New insights on linear cryptanalysis

Abstract

Linear cryptanalysis is one of the most important cryptanalytic tools against block ciphers, thus modern block ciphers are always deliberately devised to avoid good long linear characteristics so as to resist linear cryptanalysis and its extensions. Differential-linear cryptanalysis, a powerful extension of linear cryptanalysis, has drawn much attention due to its applicability even in certain case that there is no good long linear characteristic of block ciphers. To further refine differential-linear cryptanalysis, we investigate the correlation distribution of differential-linear hull over random permutation and derive a concrete and concise correlation distribution accordingly. Theoretically, this could make differential-linear cryptanalysis more reasonable and precise. Moreover, the newly-proposed correlation distribution could lead to an interesting potential for improving the effectiveness of differential-linear cryptanalysis.

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References

  1. 1

    Matsui M. Linear cryptanalysis method for DES cipher. In: Advances in Cryptology — EUROCRYPT 1993. Berlin: Springer, 1994. 386–397

    Google Scholar 

  2. 2

    Kaliski B S, Robshaw M J B. Linear cryptanalysis using multiple aprroximations. In: Advances in Cryptology — CRYPTO 1994. Berlin: Springer, 1994. 26–39

    Google Scholar 

  3. 3

    Biryukov A, de Canniere C, Quisquater M. On multiple linear approximations. In: Advances in Cryptology — CRYPTO 2004. Berlin: Springer, 2004. 1–22

    Google Scholar 

  4. 4

    Baigneres T, Junod P, Vaudenay S. How far can we go beyond linear cryptanalysis? In: Advances in Cryptology — ASIACRYPT 2004. Berlin: Springer, 2004. 432–450

    Google Scholar 

  5. 5

    Hermelin M, Cho J Y, Nyberg K. Multidimensional linear cryptanalysis of reduced round Serpent. In: Proceedings of Australasian Conference on Information Security and Privacy — ACISP 2008. Berlin: Springer, 2008. 203–215

    Google Scholar 

  6. 6

    Hermelin M, Cho J Y, Nyberg K. Statistical tests for key recovery using multidimensional extension of Matsui’s algorithm 1. In: Advances in Cryptology — EUROCRYPT 2009 — Poster Session, 2009

  7. 7

    Cho J Y, Hermelin M, Nyberg K. A new technique for multidimensional linear cryptanalysis with applications on reduced round Serpent. In: Proceedings of International Conference on Information Security and Cryptology — ICISC 2008. Berlin: Springer, 2009. 383–398

    Google Scholar 

  8. 8

    Hermelin M, Cho J Y, Nyberg K. Multidimensional extension of Matsui’s algorithm 2. In: Fast Software Encryption — FSE 2009. Berlin: Springer, 2009. 209–227

    Google Scholar 

  9. 9

    Harpes C, Kramer G, Massey J. A generalization of linear cryptanalysis and the applicability of Matsui’s piling-up lemma. In: Advances in Cryptology — EUROCRYPT 1995. Berlin: Springer, 1995. 24–38

    Google Scholar 

  10. 10

    Knudsen L, Robshaw M. Non-linear approximations in linear cryptanalysis. In: Advances in Cryptology — EUROCRYPT 1996. Berlin: Springer, 1996. 224–236

    Google Scholar 

  11. 11

    Courtois N T. Feistel schemes and bi-linear cryptanalysis. In: Advances in Cryptology — CRYPTO 2004. Berlin: Springer, 2004. 23–40

    Google Scholar 

  12. 12

    Langford S K, Hellman M E. Differential-linear cryptanalysis. In: Advances in Cryptology — CRYPTO 1994. Berlin: Springer, 1994. 17–25

    Google Scholar 

  13. 13

    Biham E, Dunkelman O, Keller N. Enhancing differential-linear cryptanalysis. In: Advances in Cryptology — ASIACRYPT 2002. Berlin: Springer, 2002. 254–266

    Google Scholar 

  14. 14

    Liu Z Q, Gu D W, Zhang J, et al. Differential-multiple linear cryptanalysis. In: Proceedings of International Conference on Information Security and Cryptology — INSCRYPT 2009. Berlin: Springer, 2010. 35–49

    Google Scholar 

  15. 15

    Lu J Q. A methodology for differential-linear cryptanalysis and its applications — (extended abstract). In: Fast Software Encryption — FSE 2012. Berlin: Springer, 2012. 69–89

    Google Scholar 

  16. 16

    Lu J Q. A methodology for differential-linear cryptanalysis and its applications. Designs Codes Cryptogr, 2015, 77: 11–48

    MathSciNet  Article  Google Scholar 

  17. 17

    Blondeau C, Leander G, Nyberg K. Differential-linear cryptanalysis revisited. In: Fast Software Encryption — FSE 2014. Berlin: Springer, 2015. 411–430

    Google Scholar 

  18. 18

    Blondeau C, Leander G, Nyberg K. Differential-linear cryptanalysis revisited. J Cryptol, 2017, 30: 859–888

    MathSciNet  Article  Google Scholar 

  19. 19

    Leurent G. Improved differential-linear cryptanalysis of 7-round Chaskey with partitioning. In: Advances in Cryptology — EUROCRYPT 2016. Berlin: Springer, 2016. 344–371

    Google Scholar 

  20. 20

    Biham E, Carmeli Y. An improvement of linear cryptanalysis with addition operations with applications to FEAL-8X. In: Selected Areas in Cryptography — SAC 2014. Berlin: Springer, 2014. 59–76

    Google Scholar 

  21. 21

    Bogdanov A, Rijmen V. Linear hulls with correlation zero and linear cryptanalysis of block ciphers. Des Codes Cryptogr, 2014, 70: 369–383

    MathSciNet  Article  Google Scholar 

  22. 22

    Bogdanov A, Leander G, Nyberg K, et al. Integral and multidimensional linear distinguishers with correlation zero. In: Advances in Cryptology — ASIACRYPT 2012. Berlin: Springer, 2012. 244–261

    Google Scholar 

  23. 23

    Bogdanov A, Wang M Q. Zero correlation linear cryptanalysis with reduced data complexity. In: Fast Software Encryption — FSE 2012. Berlin: Springer, 2012. 29–48

    Google Scholar 

  24. 24

    Wang Y F, Wu W L. Improved multidimensional zero-correlation linear cryptanalysis and applications to LBlock and TWINE. In: Proceedings of Australasian Conference on Information Security and Privacy — ACISP 2014. Berlin: Springer, 2014. 1–16

    Google Scholar 

  25. 25

    Wen L, Wang M Q, Bogdanov A, et al. Multidimensional zero-correlation attacks on lightweight block cipher HIGHT: improved cryptanalysis of an ISO standard. Inf Process Lett, 2014, 114: 322–330

    Article  Google Scholar 

  26. 26

    Yi W T, Chen S Z. Multidimensional zero-correlation linear cryptanalysis of the block cipher KASUMI. 2016, 10: 215–221

    Google Scholar 

  27. 27

    Tolba M, Abdelkhalek A, Youssef A M. Multidimensional zero-correlation linear cryptanalysis of reduced round SPARX-128. In: Selected Areas in Cryptography — SAC 2017. Berlin: Springer, 2017. 423–441

    Google Scholar 

  28. 28

    Chabaud F, Vaudenay S. Links between differential and linear cryptanalysis. In: Advances in Cryptology — EUROCRYPT 1994. Berlin: Springer, 1995. 356–365

    Google Scholar 

  29. 29

    Leander G. On linear hulls, statistical saturation attacks, PRESENT and a cryptanalysis of PUFFIN. In: Advances in Cryptology — EUROCRYPT 2011. Berlin: Springer, 2011. 303–322

    Google Scholar 

  30. 30

    Blondeau C, Nyberg K. New links between differential and linear cryptanalysis. In: Advances in Cryptology — EUROCRYPT 2013. Berlin: Springer, 2013. 388–404

    Google Scholar 

  31. 31

    Blondeau C, Bogdanov A, Wang M Q. On the (in)equivalence of impossible differential and zero-correlation distinguishes for Feistel- and Skipjack-type ciphers. In: Applied Cryptography and Network Security — ACNS 2014. Berlin: Springer, 2014. 271–288

    Google Scholar 

  32. 32

    Blondeau C, Nyberg K. Links between truncated differential and multidimensional linear properties of block ciphers and underlying attack complexities. In: Advances in Cryptology — EUROCRYPT 2014. Berlin: Springer, 2014. 165–182

    Google Scholar 

  33. 33

    Sun B, Liu Z Q, Rijmen V, et al. Links among impossible differential, integral and zero-correlation linear cryptanalysis. In: Advances in Cryptology — CRYPTO 2015. Berlin: Springer, 2015. 95–115

    Google Scholar 

  34. 34

    Blondeau C, Nyberg K. Joint data and key distribution of simple, multiple, and multidimensional linear cryptanalysis test statistic and its impact to data complexity. Des Codes Cryptogr, 2017, 82: 319–349

    MathSciNet  Article  Google Scholar 

  35. 35

    Blondeau C, Nyberg K. Improved parameter estimates for correlation and capacity deviates in linear cryptanalysis. IACR Trans Symmetric Cryptol, 2017, 2016: 162–191

    Google Scholar 

  36. 36

    Daemen J, Rijmen V. Probability distributions of correlation and differentials in block ciphers. J Math Cryptol, 2007, 1: 221–242

    MathSciNet  Article  Google Scholar 

  37. 37

    Beaulieu R, Shors D, Smith J, et al. The SIMON and SPECK families of lightweight block ciphers. IACR Cryptol ePrint Archive, 2013, 2013: 404

    Google Scholar 

  38. 38

    Biryukov A, Roy A, Velichkov V. Differential analysis of block ciphers SIMON and SPECK. In: Fast Software Encryption — FSE 2014. Berlin: Springer, 2015. 546–570

    Google Scholar 

  39. 39

    Wang Q J, Liu Z Q, Varici K, et al. Cryptanalysis of reduced-round SIMON32 and SIMON48. In: Progress in Cryptology — INDOCRYPT 2014. Berlin: Springer, 2014. 143–160

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61672347, 61772129, 61472250, 61402288). The authors are grateful to the reviewers for their valuable suggestions and comments.

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Correspondence to Wei Li.

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Liu, Z., Han, S., Wang, Q. et al. New insights on linear cryptanalysis. Sci. China Inf. Sci. 63, 112104 (2020). https://doi.org/10.1007/s11432-018-9758-4

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Keywords

  • block cipher
  • linear cryptanalysis
  • differential-linear cryptanalysis
  • correlation distribution
  • key-dependent differential-linear hull