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Title:
Quantum Cryptanalysis on Contracting Feistel Structures and Observation on Related-key Settings
Authors: Carlos Cid, Akinori Hosoyamada, Yunwen Liu, Siang Meng Sim
Abstract:In this paper we show several quantum chosen-plaintext attacks (qCPAs) on contracting Feistel structures. In the classical setting, a d-branch r-round contracting Feistel structure can be shown to be PRP-secure when d is even and r \geq 2d-1, meaning it is secure against polynomial-time chosen-plaintext attacks. We propose a polynomial-time qCPA distinguisher on the d-branch (2d-1)-round contracting Feistel structure, which solves an open problem by Dong et al. In addition, we show a polynomial-time qCPA that recovers the keys of the d-branch r-round contracting Feistel structure when each round function F^{(i)}_{k_i} has the form F^{(i)}_{k_i}(x) = F_i(x \oplus k_i) for a public random function F_i. This is applicable to the Chinese block cipher standard {\texttt{SM4}}, which is a special case where d=4. Finally, in addition to quantum attacks under single-key setting, we also show related-key quantum attacks on balanced Feistel structures in the model that adversaries can only control part of the key difference in quantum superposition. Our related-key attacks on balanced Feistel structures can easily be extended to ones on contracting Feistel structures.
ePrint: https://eprint.iacr.org/2020/959
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