## FP4 **Kind**: global class **this**: {FP4} * [FP4](#FP4) * [new FP4()](#new_FP4_new) * [.reduce()](#FP4+reduce) * [.norm()](#FP4+norm) * [.iszilch()](#FP4+iszilch) * [.isunity()](#FP4+isunity) * [.cmove(g, d)](#FP4+cmove) * [.isreal()](#FP4+isreal) * [.real()](#FP4+real) * [.geta()](#FP4+geta) * [.getb()](#FP4+getb) * [.equals(x)](#FP4+equals) * [.copy(x)](#FP4+copy) * [.zero()](#FP4+zero) * [.one(x)](#FP4+one) * [.set(c, d)](#FP4+set) * [.seta(c)](#FP4+seta) * [.neg()](#FP4+neg) * [.conj()](#FP4+conj) * [.nconj()](#FP4+nconj) * [.add(x)](#FP4+add) * [.sub(x)](#FP4+sub) * [.pmul(s)](#FP4+pmul) * [.imul(s)](#FP4+imul) * [.sqr()](#FP4+sqr) * [.mul(y)](#FP4+mul) * [.toString()](#FP4+toString) * [.inverse()](#FP4+inverse) * [.times_i()](#FP4+times_i) * [.frob(f)](#FP4+frob) * [.pow(e)](#FP4+pow) * [.xtr_A(w, y, z)](#FP4+xtr_A) * [.xtr_D()](#FP4+xtr_D) * [.xtr_pow(n)](#FP4+xtr_pow) * [.xtr_pow2()](#FP4+xtr_pow2) * [.div2()](#FP4+div2) * [.div_i()](#FP4+div_i) * [.div_2i()](#FP4+div_2i) * [.qmul(s)](#FP4+qmul) * [.sqrt()](#FP4+sqrt) ### new FP4() Creates an instance of FP4 ### fP4.reduce() Reduces all components of possibly unreduced FP4 mod Modulus **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.norm() Normalises the components of an FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.iszilch() Tests for FP4 equal to zero **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.isunity() Tests for FP4 equal to unity **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.cmove(g, d) Conditional copy of FP4 number **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | g | FP4 instance | | d | copy depends on this value | ### fP4.isreal() test is w real? That is in a+ib test b is zero **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.real() extract real part a **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.geta() extract a from this **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.getb() extract b from this **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.equals(x) Tests for equality of two FP4s **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | x | FP4 instance to compare | ### fP4.copy(x) Copy FP4 to another FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | x | FP4 instance to be copied | ### fP4.zero() Set FP4 to zero **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.one(x) Set FP4 to unity **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | x | FP4 instance to be set to one | ### fP4.set(c, d) Set FP4 from two FP2 values **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | c | FP2 instance | | d | FP2 instance | ### fP4.seta(c) Set FP4 from one FP2 value **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | c | FP2 instance | ### fP4.neg() Negation of FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.conj() Conjugation of FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.nconj() Negative conjugation of FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.add(x) addition of two FP4s **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | x | FP4 instance | ### fP4.sub(x) subtraction of two FP4s **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | x | FP4 instance | ### fP4.pmul(s) Multiplication of an FP4 by an FP8 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | s | FP8 instance | ### fP4.imul(s) Multiplication of an FP4 by an integer **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | s | integer multiplier | ### fP4.sqr() Fast Squaring of an FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.mul(y) Full unconditional Multiplication of two FP4s **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | y | FP4 instance, the multiplier | ### fP4.toString() convert to hex string **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.inverse() Inverting an FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.times\_i() multiplies an FP4 instance by irreducible polynomial sqrt(1+sqrt(-1)) **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.frob(f) Raises an FP4 to the power of the internal modulus p, using the Frobenius **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | f | Modulus | ### fP4.pow(e) Raises an FP4 to the power of a BIG **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | e | BIG instance exponent | ### fP4.xtr\_A(w, y, z) Calculates the XTR addition function r=w*x-conj(x)*y+z **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | w | FP4 instance | | y | FP4 instance | | z | FP4 instance | ### fP4.xtr\_D() Calculates the XTR doubling function r=x^2-2*conj(x) **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.xtr\_pow(n) Calculates FP4 trace of an FP4 raised to the power of a BIG number **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | n | Big number | ### fP4.xtr\_pow2() Calculates FP4 trace of c^a.d^b, where c and d are derived from FP4 traces of FP4s **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.div2() Divide an FP4 by 2 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.div\_i() Divide FP4 number by QNR **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.div\_2i() Divide an FP4 by QNR/2 **Kind**: instance method of [FP4](#FP4) **this**: {FP4} ### fP4.qmul(s) Multiplication of an FP4 by an FP **Kind**: instance method of [FP4](#FP4) **this**: {FP4} | Param | Description | | --- | --- | | s | FP multiplier | ### fP4.sqrt() Calculate square root of an FP4 **Kind**: instance method of [FP4](#FP4) **this**: {FP4}