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

  • Jun Yin
  • Chuyan Ma
  • Lijun Lyu
  • Jian Song
  • Guang Zeng
  • Chuangui Ma
  • Fushan Wei
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Lightweight block cipher Differential attack Linear attack HIGHT MILP 

Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jun Yin
    • 1
    • 3
    • 4
    • 5
  • Chuyan Ma
    • 6
  • Lijun Lyu
    • 3
    • 4
    • 5
  • Jian Song
    • 1
  • Guang Zeng
    • 1
  • Chuangui Ma
    • 7
  • Fushan Wei
    • 1
    • 2
  1. 1.State Key Laboratory of Mathematical Engineering and Advanced ComputingZhengzhouChina
  2. 2.State Key Laboratory of CryptologyBeijingChina
  3. 3.Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  4. 4.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  5. 5.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina
  6. 6.National University of Defense TechnologyChangshaChina
  7. 7.Army Aviation InstituteBeijingChina

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