Abstract
AbstractIn the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of \((1/4)\lfloor \log_2 r\rfloor\). On the other hand, the twisted Ate pairing requires \((3/4) \lfloor \log_2 r\rfloor\) loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposal splits the Miller’s algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Miller’s algorithm for the proposed twisted Ate pairing is equal to the \((1/4) \lfloor \log_2 r \rfloor\) attained by the most efficient Ate pairings.Keywords twisted Ate pairingMiller’s algorithmFrobenius map multi–pairing thread computing
Published Version
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