Fast Cryptography in Genus 2 View Full Text


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Article Info

DATE

2016-01

AUTHORS

Joppe W. Bos, Craig Costello, Huseyin Hisil, Kristin Lauter

ABSTRACT

In this paper, we highlight the benefits of using genus 2 curves in public-key cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically more involved but allows us to work with moduli of half the size. We give a taxonomy of the best known techniques to realize genus 2-based cryptography, which includes fast formulas on the Kummer surface and efficient four-dimensional GLV decompositions. By studying different modular arithmetic approaches on these curves, we present a range of genus 2 implementations. On a single core of an Intel Core i7-3520M (Ivy Bridge), our implementation on the Kummer surface breaks the 125 thousand cycle barrier which sets a new software speed record at the 128-bit security level for constant-time scalar multiplications compared to all previous genus 1 and genus 2 implementations. More... »

PAGES

28-60

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    http://scigraph.springernature.com/pub.10.1007/s00145-014-9188-7

    DOI

    http://dx.doi.org/10.1007/s00145-014-9188-7

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    https://app.dimensions.ai/details/publication/pub.1023105834


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