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

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.