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Automatic Search Model for Related-Tweakey Impossible Differential Cryptanalysis

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Applied Cryptography and Network Security Workshops (ACNS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13907))

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Abstract

The design and analysis of dedicated tweakable block ciphers constitute a dynamic and relatively recent research field in symmetric cryptanalysis. The assessment of security in the related-tweakey model is of utmost importance owing to the existence of a public tweak. This paper proposes an automatic search model for identifying related-tweakey impossible differentials based on the propagation of states under specific constraints, which is inspired by the research of Hu et al. in ASIACRYPT 2020. Our model is universally applicable to block ciphers, but its search efficiency may be limited in some cases. To address this issue, we introduce the Locality Constraint Analysis (LCA) technique to impossible differential cryptanalysis and propose a generalized automatic search model. Technically, we transform our models into Satisfiability Modulo Theories (SMT) problems and solve them using the STP solver. We have applied our tools to several tweakable block ciphers, such as Joltik-BC, SKINNY, QARMA, and CRAFT, to evaluate their effectiveness and practicality. Specifically, we have discovered 7-round related-tweakey impossible differentials for Joltik-BC-192, and 12-round related-tweak impossible differentials, as well as 15-round related-tweakey impossible differentials for CRAFT for the first time. Based on the search results, we demonstrate that the LCA technique can be effectively performed when searching and determining the contradictory positions for the distinguisher with long trails or ciphers with large sizes in impossible differential cryptanalysis.

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Notes

  1. 1.

    https://github.com/stp/.

  2. 2.

    The proof of Theorem 1 can refer to the full version of this paper in https://eprint.iacr.org.

  3. 3.

    The size of the search space is about \((16*15)^3 \approx 2^{23.7}\).

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Acknowledgements

We thank the associate editor and the anonymous reviewers for their useful feedback that improved this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 12371525) and the National Key Research and Development Program of China (Grant No. 2022YFF0604702).

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Authors and Affiliations

  1. Institute of Information Engineering, Chinese Academy of Science, Beijing, China

    Huiqin Chen, Yongqiang Li, Xichao Hu & Mingsheng Wang

  2. Science and Technology on Communication Security Laboratory, Chengdu, China

    Zhengbin Liu

  3. State Key Laboratory of Cryptology, Beijing, China

    Lin Jiao

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

    Huiqin Chen, Yongqiang Li, Xichao Hu & Mingsheng Wang

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  1. Huiqin Chen
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  6. Mingsheng Wang
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Corresponding author

Correspondence to Yongqiang Li .

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Editors and Affiliations

  1. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  2. Radboud University Nijmegen, Nijmegen, The Netherlands

    Lejla Batina

  3. Shandong University of Science and Technology, Qingdao, China

    Zengpeng Li

  4. University of Science and Technology of China, Hefei, China

    Jingqiang Lin

  5. University of Padua, Padua, Italy

    Eleonora Losiouk

  6. Concordia University, Montreal, QC, Canada

    Suryadipta Majumdar

  7. Illinois at Singapore Pte Ltd., Singapore, Singapore

    Daisuke Mashima

  8. Technical University Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  9. Radboud University Nijmegen, Nijmegen, The Netherlands

    Stjepan Picek

  10. Florida International University, Miami, FL, USA

    Mohammad Ashiqur Rahman

  11. Zhejiang Gongshang University, Hangzhou, China

    Jun Shao

  12. SECOM Co., Ltd., University of Tsukuba, Tokyo / Ibaraki, Japan

    Masaki Shimaoka

  13. Royal Holloway University of London, Egham, UK

    Ezekiel Soremekun

  14. University of Aizu, Aizuwakamatsu, Fukushima, Japan

    Chunhua Su

  15. Universiti Sains Malaysia, Gelugor, Malaysia

    Je Sen Teh

  16. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Aleksei Udovenko

  17. City University of Hong Kong, Hong Kong, Hong Kong

    Cong Wang

  18. Griffith University, Southport, QLD, Australia

    Leo Zhang

  19. Delft University of Technology, Delft, The Netherlands

    Yury Zhauniarovich

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Chen, H., Li, Y., Hu, X., Liu, Z., Jiao, L., Wang, M. (2023). Automatic Search Model for Related-Tweakey Impossible Differential Cryptanalysis. In: Zhou, J., et al. Applied Cryptography and Network Security Workshops. ACNS 2023. Lecture Notes in Computer Science, vol 13907. Springer, Cham. https://doi.org/10.1007/978-3-031-41181-6_1

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  • DOI: https://doi.org/10.1007/978-3-031-41181-6_1

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