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

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

Paper 2013/146

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

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

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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: GLV GLS Genus 2
Contact author(s): jbos @ microsoft com
History: 2013-03-14: received
Short URL: https://ia.cr/2013/146
License: CC BY

BibTeX

@misc{cryptoeprint:2013/146,
      author = {Joppe W.  Bos and Craig Costello and Huseyin Hisil and Kristin Lauter},
      title = {High-Performance Scalar Multiplication using 8-Dimensional GLV/GLS Decomposition},
      howpublished = {Cryptology ePrint Archive, Paper 2013/146},
      year = {2013},
      note = {\url{https://eprint.iacr.org/2013/146}},
      url = {https://eprint.iacr.org/2013/146}
}