Abstract
Lyubashevky’s signatures are based on the Fiat-Shamir with Aborts paradigm. It transforms an interactive identification protocol that has a non-negligible probability of aborting into a signature by repeating executions until a loop iteration does not trigger an abort. Interaction is removed by replacing the challenge of the verifier by the evaluation of a hash function, modeled as a random oracle in the analysis. The access to the random oracle is classical (ROM), resp. quantum (QROM), if one is interested in security against classical, resp. quantum, adversaries. Most analyses in the literature consider a setting with a bounded number of aborts (i.e., signing fails if no signature is output within a prescribed number of loop iterations), while practical instantiations (e.g., Dilithium) run until a signature is output (i.e., loop iterations are unbounded).
In this work, we emphasize that combining random oracles with loop iterations induces numerous technicalities for analyzing correctness, run-time, and security of the resulting schemes, both in the bounded and unbounded case. As a first contribution, we put light on errors in all existing analyses. We then provide two detailed analyses in the QROM for the bounded case, adapted from Kiltz et al [EUROCRYPT’18] and Grilo et al [ASIACRYPT’21]. In the process, we prove the underlying \(\varSigma \)-protocol to achieve a stronger zero-knowledge property than usually considered for \(\varSigma \)-protocols with aborts, which enables a corrected analysis. A further contribution is a detailed analysis in the case of unbounded aborts, the latter inducing several additional subtleties.
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Acknowledgments
We thank Andreas Hülsing, Chistian Majenz, and Thomas Prest for helpful discussions. This work was supported by the ANR Project ANR-21-ASTR-0016 AMIRAL, the France 2030 ANR Project ANR-22-PECY-003 SecureCompute, and the France 2030 ANR Project ANR-22-PETQ-0008 PQ-TLS.
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Devevey, J., Fallahpour, P., Passelègue, A., Stehlé, D. (2023). A Detailed Analysis of Fiat-Shamir with Aborts. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14085. Springer, Cham. https://doi.org/10.1007/978-3-031-38554-4_11
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