Paper 2023/178

Rotational-XOR Differential Rectangle Cryptanalysis on Simon-like Ciphers

Siwei Chen, Hubei University
Mingming Zhu, Hubei University
Zejun Xiang, Hubei University
Runqing Xu, Hubei University
Xiangyong Zeng, Hubei University
Shasha Zhang, Hubei University

In this paper, we propose a rectangle-like method called \textit{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 \textsc{Simon} and \textsc{Simeck} block ciphers. As a result, we obtain rotational-XOR differential rectangle distinguishers up to 16, 16, 17, 16 and 21 rounds for \textsc{Simon}32/64, \textsc{Simon}48/72, \textsc{Simon}48/96, \textsc{Simeck}32 and \textsc{Simeck}48, respectively. Our distinguishers for \textsc{Simon}32/64 is longer than the best differential and rotational-XOR distinguishers. As for \textsc{Simon}48/96, the distinguisher is longer than the rotational-XOR distinguisher and as long as the best differential distinguisher. Also, our distinguisher for \textsc{Simeck}32 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 \textsc{Simeck}48 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.

Available format(s)
Attacks and cryptanalysis
Publication info
Published elsewhere. CT-RSA 2023
Rotational-XOR cryptanalysisDifferential cryptanalysisRectangleSimonSimeckDistinguisher
Contact author(s)
chensiwei_hubu @ 163 com
1942742852 @ qq com
xiangzejun @ hubu edu cn
xu_runqing @ foxmail com
xzeng @ hubu edu cn
amushasha @ 163 com
2023-02-16: revised
2023-02-13: received
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Creative Commons Attribution


      author = {Siwei Chen and Mingming Zhu and Zejun Xiang and Runqing Xu and Xiangyong Zeng and Shasha Zhang},
      title = {Rotational-XOR Differential Rectangle Cryptanalysis on Simon-like Ciphers},
      howpublished = {Cryptology ePrint Archive, Paper 2023/178},
      year = {2023},
      note = {\url{}},
      url = {}
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