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Conference Papers Year : 2022

Beyond quadratic speedups in quantum attacks on symmetric schemes


In this paper, we report the first quantum key-recovery attack on a symmetric block cipher design, using classical queries only, with a more than quadratic time speedup compared to the best classical attack. We study the 2XOR-Cascade construction of Gaži and Tessaro (EURO-CRYPT 2012). It is a key length extension technique which provides an n-bit block cipher with 5n 2 bits of security out of an n-bit block cipher with 2n bits of key, with a security proof in the ideal model. We show that the offline-Simon algorithm of Bonnetain et al. (ASIACRYPT 2019) can be extended to, in particular, attack this construction in quantum time O(2 n), providing a 2.5 quantum speedup over the best classical attack. Regarding post-quantum security of symmetric ciphers, it is commonly assumed that doubling the key sizes is a sufficient precaution. This is because Grover's quantum search algorithm, and its derivatives, can only reach a quadratic speedup at most. Our attack shows that the structure of some symmetric constructions can be exploited to overcome this limit. In particular, the 2XOR-Cascade cannot be used to generically strengthen block ciphers against quantum adversaries, as it would offer only the same security as the block cipher itself.
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Dates and versions

hal-03926591 , version 1 (06-01-2023)



Xavier Bonnetain, André Schrottenloher, Ferdinand Sibleyras. Beyond quadratic speedups in quantum attacks on symmetric schemes. EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, May 2022, Trondheim, Norway. pp.315-344, ⟨10.1007/978-3-031-07082-2_12⟩. ⟨hal-03926591⟩
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