# ECFieldF2m public class **ECFieldF2m** extends [Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) implements [ECField](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECField.html) This immutable class defines an elliptic curve (EC) characteristic 2 finite field. ##### See Also - `https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECField.html` ### Public Constructor Summary |---|---| | | [ECFieldF2m](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#ECFieldF2m(int))(int m) Creates an elliptic curve characteristic 2 finite field which has 2\^`m` elements with normal basis. | | | [ECFieldF2m](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#ECFieldF2m(int,%20java.math.BigInteger))(int m, BigInteger rp) Creates an elliptic curve characteristic 2 finite field which has 2\^`m` elements with polynomial basis. | | | [ECFieldF2m](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#ECFieldF2m(int,%20int[]))(int m, int\[\] ks) Creates an elliptic curve characteristic 2 finite field which has 2\^`m` elements with polynomial basis. | ### Public Method Summary |---|---| | boolean | [equals](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#equals(java.lang.Object))([Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) obj) Compares this finite field for equality with the specified object. | | int | [getFieldSize](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#getFieldSize())() Returns the field size in bits which is `m` for this characteristic 2 finite field. | | int | [getM](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#getM())() Returns the value `m` of this characteristic 2 finite field. | | int\[\] | [getMidTermsOfReductionPolynomial](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#getMidTermsOfReductionPolynomial())() 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. | | BigInteger | [getReductionPolynomial](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#getReductionPolynomial())() 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. | | int | [hashCode](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECFieldF2m.html#hashCode())() Returns a hash code value for this characteristic 2 finite field. | ### Inherited Method Summary From class [java.lang.Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) |---|---| | [Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) | [clone](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#clone())() Creates and returns a copy of this `Object`. | | boolean | [equals](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#equals(java.lang.Object))([Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) obj) Compares this instance with the specified object and indicates if they are equal. | | void | [finalize](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#finalize())() Invoked when the garbage collector has detected that this instance is no longer reachable. | | final [Class](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Class.html)\ | [getClass](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#getClass())() Returns the unique instance of `https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Class.html` that represents this object's class. | | int | [hashCode](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#hashCode())() Returns an integer hash code for this object. | | final void | [notify](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#notify())() Causes a thread which is waiting on this object's monitor (by means of calling one of the `wait()` methods) to be woken up. | | final void | [notifyAll](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#notifyAll())() Causes all threads which are waiting on this object's monitor (by means of calling one of the `wait()` methods) to be woken up. | | [String](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/String.html) | [toString](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#toString())() Returns a string containing a concise, human-readable description of this object. | | final void | [wait](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#wait(long,%20int))(long timeout, int nanos) Causes the calling thread to wait until another thread calls the `notify()` or `notifyAll()` method of this object or until the specified timeout expires. | | final void | [wait](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#wait(long))(long timeout) Causes the calling thread to wait until another thread calls the `notify()` or `notifyAll()` method of this object or until the specified timeout expires. | | final void | [wait](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html#wait())() Causes the calling thread to wait until another thread calls the `notify()` or `notifyAll()` method of this object. | From interface [java.security.spec.ECField](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECField.html) |---|---| | abstract int | [getFieldSize](https://developers.google.com/j2objc/javadoc/jre/reference/java/security/spec/ECField.html#getFieldSize())() Returns the field size in bits. | ## Public Constructors #### public **ECFieldF2m** (int m) Creates an elliptic curve characteristic 2 finite field which has 2\^`m` elements with normal basis. ##### Parameters | m | with 2\^`m` being the number of elements. | |---|---| ##### Throws | [IllegalArgumentException](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/IllegalArgumentException.html) | if `m` is not positive. | |---|---| #### public **ECFieldF2m** (int m, BigInteger rp) 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). ##### Parameters | 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](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/NullPointerException.html) | if `rp` is null. | | [IllegalArgumentException](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/IllegalArgumentException.html) | if `m` is not positive, or `rp` does not represent a valid reduction polynomial. | |---|---| #### public **ECFieldF2m** (int m, int\[\] ks) 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. ##### Parameters | 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](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/NullPointerException.html) | if `ks` is null. | | [IllegalArgumentException](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/IllegalArgumentException.html) | 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. | |---|---| ## Public Methods #### public boolean **equals** ([Object](https://developers.google.com/j2objc/javadoc/jre/reference/java/lang/Object.html) obj) Compares this finite field for equality with the specified object. ##### Parameters | 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. #### public int **getFieldSize** () Returns the field size in bits which is `m` for this characteristic 2 finite field. ##### Returns - the field size in bits. #### public int **getM** () Returns the value `m` of this characteristic 2 finite field. ##### Returns - `m` with 2\^`m` being the number of elements. #### public int\[\] **getMidTermsOfReductionPolynomial** () 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. #### public BigInteger **getReductionPolynomial** () 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. #### public int **hashCode** () Returns a hash code value for this characteristic 2 finite field. ##### Returns - a hash code value.