Cryptology ePrint Archive: Report 2021/1239

Quantum Linearization Attacks

Xavier Bonnetain and Gaëtan Leurent and María Naya-Plasencia and André Schrottenloher

Abstract: Recent works have shown that quantum period-finding can be used to break many popular constructions (some block ciphers such as Even-Mansour, multiple MACs and AEs...) in the superposition query model. So far, all the constructions broken exhibited a strong algebraic structure, which enables to craft a periodic function of a single input block. Recovering the secret period allows to recover a key, distinguish, break the confidentiality or authenticity of these modes.

In this paper, we introduce the \emph{quantum linearization attack}, a new way of using Simon's algorithm to target MACs in the superposition query model. Specifically, we use inputs of multiple blocks as an interface to a function hiding a linear structure. Recovering this structure allows to perform forgeries.

We also present some variants of this attack that use other quantum algorithms, which are much less common in quantum symmetric cryptanalysis: Deutsch's, Bernstein-Vazirani's, and Shor's. To the best of our knowledge, this is the first time these algorithms have been used in quantum forgery or key-recovery attacks.

Our attack breaks many parallelizable MACs such as LightMac, PMAC, and numerous variants with (classical) beyond-birthday-bound security (LightMAC+, PMAC) or using tweakable block ciphers (ZMAC). More generally, it shows that constructing parallelizable quantum-secure PRFs might be a challenging task.

Category / Keywords: secret-key cryptography / Quantum cryptanalysis, MACs, Superposition query model, Simon's algorithm, Deutsch's algorithm, Shor's algorithm, Bernstein-Vazirani algorithm

Original Publication (in the same form): IACR-ASIACRYPT-2021

Date: received 18 Sep 2021

Contact author: xavier bonnetain at uwaterloo ca, gaetan leurent at inria fr, maria naya_plasencia at inria fr, andre schrottenloher at m4x org

Available format(s): PDF | BibTeX Citation

Version: 20210920:114727 (All versions of this report)

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