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International Conference on Information Security and Cryptology

Inscrypt 2017: Information Security and Cryptology pp 404–426Cite as

Improved Cryptanalysis of an ISO Standard Lightweight Block Cipher with Refined MILP Modelling

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10726))

Abstract

Differential and linear cryptanalysis are two of the most effective attacks on block ciphers. Searching for (near) optimal differential or linear trails is not only useful for the security evaluation of block ciphers against these attacks, but also indispensable to the cryptanalysts who want to attack a cipher with these techniques. In recent years, searching for trails automatically with Mixed-Integer Linear Programming (MILP) gets a lot of attention. At first, Mouha et al. translated the problem of counting the minimum number of differentially active S-boxes into an MILP problem for word-oriented block ciphers. Subsequently, in Asiacrypt 2014, Sun et al. extended Mouha et al.’s method, and presented a technique which can find actual differential or linear characteristics of a block cipher in both the single-key and related-key models. In this paper, we refine the constraints of the 2-XOR operation in order to reduce the overall number of variables and constraints. Experimental results show that MILP models with the refined constraints can be solved more efficiently. We apply our method to HIGHT (an ISO standard), and we find differential (covering 11 rounds) or linear trails (covering 10 rounds) with higher probability or correlation. Moreover, we find so far the longest differential and linear distinguishers of HIGHT.

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Notes

  1. 1.

    In [5], the 10-round linear approximation with \(\varepsilon ^{2}=2^{-54}\), \(\varepsilon \) is called bias. Correspondingly, converted into the 10-round linear approximation with correlation \(2^{-26}\).

  2. 2.

    The Figs. 1, 2 and 3 are generated by TikZ for Cryptographers, please refer to http://www.iacr.org/authors/tikz/.

  3. 3.

    The constraints appear in the slide that Sasaki et al. were reported in Eurocrypt 2017, please refer to https://eurocrypt2017.di.ens.fr/slides/A09-new-impossible-differential.pdf

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions. The work of this paper was supported by the National Natural Science Foundation of China (61772519, 61502532, 61379150, 61309016, 61502529), the Open Foundation of the Key State Key Laboratory of Mathematical Engineering and Advanced Computing (2016A02), and the State Key Laboratory of Information Security. The work of Jun Yin and Lijun Lyu is supported by the Youth Innovation Promotion Association of Chinese Academy of Sciences.

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Authors and Affiliations

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450001, China

    Jun Yin, Jian Song, Guang Zeng & Fushan Wei

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Fushan Wei

  3. Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Jun Yin & Lijun Lyu

  4. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, 100093, China

    Jun Yin & Lijun Lyu

  5. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, China

    Jun Yin & Lijun Lyu

  6. National University of Defense Technology, Changsha, 410073, China

    Chuyan Ma

  7. Army Aviation Institute, Beijing, 101116, China

    Chuangui Ma

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Correspondence to Jun Yin .

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  1. Xidian University, Xi’an, China

    Xiaofeng Chen

  2. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  3. Columbia University, New York, New York, USA

    Moti Yung

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Yin, J. et al. (2018). Improved Cryptanalysis of an ISO Standard Lightweight Block Cipher with Refined MILP Modelling. In: Chen, X., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2017. Lecture Notes in Computer Science(), vol 10726. Springer, Cham. https://doi.org/10.1007/978-3-319-75160-3_24

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  • DOI: https://doi.org/10.1007/978-3-319-75160-3_24

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