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Accurate estimates of the data complexity and success probability for various cryptanalyses

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Abstract

Many attacks on encryption schemes rely on statistical considerations using plaintext/ciphertext pairs to find some information on the key. We provide here simple formulae for estimating the data complexity and the success probability which can be applied to a lot of different scenarios (differential cryptanalysis, linear cryptanalysis, truncated differential cryptanalysis, etc.). Our work does not rely here on Gaussian approximation which is not valid in every setting but use instead a simple and general approximation of the binomial distribution and asymptotic expansions of the beta distribution.

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References

  1. Vaudenay S.: Decorrelation: a theory for block cipher security. J. Cryptol. 16, 249–286 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tardy-Corfdir A., Gilbert H.: A known plaintext attack of FEAL-4 and FEAL-6. In: CRYPTO ’91. LNCS, vol. 576, pp. 172–181. Springer-Verlag, Heidleberg (1992).

  3. Matsui M.: Linear cryptanalysis method for DES cipher. In: EUROCRYPT ’93. LNCS, vol. 765, pp. 386–397. Springer-Verlag, Heidlberg (1993).

  4. Matsui M.: The first experimental cryptanalysis of the data encryption standard. In: CRYPTO ’94. LNCS, vol. 839, pp. 1–11. Springer-Verlag, Heidleberg (1994).

  5. Biham E., Shamir A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4, 3–72 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  6. Selçuk A.A.: On probability of success in linear and differential cryptanalysis. J. Cryptol. 21, 131–147 (2008)

    Article  MATH  Google Scholar 

  7. Lai X., Massey J.L., Murphy S.: Markov Ciphers and differential cryptanalysis. In: LNCS, vol. 547, pp. 17–38. Springer, Heidleberg (1991).

  8. Knudsen L.R.: Truncated and higher order differentials. In: FSE ’94. LNCS, vol. 1008, pp. 196–211. Springer-Verlag, Heidleberg (1994).

  9. Junod P.: On the optimality of linear, differential, and sequential distinguishers. In: EUROCRYPT ’03. LNCS, vol. 2656, pp. 17–32. Springer-Verlag, Heidleberg (2003).

  10. Baignères T., Junod P., Vaudenay S.: How far can we go beyond linear cryptanalysis? In: ASIACRYPT ’04. LNCS, vol. 3329, pp. 432–450. Springer-Verlag, Heidleberg (2004).

  11. Baignères T., Vaudenay S.: The complexity of distinguishing distributions. In: ICITS ’08. LNCS, vol. 5155, pp. 210–222. Springer-Verlag, Heidleberg (2008).

  12. Junod P.: On the complexity of Matsui’s attack. In: SAC ’01. LNCS, vol. 2259, pp. 199–211. Springer-Verlag, Heidleberg (2001).

  13. Junod P., Vaudenay S.: Optimal key ranking procedures in a statistical cryptanalysis. In: FSE ’03. LNCS, vol. 2887, pp. 235–246. Springer-Verlag, Heidleberg (2003).

  14. Nyberg K.: Generalized Feistel networks. In: ASIACRYPT ’96. LNCS, vol. 1163, pp. 91–104. Springer-Verlag, Heidleberg (1996).

  15. Harpes C., Kramer G., Massey J.: A generalization of linear cryptanalysis and the applicability of Matsui’s piling-up lemma. In: EUROCRYPT ’95. LNCS, vol. 921, pp. 24–38. Springer-Verlag, Heidleberg (1995).

  16. Cover T., Thomas J.: Information theory. Wiley series in communications. Wiley, New York (1991)

    Google Scholar 

  17. Arriata R., Gordon L.: Tutorial on large deviations for the binomial distribution. Bull. Math. Biol. 51, 125–131 (1989)

    MathSciNet  Google Scholar 

  18. Langford S.K., Hellman M.E.: Differential-linear cryptanalysis. In: CRYPTO ’94. LNCS, vol. 839, pp. 17–25. Springer-Verlag, Heidleberg (1994).

  19. Biham E., Shamir A.: Differential cryptanalysis of the full 16-round DES. In: CRYPTO’92. LNCS, vol. 740, pp. 487–496. Springer-Verlag, Heidleberg (1993).

  20. Biham E., Biryukov A., Shamir A.: Cryptanalysis of skipjack reduced to 31 rounds using impossible differentials. In: EUROCRYPT ’99. LNCS, vol. 1592, pp. 12–23. Springer-Verlag, Heidleberg (1999).

  21. David H., Nagaraja H.: Order Statistics, third edn. Wiley series in Probability Theory. Wiley, New York (2003)

    Google Scholar 

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Authors and Affiliations

  1. INRIA project-team SECRET, Le Chesnay Cedex, France

    Céline Blondeau, Benoît Gérard & Jean-Pierre Tillich

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  1. Céline Blondeau
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  2. Benoît Gérard
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  3. Jean-Pierre Tillich
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Correspondence to Céline Blondeau.

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Blondeau, C., Gérard, B. & Tillich, JP. Accurate estimates of the data complexity and success probability for various cryptanalyses. Des. Codes Cryptogr. 59, 3–34 (2011). https://doi.org/10.1007/s10623-010-9452-2

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  • DOI: https://doi.org/10.1007/s10623-010-9452-2

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