High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition

  • Joppe W. Bos
  • Craig Costello
  • Huseyin Hisil
  • Kristin Lauter
Conference paper

DOI: 10.1007/978-3-642-40349-1_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8086)
Cite this paper as:
Bos J.W., Costello C., Hisil H., Lauter K. (2013) High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition. In: Bertoni G., Coron JS. (eds) Cryptographic Hardware and Embedded Systems - CHES 2013. CHES 2013. Lecture Notes in Computer Science, vol 8086. Springer, Berlin, Heidelberg

Abstract

This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography, motivated by the fact that they allow for an 8-dimensional scalar decomposition when using a combination of the GLV/GLS algorithms. Besides lowering the number of doublings required in a scalar multiplication, this approach has the advantage of performing arithmetic operations in a 64-bit ground field, making it an attractive candidate for embedded devices. We found cryptographically secure genus 2 curves which, although susceptible to index calculus attacks, aim for the standardized 112-bit security level. Our implementation results on both high-end architectures (Ivy Bridge) and low-end ARM platforms (Cortex-A8) highlight the practical benefits of this approach.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joppe W. Bos
    • 1
  • Craig Costello
    • 1
  • Huseyin Hisil
    • 2
  • Kristin Lauter
    • 1
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Yasar UniversityIzmirTurkey

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