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Speeding up MILP Aided Differential Characteristic Search with Matsui’s Strategy

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Information Security (ISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11060))

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Abstract

Being the first generic algorithm for finding the best differential and linear characteristics, Matsui’s branch and bound search algorithm (EUROCRYPT 1994) and its variants have played an important role in the security analysis of symmetric-key primitives. However, Matsui’s algorithm is difficult to implement, optimize, and be applied to different ciphers with reusable code. Another approach getting popular in recent years is to encode the search problem as a Mixed Integer Linear Programming (MILP) model which can be solved by open-source or commercially available optimizers. In this work, we show how to tweak the objective functions of the MILP models for finding differential characteristics such that a set of constraints derived from the bounding condition of Matsui’s algorithm can be incorporated into the models. We apply the new modeling strategy to PRESENT (S-box based SPN design), SIMON (Feistel structure), and SPECK (ARX construction). For PRESENT, the resolution time is significantly reduced. For example, the time to prove that the exact lower bound of the probabilities of the differential characteristics for 7-round PRESENT is reduced from 48638 s to 656 s. For SIMON, obvious acceleration is also observed, and for the ARX cipher SPECK, the new model is unable to speed up the resolution. In the future, it is interesting to investigate how to integrate other search heuristics proposed in the literature of symmetric-key cryptanalysis into the MILP models, and how to accelerate the resolution of MILP models for finding characteristics of ARX ciphers.

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Acknowledgments

The authors thank the anonymous reviewers for many helpful comments. The work is supported by the National Natural Science Foundation of China (61732021, 61772519), the Youth Innovation Promotion Association of Chinese Academy of Sciences, the Chinese Major Program of National Cryptography Development Foundation, and the Institute of Information Engineering, CAS (Grant No. Y7Z0341103).

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Yingjie Zhang, Siwei Sun, Jiahao Cai & Lei Hu

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

    Yingjie Zhang, Siwei Sun, Jiahao Cai & Lei Hu

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

    Yingjie Zhang, Siwei Sun, Jiahao Cai & Lei Hu

Authors
  1. Yingjie Zhang
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  2. Siwei Sun
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  3. Jiahao Cai
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  4. Lei Hu
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Corresponding author

Correspondence to Siwei Sun .

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Editors and Affiliations

  1. University of Surrey, Guildford, United Kingdom

    Liqun Chen

  2. University of Surrey, Guildford, United Kingdom

    Mark Manulis

  3. University of Surrey, Guildford, United Kingdom

    Steve Schneider

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Zhang, Y., Sun, S., Cai, J., Hu, L. (2018). Speeding up MILP Aided Differential Characteristic Search with Matsui’s Strategy. In: Chen, L., Manulis, M., Schneider, S. (eds) Information Security. ISC 2018. Lecture Notes in Computer Science(), vol 11060. Springer, Cham. https://doi.org/10.1007/978-3-319-99136-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-99136-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99135-1

  • Online ISBN: 978-3-319-99136-8

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