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In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, the authors study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller's algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. They propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation.
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