An analysis of affine coordinates for pairing computation

K. Lauter, P.L. Montgomery, M. Naehrig

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    27 Citations (Scopus)
    124 Downloads (Pure)


    In this paper we analyze the use of affine coordinates for pairing computation. We observe that in many practical settings, e. g. when implementing optimal ate pairings in high security levels, affine coordinates are faster than using the best currently known formulas for projective coordinates. This observation relies on two known techniques for speeding up field inversions which we analyze in the context of pairing computation. We give detailed performance numbers for a pairing implementation based on these ideas, including timings for base field and extension field arithmetic with relative ratios for inversion-to-multiplication costs, timings for pairings in both affine and projective coordinates, and average timings for multiple pairings and products of pairings. Keywords: Pairing computation - affine coordinates - optimal ate pairing - finite field inversions - pairing cost - multiple pairings - pairing products.
    Original languageEnglish
    Title of host publicationPairing-Based Cryptography - Pairing 2010 (4th International Conference, Yamanaka Hot Spring, Japan, December 2010. Proceedings)
    EditorsM. Joye, A. Miyaji, A. Otsuka
    Place of PublicationBerlin
    Publication statusPublished - 2010

    Publication series

    NameLecture Notes in Computer Science
    ISSN (Print)0302-9743


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