## PAIR **Kind**: global class **this**: {PAIR} * [PAIR](#PAIR) * [new PAIR()](#new_PAIR_new) * [.line()](#PAIR.line) * [.initmp()](#PAIR.initmp) * [.miller(r, res)](#PAIR.miller) * [.another(r, P1, Q1)](#PAIR.another) * [.ate(P1, Q1)](#PAIR.ate) * [.ate2(P1, Q1, R1, S1)](#PAIR.ate2) * [.fexp(m)](#PAIR.fexp) * [.lbits()](#PAIR.lbits) * [.glv()](#PAIR.glv) * [.gs()](#PAIR.gs) * [.G1mul(P, e)](#PAIR.G1mul) ⇒ * [.G2mul(P, e)](#PAIR.G2mul) ⇒ * [.GTpow(d, e)](#PAIR.GTpow) ⇒ ### new PAIR() Creates an instance of PAIR ### PAIR.line() Line function **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} ### PAIR.initmp() prepare for multi-pairing **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} ### PAIR.miller(r, res) basic Miller loop **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} | Param | Description | | --- | --- | | r | FP12 precomputed array of accumulated line functions | | res | FP12 result | ### PAIR.another(r, P1, Q1) Precompute line functions for n-pairing **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} | Param | Description | | --- | --- | | r | array of precomputed FP48 products of line functions | | P1 | An element of G2 | | Q1 | An element of G1 | ### PAIR.ate(P1, Q1) Calculate Miller loop for Optimal ATE pairing e(P,Q) **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} **Result**: r An element of GT i.e. result of the pairing calculation e(P,Q) | Param | Description | | --- | --- | | P1 | An element of G2 | | Q1 | An element of G1 | ### PAIR.ate2(P1, Q1, R1, S1) Calculate Miller loop for Optimal ATE double-pairing e(P,Q).e(R,S) **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} **Result**: r An element of GT i.e. result of the double pairing calculation e(P,Q).e(R,S) | Param | Description | | --- | --- | | P1 | An element of G2 | | Q1 | An element of G1 | | R1 | An element of G2 | | S1 | An element of G1 | ### PAIR.fexp(m) Final exponentiation of pairing, converts output of Miller loop to element in GT **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} **Result**: r m^((p^12-1)/r) where p is modulus and r is the group order | Param | Description | | --- | --- | | m | FP12 value | ### PAIR.lbits() prepare ate parameter, n=6u+2 (BN) or n=u (BLS), n3=3*n **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} ### PAIR.glv() GLV method **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} ### PAIR.gs() Galbraith & Scott Method **Kind**: static method of [PAIR](#PAIR) **this**: {PAIR} ### PAIR.G1mul(P, e) ⇒ Fast point multiplication of a member of the group G1 by a BIG number **Kind**: static method of [PAIR](#PAIR) **Returns**: R Member of G1 R=e.P **this**: {PAIR} | Param | Description | | --- | --- | | P | Member of G1 | | e | BIG multiplier | ### PAIR.G2mul(P, e) ⇒ Multiply P by e in group G2 **Kind**: static method of [PAIR](#PAIR) **Returns**: R Member of G2 R=e.P **this**: {PAIR} | Param | Description | | --- | --- | | P | Member of G2 | | e | BIG multiplier | ### PAIR.GTpow(d, e) ⇒ Fast raising of a member of GT to a BIG power **Kind**: static method of [PAIR](#PAIR) **Returns**: r d^e **this**: {PAIR} | Param | Description | | --- | --- | | d | Member of GT | | e | BIG exponent |