Fast Cryptography in Genus 2

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

Paper 2012/670

Fast Cryptography in Genus 2

Joppe W. Bos, Craig Costello, 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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Major revision. EUROCRYPT 2013
DOI: 10.1007/978-3-642-38348-9_12
Keywords: Genus 2 Jacobian Kummer surface GLV Diffie-Hellman speed record
Contact author(s): craigco @ microsoft com
History: 2014-03-13: last of 5 revisions; 2012-11-28: received; See all versions
Short URL: https://ia.cr/2012/670
License: CC BY

BibTeX

@misc{cryptoeprint:2012/670,
      author = {Joppe W.  Bos and Craig Costello and Huseyin Hisil and Kristin Lauter},
      title = {Fast Cryptography in Genus 2},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/670},
      year = {2012},
      doi = {10.1007/978-3-642-38348-9_12},
      url = {https://eprint.iacr.org/2012/670}
}