Efficient Non Symmetric Pairing Groups on Ordinary Pairing Friendly Curve of Embedding Degree 1

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 Rate 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.