Abstract
Mitaka is a lattice-based signature proposed at Eurocrypt 2022. A key advertised feature of Mitaka is that it can be masked at high orders efficiently, making it attractive in scenarios where side-channel attacks are a concern. Mitaka comes with a claimed security proof in the t-probing model.
We uncover a flaw in the security proof of Mitaka, and subsequently show that it is not secure in the t-probing model. For any number of shares \(d \ge 4\), probing \(t < d\) variables per execution allows an attacker to recover the private key efficiently with approximately \(2^{21}\) executions. Our analysis shows that even a constant number of probes suffices (\(t = 3\)), as long as the attacker has access to a number of executions that is linear in d/t.
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Notes
- 1.
In [EFG+22], it is shown that \(\Vert \textbf{b}_0\Vert \le \alpha \sqrt{q}\), with \(\alpha \approx 2.04\) for Mitaka-512 and \(\alpha \approx 2.33\) for Mitaka-1024.
- 2.
Alternatively, (19) implies that pure rounding requires \(\sigma _X \lesssim 0.1066\) to be practical. Hence it is applicable on a more narrow range than our guessing-based approach.
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Acknowledgements
I would like to thank Mélissa Rossi, Thomas Espitau, Alexandre Wallet, Morgane Guerreau and Eamonn Postlethwaite for useful discussions about [EFG+22, GMRR22], and the attack presented in this paper. I am particularly grateful to my PQShield colleagues Rafaël del Pino and Fabrice Mouhartem for discussing the subtleties of lattice attacks with me. Finally, I would like to thank the anonymous reviewers of PKC 2023 for their insightful comments.
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Prest, T. (2023). A Key-Recovery Attack Against Mitaka in the t-Probing Model. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13940. Springer, Cham. https://doi.org/10.1007/978-3-031-31368-4_8
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