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Paper 2016/366

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

Joost Renes and Peter Schwabe and 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.

Metadata
Available format(s)
PDF
Publication info
Published by the IACR in CHES 2016
Keywords
Hyperelliptic curve cryptographyKummer surfaceAVR ATmegaARM Cortex M0
Contact author(s)
j renes @ cs ru nl
History
2017-01-26: last of 3 revisions
2016-04-12: received
See all versions
Short URL
https://ia.cr/2016/366
License
Creative Commons Attribution
CC BY
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