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

Joost Renes 1 Peter Schwabe 1 Benjamin Smith 2, 3 Lejla Batina 1
1 Digital Security Group [Nijmegen]
ICIS - Institute for Computing and Information Sciences [Nijmegen]
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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 Costello, Chung, 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 9740k cycles on the ATmega, and under 2650k cycles on the Cortex M0.
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https://hal.inria.fr/hal-01300727
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Submitted on : Monday, April 11, 2016 - 1:38:34 PM
Last modification on : Thursday, March 5, 2020 - 6:33:26 PM
Long-term archiving on: : Tuesday, July 12, 2016 - 11:33:09 AM

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Joost Renes, Peter Schwabe, Benjamin Smith, Lejla Batina. $\mu$Kummer: efficient hyperelliptic signatures and key exchange on microcontrollers. Cryptographic Hardware and Embedded Systems – CHES 2016, IACR, Aug 2016, Santa Barbara, United States. pp.20, ⟨10.1007/978-3-662-53140-2_15⟩. ⟨hal-01300727⟩

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