(\mu)Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers (original) (raw)

Paper 2016/366

\(\mu\)Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers

Joost Renes, Peter Schwabe, Benjamin Smith, and Lejla Batina

Abstract

We describe the design and implementation of efficient signature and key-exchange schemes for the AVR~ATmega and ARM Cortex~M0 microcontrollers, targeting the 128-bit security level. Our algorithms are based on an efficient Montgomery ladder scalar multiplication on the Kummer surface of Gaudry and Schost's genus-2 hyperelliptic curve, combined with the Jacobian point recovery technique of Chung, Costello, and Smith. Our results are the first to show the feasibility of software-only hyperelliptic cryptography on constrained platforms, and represent a significant improvement on the elliptic-curve state-of-the-art for both key exchange and signatures on these architectures. Notably, our key-exchange scalar-multiplication software runs in under 9520k cycles on the ATmega and under 2640k cycles on the Cortex M0, improving on the current speed records by 32% and 75% respectively.

BibTeX

@misc{cryptoeprint:2016/366, author = {Joost Renes and Peter Schwabe and Benjamin Smith and Lejla Batina}, title = {(\mu)Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers}, howpublished = {Cryptology {ePrint} Archive, Paper 2016/366}, year = {2016}, url = {https://eprint.iacr.org/2016/366} }