Abstract
In the last few years, post-quantum cryptography has received much attention. NIST is running a competition to select some post-quantum schemes as standard. As a consequence, implementations of post-quantum schemes have become important and with them side-channel attacks. In this paper, we show a timing attack on a code-based scheme which was submitted to the NIST competition. This timing attack recovers secret information because of a timing variance in finding roots in a polynomial. We present four algorithms to find roots that are protected against remote timing exploitation.
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001; through the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 643161; and by Sweden through the WASP expedition project Massive, Secure, and Low-Latency Connectivity for IoT Applications.
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Notes
- 1.
available in https://git.dags-project.org/gustavo/roots_finding.
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Acknowledgments
We want to thank the reviewers for the thoughtful comments on this work. We would also like to thank Tanja Lange for her valuable feedback. We want to extend the acknowledgments to Sonia Belaïd from Cryptoexperts for the discussions about timing attacks.
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Martins, D., Banegas, G., Custódio, R. (2019). Don’t Forget Your Roots: Constant-Time Root Finding over \(\mathbb {F}_{2^m}\). In: Schwabe, P., Thériault, N. (eds) Progress in Cryptology – LATINCRYPT 2019. LATINCRYPT 2019. Lecture Notes in Computer Science(), vol 11774. Springer, Cham. https://doi.org/10.1007/978-3-030-30530-7_6
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