## FP12 **Kind**: global class **this**: {FP12} * [FP12](#FP12) * [new FP12()](#new_FP12_new) * _instance_ * [.reduce()](#FP12+reduce) * [.norm()](#FP12+norm) * [.iszilch()](#FP12+iszilch) * [.isunity()](#FP12+isunity) * [.cmove(g, d)](#FP12+cmove) * [.select()](#FP12+select) * [.geta()](#FP12+geta) * [.getb()](#FP12+getb) * [.getc()](#FP12+getc) * [.equals(x)](#FP12+equals) * [.copy(x)](#FP12+copy) * [.one(x)](#FP12+one) * [.zero()](#FP12+zero) * [.conj()](#FP12+conj) * [.set(d, e, f)](#FP12+set) * [.seta(d)](#FP12+seta) * [.usqr()](#FP12+usqr) * [.sqr()](#FP12+sqr) * [.mul(y)](#FP12+mul) * [.smul(y)](#FP12+smul) * [.ssmul(y)](#FP12+ssmul) * [.inverse()](#FP12+inverse) * [.frob(f)](#FP12+frob) * [.trace()](#FP12+trace) * [.toString()](#FP12+toString) * [.toBytes(w)](#FP12+toBytes) * [.pow(e)](#FP12+pow) * [.pinpow(e, bts)](#FP12+pinpow) * [.compow(e, r)](#FP12+compow) * _static_ * [.fromBytes(w)](#FP12.fromBytes) * [.teq()](#FP12.teq) * [.pow4()](#FP12.pow4) ### new FP12() Creates an instance of FP12. ### fP12.reduce() Reduces all components of possibly unreduced FP12 mod Modulus **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.norm() Normalises the components of an FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.iszilch() Tests for FP12 equal to zero **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.isunity() Tests for FP12 equal to unity **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.cmove(g, d) Conditional copy of FP12 number **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | g | FP12 instance | | d | copy depends on this value | ### fP12.select() Constant time select from pre-computed table **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.geta() extract a from this **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.getb() extract b from this **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.getc() extract c from this **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.equals(x) Tests for equality of two FP12s **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | x | FP12 instance to compare | ### fP12.copy(x) Copy FP12 to another FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | x | FP12 instance to be copied | ### fP12.one(x) Set FP12 to unity **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | x | FP12 instance to be set to one | ### fP12.zero() Set FP12 to zero **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.conj() Conjugation of FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.set(d, e, f) Set FP12 from three FP4 values **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | d | FP4 instance | | e | FP4 instance | | f | FP4 instance | ### fP12.seta(d) Set FP12 from one FP4 value **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | d | FP4 instance | ### fP12.usqr() Fast Squaring of an FP12 in "unitary" form **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.sqr() Fast Squaring of an FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.mul(y) Full unconditional Multiplication of two FP12s **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | y | FP12 instance, the multiplier | ### fP12.smul(y) Fast multiplication of two sparse FP12s that arises from ATE pairing line functions **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | y | FP12 instance, the multiplier | ### fP12.ssmul(y) Fast multiplication of what may be sparse multiplicands **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | y | FP12 instance, the multiplier | ### fP12.inverse() Inverting an FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.frob(f) Raises an FP12 to the power of the internal modulus p, using the Frobenius **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | f | Modulus | ### fP12.trace() Calculate the trace of an FP12 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.toString() convert this to hex string **Kind**: instance method of [FP12](#FP12) **this**: {FP12} ### fP12.toBytes(w) convert this to byte array **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | w | Byte array | ### fP12.pow(e) Raises an FP12 to the power of a BIG **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | e | BIG instance exponent | ### fP12.pinpow(e, bts) Raises an FP12 instance x to a small integer power, side-channel resistant **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | e | small integer exponent | | bts | maximum number of bits in exponent | ### fP12.compow(e, r) Raises an FP12 instance to a BIG power, compressed to FP4 **Kind**: instance method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | e | BIG exponent | | r | BIG group order | ### FP12.fromBytes(w) convert from byte array to FP12 **Kind**: static method of [FP12](#FP12) **this**: {FP12} | Param | Description | | --- | --- | | w | Byte array | ### FP12.teq() return 1 if b==c, no branching **Kind**: static method of [FP12](#FP12) **this**: {FP12} ### FP12.pow4() p=q0^u0.q1^u1.q2^u2.q3^u3 **Kind**: static method of [FP12](#FP12) **this**: {FP12}