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On the Provable Security Against Truncated Impossible Differential Cryptanalysis for AES in the Master-Key Setting

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Information Security and Cryptology (Inscrypt 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13007))

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Abstract

Impossible differential cryptanalysis is a powerful cryptanalysis technique of block ciphers. Length of impossible differentials is important for the security evaluation of a block cipher against impossible differential cryptanalysis. Many previous studies on finding impossible differentials of AES assumed that round keys are independent and uniformly random. There are few results on security evaluation of AES in the master-key setting. In ASIACRYPT 2020, Hu et al. redefined impossible differential with the key schedule considered, and showed that there exists no one-byte active input and one-byte active output impossible differential for 5-round AES-128 even considering the relations of 3-round keys. In this paper, we prove theoretically that even though the relations of all round keys are considered, there do not exist three kinds of truncated impossible differentials for 5-round AES: (1) the input truncated differences are nonzero only in any diagonal and the output truncated differences are nonzero only in any inverse diagonal; (2) the input truncated differences are nonzero only in any two diagonals and the output truncated differences are nonzero only in any inverse diagonal; (3) the input truncated differences are nonzero only in any diagonal and the output truncated differences are nonzero only in any two inverse diagonals. Furthermore, for any given truncated differentials of these three kinds, the lower bounds of the number of master keys such that the truncated differentials are possible for 5-round AES-128 are presented.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Cryptography Development Fund of China under grant numbers MMJJ20170103 and MMJJ20180204.

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Authors and Affiliations

  1. PLA Strategic Support Force Information Engineering University, Zhengzhou, China

    Xueping Yan, Lin Tan, Hong Xu & Wenfeng Qi

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  1. Xueping Yan
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  2. Lin Tan
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  1. Shanghai Jiao Tong University, Shanghai, China

    Yu Yu

  2. Columbia University, New York, NY, USA

    Moti Yung

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Yan, X., Tan, L., Xu, H., Qi, W. (2021). On the Provable Security Against Truncated Impossible Differential Cryptanalysis for AES in the Master-Key Setting. In: Yu, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2021. Lecture Notes in Computer Science(), vol 13007. Springer, Cham. https://doi.org/10.1007/978-3-030-88323-2_21

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  • DOI: https://doi.org/10.1007/978-3-030-88323-2_21

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