and in descending order.
/**
* Creates an elliptic curve characteristic 2 finite
* field which has 2^{@code m} elements with
* polynomial basis. The reduction polynomial for this
* field is based on {@code ks} whose content
* contains the order of the middle term(s) of the
* reduction polynomial.
* Note: A valid reduction polynomial is either a
* trinomial (X^{@code m} + X^{@code k} + 1
* with {@code m} > {@code k} >= 1) or a
* pentanomial (X^{@code m} + X^{@code k3}
* + X^{@code k2} + X^{@code k1} + 1 with
* {@code m} > {@code k3} > {@code k2}
* > {@code k1} >= 1), so {@code ks} should
* have length 1 or 3.
* @param m with 2^{@code m} being the number of elements.
* @param ks the order of the middle term(s) of the
* reduction polynomial. Contents of this array are copied
* to protect against subsequent modification.
* @exception NullPointerException if {@code ks} is null.
* @exception IllegalArgumentException if{@code m}
* is not positive, or the length of {@code ks}
* is neither 1 nor 3, or values in {@code ks}
* are not between {@code m}-1 and 1 (inclusive)
* and in descending order.
*/
public ECFieldF2m(int m, int[] ks) {
// check m and ks
this.m = m;
this.ks = ks.clone();
if (m <= 0) {
throw new IllegalArgumentException("m is not positive");
}
if ((this.ks.length != 1) && (this.ks.length != 3)) {
throw new IllegalArgumentException
("length of ks is neither 1 nor 3");
}
for (int i = 0; i < this.ks.length; i++) {
if ((this.ks[i] < 1) || (this.ks[i] > m-1)) {
throw new IllegalArgumentException
("ks["+ i + "] is out of range");
}
if ((i != 0) && (this.ks[i] >= this.ks[i-1])) {
throw new IllegalArgumentException
("values in ks are not in descending order");
}
}
// convert ks into rp
this.rp = BigInteger.ONE;
this.rp = rp.setBit(m);
for (int j = 0; j < this.ks.length; j++) {
rp = rp.setBit(this.ks[j]);
}
}
Returns the field size in bits which is m for this characteristic 2 finite field. Returns: the field size in bits.
/**
* Returns the field size in bits which is {@code m}
* for this characteristic 2 finite field.
* @return the field size in bits.
*/
public int getFieldSize() {
return m;
}
Returns the value m of this characteristic 2 finite field. Returns: m with 2^m being the number of elements.
/**
* Returns the value {@code m} of this characteristic
* 2 finite field.
* @return {@code m} with 2^{@code m} being the
* number of elements.
*/
public int getM() {
return m;
}
Returns a BigInteger whose i-th bit corresponds to the
i-th coefficient of the reduction polynomial for polynomial
basis or null for normal basis.
Returns: a BigInteger whose i-th bit corresponds to the
i-th coefficient of the reduction polynomial for polynomial
basis or null for normal basis.
/**
* Returns a BigInteger whose i-th bit corresponds to the
* i-th coefficient of the reduction polynomial for polynomial
* basis or null for normal basis.
* @return a BigInteger whose i-th bit corresponds to the
* i-th coefficient of the reduction polynomial for polynomial
* basis or null for normal basis.
*/
public BigInteger getReductionPolynomial() {
return rp;
}
Returns an integer array which contains the order of the
middle term(s) of the reduction polynomial for polynomial
basis or null for normal basis.
Returns: an integer array which contains the order of the
middle term(s) of the reduction polynomial for polynomial
basis or null for normal basis. A new array is returned
each time this method is called.
/**
* Returns an integer array which contains the order of the
* middle term(s) of the reduction polynomial for polynomial
* basis or null for normal basis.
* @return an integer array which contains the order of the
* middle term(s) of the reduction polynomial for polynomial
* basis or null for normal basis. A new array is returned
* each time this method is called.
*/
public int[] getMidTermsOfReductionPolynomial() {
if (ks == null) {
return null;
} else {
return ks.clone();
}
}
Compares this finite field for equality with the
specified object.
Params: - obj – the object to be compared.
Returns: true if obj is an instance of ECFieldF2m and both m and the reduction polynomial match, false otherwise.
/**
* Compares this finite field for equality with the
* specified object.
* @param obj the object to be compared.
* @return true if {@code obj} is an instance
* of ECFieldF2m and both {@code m} and the reduction
* polynomial match, false otherwise.
*/
public boolean equals(Object obj) {
if (this == obj) return true;
if (obj instanceof ECFieldF2m) {
// no need to compare rp here since ks and rp
// should be equivalent
return ((m == ((ECFieldF2m)obj).m) &&
(Arrays.equals(ks, ((ECFieldF2m) obj).ks)));
}
return false;
}
Returns a hash code value for this characteristic 2
finite field.
Returns: a hash code value.
/**
* Returns a hash code value for this characteristic 2
* finite field.
* @return a hash code value.
*/
public int hashCode() {
int value = m << 5;
value += (rp==null? 0:rp.hashCode());
// no need to involve ks here since ks and rp
// should be equivalent.
return value;
}
}