Cryptology ePrint Archive: Report 2012/670

Fast Cryptography in Genus 2

Joppe W. Bos and Craig Costello and Huseyin Hisil and 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 4-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.

Category / Keywords: Genus 2, Jacobian, Kummer surface, GLV, Diffie-Hellman, speed record

Original Publication (with major differences): EUROCRYPT 2013

Date: received 27 Nov 2012, last revised 13 Mar 2014

Contact author: craigco at microsoft com

Available format(s): PDF | BibTeX Citation

Version: 20140313:182324 (All versions of this report)

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