Affine pairings on ARM

T. Acar, K. Lauter, M. Naehrig, D. Shumow

    Research output: Book/ReportReportAcademic

    Abstract

    Pairings on elliptic curves are being used in an increasing number of cryptographic applications on many different devices and platforms, but few performance numbers for cryptographic pairings have been reported on embedded and mobile devices. In this paper we give performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor and compare performance of the same implementation across three platforms: x86, x86-64 and ARM. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to convert to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs on all three platforms. This favors using affine coordinates for pairing implementations, even for the current 128-bit minimum security level specified by NIST. Our implementation shows another platform where affine coordinates are a better choice. We compare with other reported performance numbers on ARM processors and find that our implementation of affine pairings compares favorably.
    Original languageEnglish
    PublisherIACR
    Number of pages14
    Publication statusPublished - 2011

    Publication series

    NameCryptology ePrint Archive
    Volume2011/243

    Fingerprint

    ARM processors
    Mobile devices
    Costs

    Cite this

    Acar, T., Lauter, K., Naehrig, M., & Shumow, D. (2011). Affine pairings on ARM. (Cryptology ePrint Archive; Vol. 2011/243). IACR.
    Acar, T. ; Lauter, K. ; Naehrig, M. ; Shumow, D. / Affine pairings on ARM. IACR, 2011. 14 p. (Cryptology ePrint Archive).
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    Acar, T, Lauter, K, Naehrig, M & Shumow, D 2011, Affine pairings on ARM. Cryptology ePrint Archive, vol. 2011/243, IACR.

    Affine pairings on ARM. / Acar, T.; Lauter, K.; Naehrig, M.; Shumow, D.

    IACR, 2011. 14 p. (Cryptology ePrint Archive; Vol. 2011/243).

    Research output: Book/ReportReportAcademic

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    N2 - Pairings on elliptic curves are being used in an increasing number of cryptographic applications on many different devices and platforms, but few performance numbers for cryptographic pairings have been reported on embedded and mobile devices. In this paper we give performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor and compare performance of the same implementation across three platforms: x86, x86-64 and ARM. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to convert to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs on all three platforms. This favors using affine coordinates for pairing implementations, even for the current 128-bit minimum security level specified by NIST. Our implementation shows another platform where affine coordinates are a better choice. We compare with other reported performance numbers on ARM processors and find that our implementation of affine pairings compares favorably.

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    Acar T, Lauter K, Naehrig M, Shumow D. Affine pairings on ARM. IACR, 2011. 14 p. (Cryptology ePrint Archive).