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Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints

  • Danping Shi
  • Siwei SunEmail author
  • Patrick Derbez
  • Yosuke Todo
  • Bing Sun
  • Lei Hu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11273)

Abstract

Cryptanalysis with SAT/SMT, MILP and CP has increased in popularity among symmetric-key cryptanalysts and designers due to its high degree of automation. So far, this approach covers differential, linear, impossible differential, zero-correlation, and integral cryptanalysis. However, the Demirci-Selçuk meet-in-the-middle (\(\mathcal {DS}\)-\(\mathsf {MITM}\)) attack is one of the most sophisticated techniques that has not been automated with this approach. By an in-depth study of Derbez and Fouque’s work on \(\mathcal {DS}\)-\(\mathsf {MITM}\) analysis with dedicated search algorithms, we identify the crux of the problem and present a method for automatic \(\mathcal {DS}\)-\(\mathsf {MITM}\) attack based on general constraint programming, which allows the cryptanalysts to state the problem at a high level without having to say how it should be solved. Our method is not only able to enumerate distinguishers but can also partly automate the key-recovery process. This approach makes the \(\mathcal {DS}\)-\(\mathsf {MITM}\) cryptanalysis more straightforward and easier to follow, since the resolution of the problem is delegated to off-the-shelf constraint solvers and therefore decoupled from its formulation. We apply the method to SKINNY, TWINE, and LBlock, and we get the currently known best \(\mathcal {DS}\)-\(\mathsf {MITM}\) attacks on these ciphers. Moreover, to demonstrate the usefulness of our tool for the block cipher designers, we exhaustively evaluate the security of \(8! = 40320\) versions of LBlock instantiated with different words permutations in the F functions. It turns out that the permutation used in the original LBlock is one of the 64 permutations showing the strongest resistance against the \(\mathcal {DS}\)-\(\mathsf {MITM}\) attack. The whole process is accomplished on a PC in less than 2 h. The same process is applied to TWINE, and similar results are obtained.

Keywords

Demirci-Selçuk meet-in-the-middle attack Automated cryptanalysis Constraint programming MILP 

Notes

Acknowledgments

The authors thank the anonymous reviewers for many helpful comments, and Gaëtan Leurent for careful reading and shepherding our paper. The work is supported by the Chinese Major Program of National Cryptography Development Foundation (Grant No. MMJJ20180102), the National Natural Science Foundation of China (61732021, 61802400, 61772519, 61802399), the Youth Innovation Promotion Association of Chinese Academy of Sciences, and the Institute of Information Engineering, CAS (Grant No. Y7Z0251103). Patrick Derbez is supported by the French Agence Nationale de la Recherche through the CryptAudit project under Contract ANR-17-CE39-0003.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Danping Shi
    • 1
    • 2
  • Siwei Sun
    • 1
    • 2
    • 3
    Email author
  • Patrick Derbez
    • 4
  • Yosuke Todo
    • 5
  • Bing Sun
    • 6
  • Lei Hu
    • 1
    • 2
    • 3
  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina
  4. 4.Univ Rennes, CNRS, IRISARennesFrance
  5. 5.NTT Secure Platform LaboratoriesTokyoJapan
  6. 6.College of Liberal Arts and SciencesNational University of Defense TechnologyChangshaChina

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