Advances in Cryptology – EUROCRYPT 2013

Volume 7881 of the series Lecture Notes in Computer Science pp 194-210

Fast Cryptography in Genus 2

  • Joppe W. BosAffiliated withMicrosoft Research
  • , Craig CostelloAffiliated withMicrosoft Research
  • , Huseyin HisilAffiliated withYasar University
  • , Kristin LauterAffiliated withMicrosoft Research

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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 120 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.