An Analysis of Affine Coordinates for Pairing Computation

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. Thi...

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Bibliographic Details
Published inPairing-Based Cryptography - Pairing 2010 pp. 1 - 20
Main Authors Lauter, Kristin, Montgomery, Peter L., Naehrig, Michael
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
affine coordinates
finite field inversions
multiple pairings
optimal ate pairing
Pairing computation
pairing cost
pairing products
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Summary: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.
ISBN:9783642174544
364217454X
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-17455-1_1