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Avoiding full extension field arithmetic in pairing computations

Costello, Craig, Boyd, Colin, Gonzalez Nieto, Juan M., & Wong, Kenneth Koon-Ho (2010) Avoiding full extension field arithmetic in pairing computations. In Progress in Cryptology - AFRICACRYPT 2010, Springer Verlag, Stellenbosch, South Africa, pp. 203-224.

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    Abstract

    The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

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    3 citations in Scopus
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    2 citations in Web of Science®

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    ID Code: 34176
    Item Type: Conference Paper
    Additional URLs:
    Keywords: Pairings, Miller's algorithm, Tate pairing, ate pairing
    DOI: 10.1007/978-3-642-12678-9_13
    ISBN: 9783642126772
    Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
    Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
    Past > Institutes > Information Security Institute
    Copyright Owner: Copyright 2010 Springer
    Copyright Statement: This is the author-version of the work. Conference proceedings published by Springer Verlag, will be available via SpringerLink http://www.springer.de/comp/lncs/
    Deposited On: 20 Aug 2010 11:17
    Last Modified: 01 Mar 2012 00:17

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