\(\mu \)Kummer: Efficient Hyperelliptic Signatures and Key Exchange on Microcontrollers
- Cite this paper as:
- Renes J., Schwabe P., Smith B., Batina L. (2016) $$\mu $$Kummer: Efficient Hyperelliptic Signatures and Key Exchange on Microcontrollers. In: Gierlichs B., Poschmann A. (eds) Cryptographic Hardware and Embedded Systems – CHES 2016. CHES 2016. Lecture Notes in Computer Science, vol 9813. Springer, Berlin, Heidelberg
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.