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Recently, ordinary pairing - friendly elliptic curves whose embedding degree is 1 have been often focused on, for example some composite order pairing - based cryptographies do. In the case of non - symmetric pairings whose embedding degree is larger than 2, recent efficient pairing techniques such as R - ate and Xate pairings adopt a certain special rational point group with an efficient isomorphic mapping and then accelerate pairing - related operations such as a pairing calculation and a scalar multiplication. Based on cubic, quartic, and sextic twists, this paper shows how to activate these efficient techniques together with point compression on pairing - friendly curves of embedding degree 1.
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