This immutable class defines an elliptic curve (EC) characteristic 2 finite field.
This immutable class defines an elliptic curve (EC) characteristic 2 finite field.
(->ec-field-f-2m m)
(->ec-field-f-2m m rp)
Constructor.
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).
m - with 2^m being the number of elements. - int
rp - the BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial. - java.math.BigInteger
throws: java.lang.NullPointerException - if rp is null.
Constructor. 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). m - with 2^m being the number of elements. - `int` rp - the BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial. - `java.math.BigInteger` throws: java.lang.NullPointerException - if rp is null.
(equals this obj)
Compares this finite field for equality with the specified object.
obj - the object to be compared. - java.lang.Object
returns: true if obj is an instance
of ECFieldF2m and both m and the reduction
polynomial match, false otherwise. - boolean
Compares this finite field for equality with the specified object. obj - the object to be compared. - `java.lang.Object` returns: true if obj is an instance of ECFieldF2m and both m and the reduction polynomial match, false otherwise. - `boolean`
(get-field-size this)
Returns the field size in bits which is m for this characteristic 2 finite field.
returns: the field size in bits. - int
Returns the field size in bits which is m for this characteristic 2 finite field. returns: the field size in bits. - `int`
(get-m this)
Returns the value m of this characteristic 2 finite field.
returns: m with 2^m being the
number of elements. - int
Returns the value m of this characteristic 2 finite field. returns: m with 2^m being the number of elements. - `int`
(get-mid-terms-of-reduction-polynomial this)
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. - int[]
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. - `int[]`
(get-reduction-polynomial this)
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. - java.math.BigInteger
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. - `java.math.BigInteger`
(hash-code this)
Returns a hash code value for this characteristic 2 finite field.
returns: a hash code value. - int
Returns a hash code value for this characteristic 2 finite field. returns: a hash code value. - `int`
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