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Rotational-XOR Differential Rectangle Cryptanalysis on Simon-Like Ciphers

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Topics in Cryptology – CT-RSA 2023 (CT-RSA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13871))

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Abstract

In this paper, we propose a rectangle-like method called rotational-XOR differential rectangle attack to search for better distinguishers. It is a combination of the rotational-XOR cryptanalysis and differential cryptanalysis in the rectangle-based way. In particular, we put a rotational-XOR characteristic before a differential characteristic to construct a rectangle structure. By choosing some appropriate rotational-XOR and differential characteristics as well as considering multiple differentials, some longer distinguishers that have the probability greater than \(2^{-2n}\) can be constructed effectively where n is the block size of a block cipher. We apply this new method to some versions of Simon and Simeck block ciphers. As a result, we obtain rotational-XOR differential rectangle distinguishers up to 16, 16, 17, 16 and 21 rounds for Simon32/64, Simon48/72, Simon48/96, Simeck32 and Simeck48, respectively. Our distinguishers for Simon32/64 and Simon48/96 are both longer than the best differential and rotational-XOR distinguishers. Also, our distinguisher for Simeck32 is longer than the best differential distinguisher (14 rounds) and has the full weak key space (i.e., \(2^{64}\)) whereas the 16-round rotational-XOR distinguisher has a weak key class of \(2^{36}\). In addition, our distinguisher for Simeck48 has a better weak key class (\(2^{72}\) weak keys) than the 21-round rotational-XOR distinguisher (\(2^{60}\) weak keys). To the best of our knowledge, this is the first time to consider the combinational cryptanalysis based on rotational-XOR and differential cryptanalysis using the rectangle structure.

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Acknowledgement

We would like to thank Maria Eichlseder and all the anonymous reviewers for their valuable comments to improve the quality of this paper. This work was supported by the National Natural Science Foundation of China (No. 62272147), the Science and Technology on Communication Security Laboratory Foundation (No. 6142103012207), the Research Foundation of Department of Education of Hubei Province (No. D2020104) and the Wuhan Science and Technology Bureau (NO. 2022010801020328).

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Authors and Affiliations

  1. School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China

    Siwei Chen, Mingming Zhu, Zejun Xiang, Runqing Xu & Shasha Zhang

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Xiangyong Zeng

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  1. Siwei Chen
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Correspondence to Zejun Xiang .

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  1. Oregon State University, Corvallis, OR, USA

    Mike Rosulek

Algorithm to Calculate \(\tilde{q}\) for Simon-Like Ciphers

Algorithm to Calculate \(\tilde{q}\) for Simon-Like Ciphers

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Chen, S., Zhu, M., Xiang, Z., Xu, R., Zeng, X., Zhang, S. (2023). Rotational-XOR Differential Rectangle Cryptanalysis on Simon-Like Ciphers. In: Rosulek, M. (eds) Topics in Cryptology – CT-RSA 2023. CT-RSA 2023. Lecture Notes in Computer Science, vol 13871. Springer, Cham. https://doi.org/10.1007/978-3-031-30872-7_12

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  • DOI: https://doi.org/10.1007/978-3-031-30872-7_12

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