Abstract
This paper considers a model for elliptic curve named Selmer curves. We study the arithmetic of Selmer curves, which includes group operations and pairing computation. We present fast formulae for point addition and doubling. Moreover, for even embedding degree k, we show that Tate pairing computation on Selmer curves is very efficient. It is almost the fastest among that on various elliptic curve models such as Weierstrass curves, Edwards curves, Hessian curves, etc.. One more advantage which Selmer curves gain over other models is that pairing computation on this model can be performed in a parallel manner. In addition, the higher twists (up to sextic twists) technique can also be applied to Selmer curves for accelerating pairing computation. We finally present some numerical examples of pairing friendly Selmer curves which can employ sextic twists.
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