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Optimal pairing computation over families of pairing-friendly elliptic curves

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log2 r)/φ(k) + log2 k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455–461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224–280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224–280, 2010) by taking the Ate or R-ate pairing approach.

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Author notes

  1. Cheol-Min Park

    Present address: National Institute for Mathematical Sciences (NIMS), Daejeon, Korea

Authors and Affiliations

  1. Department of Mathematics, Ewha Womans University, Seoul, Korea

    Soo-Kyung Eom, Hyang-Sook Lee & Cheol-Min Park

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  1. Soo-Kyung Eom
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  2. Hyang-Sook Lee
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Correspondence to Hyang-Sook Lee.

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Eom, SK., Lee, HS. & Park, CM. Optimal pairing computation over families of pairing-friendly elliptic curves. AAECC 22, 235–248 (2011). https://doi.org/10.1007/s00200-011-0146-4

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  • DOI: https://doi.org/10.1007/s00200-011-0146-4

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