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

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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Cryptographic Hardware and Embedded Systems – CHES 2016, Aug 2016, Santa Barbara, United States. Springer-Verlag, Lecture Notes in Computer Science, 9813, pp.20, 2016, Cryptographic Hardware and Embedded Systems – CHES 2016. 〈10.1007/978-3-662-53140-2_15〉
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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, Aug 2016, Santa Barbara, United States. Springer-Verlag, Lecture Notes in Computer Science, 9813, pp.20, 2016, Cryptographic Hardware and Embedded Systems – CHES 2016. 〈10.1007/978-3-662-53140-2_15〉. 〈hal-01300727〉

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