Cryptanalysis of Elisabeth-4 - Université de Versailles Saint-Quentin-en-Yvelines
Article Dans Une Revue Lecture Notes in Computer Science Année : 2023

Cryptanalysis of Elisabeth-4

Résumé

Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of 2$^{88}$ elementary operations, a memory complexity of 2$^{54}$ bits and a data complexity of 2$^{41}$ bits. Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity. We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.
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hal-04477478 , version 1 (13-06-2024)

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Henri Gilbert, Rachelle Heim Boissier, Jérémy Jean, Jean-René Reinhard. Cryptanalysis of Elisabeth-4. Lecture Notes in Computer Science, 2023, Advances in Cryptology – ASIACRYPT 2023 29th International Conference on the Theory and Application of Cryptology and Information Security, Guangzhou, China, December 4–8, 2023, Proceedings, Part III, 14440, pp.256-284. ⟨10.1007/978-981-99-8727-6_9⟩. ⟨hal-04477478⟩
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