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Correlation attacks on combination generators

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Abstract

The combination generator is a popular stream cipher construction. It consists of several independent devices working in parallel whose outputs are combined by a Boolean function. The output of this function is the keystream. The security of this generator has been extensively studied in the case where the devices are LFSRs. Some particular cases where the devices are nonlinear have also been studied, most notably the different versions of the eSTREAM proposal named Achterbahn. Several cryptanalysis techniques against these ciphers have been published, extending the classical correlation attack. But each of these attacks has been presented mainly in a very particular scenario. Therefore, this paper aims at generalising these methods to any combination generator in order to be able to compare their respective advantages and to determine the optimal attack for each particular generator. Generic formulas for the data-time-space complexities are then provided, which only depend on the number of devices, their periods and the number of their internal states and of the Boolean combining function. Some of the considered improvements can also be used in a much more general context, which includes linear attacks against some block ciphers.

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References

  1. Biryukov, A., De Cannière, C., Quisquater, M.: On multiple linear approximations. In: Advances in Cryptology—CRYPTO 2004. Lecture Notes in Computer Science, vol. 3152, pp. 1–22. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Blahut, R.E.: Fast Algorithms for Digital Signal Processing. Addison Wesley (1985)

  3. Canteaut, A., Filiol, E.: Ciphertext only reconstruction of stream ciphers based on combination generators. In: Fast Software Encryption—FSE 2000. Lecture Notes in Computer Science, vol. 1978, pp. 165–180. Springer-Verlag (2001)

  4. Canteaut, A., Naya-Plasencia, M.: Parity-check relations on combination generators. IEEE Trans. Inf. Theory 58(6), 3900–3911 (2012)

    Article  Google Scholar 

  5. Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity-check equations of weight 4 and 5. In: Advances in Cryptology—EUROCRYPT 2000. Lecture Notes in Computer Science, vol. 1807, pp. 573–588. Springer-Verlag (2000)

  6. Chepyshov, V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Fast Software Encryption—FSE 2000, Lecture Notes in Computer Science, vol. 1978, pp. 124–135. Springer-Verlag (2000)

  7. Chose, P., Joux, A., Mitton, M.: Fast correlation attacks: an algorithmic point of view. In: Advances in Cryptology—EUROCRYPT 2002. Lecture Notes in Computer Science, vol. 2332, pp. 209–221. Springer-Verlag (2002)

  8. Coppersmith, D., Halevi, S., Jutla, C.: Cryptanalysis of stream ciphers with linear masking. In: Advances in Cryptology—CRYPTO 2002. Lecture Notes in Computer Science, vol. 2442. Springer-Verlag (2002)

  9. Courtois, N.: Fast algebraic attacks on stream ciphers with linear feedback. In: Advances in Cryptology—CRYPTO 2003. Lecture Notes in Computer Science, vol. 2729, pp. 176–194. Springer-Verlag (2003)

  10. Courtois, N., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Advances in Cryptology—EUROCRYPT 2003. Lecture Notes in Computer Science, vol. 2656, pp. 345–359. Springer-Verlag (2003)

  11. ECRYPT—European Network of Excellence in Cryptology: The eSTREAM Stream Cipher Project. http://www.ecrypt.eu.org/stream/ (2004)

  12. Ekdahl, P., Johansson, T.: Distinguishing attacks on SOBER-t16 and t32. In: Fast Software Encryption—FSE 2002. LNCS, vol. 2365, pp. 210–224. Springer (2002)

  13. Gammel, B., Göttfert, R., Kniffler, O.: The Achterbahn stream cipher. Submission to eSTREAM. http://www.ecrypt.eu.org/stream/ (2005)

  14. Gammel, B., Göttfert, R., Kniffler, O.: Achterbahn-128/80. Submission to eSTREAM. http://www.ecrypt.eu.org/stream/ (2006)

  15. Gammel, B., Göttfert, R., Kniffler, O.: Status of Achterbahn and Tweaks. In: Proceedings of SASC 2006—Stream Ciphers Revisited. http://www.ecrypt.eu.org/stream/papersdir/2006/027.pdf (2006)

  16. Gammel, B., Göttfert, R., Kniffler, O.: Achterbahn-128/80: design and analysis. In: Proceedings of SASC 2007—Stream Ciphers Revisited. http://www.ecrypt.eu.org/stream/papersdir/2007/020.pdf (2007)

  17. Gérard, B., Tillich, J.P.: On linear cryptanalysis with many linear approximations. In: IMA International Conference, Cryptography and Coding. Lecture Notes in Computer Science, vol. 5921, pp. 112–132. Springer (2009)

  18. Gérard, B., Tillich, J.P.: Advanced Linear Cryptanalysis of Block and Stream Ciphers, vol. 7, chap. Using Tools from Error Correcting Theory in Linear Cryptanalysis, pp. 87–114. IOS Press (2011)

  19. Göttfert, R., Gammel, B.: On the frame length of Achterbahn-128/80. In: Proceedings of the 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, pp. 1–5. IEEE (2007)

  20. Hell, M., Johansson, T.: Cryptanalysis of Achterbahn-Version 2. In: Selected Areas in Cryptography—SAC 2006. Lecture Notes in Computer Science, vol. 4356, pp. 45–55. Springer (2006)

  21. Hell, M., Johansson, T.: Cryptanalysis of Achterbahn-128/80. IET Inf. Secur. 1(2), 47–52 (2007)

    Article  Google Scholar 

  22. Hell, M., Johansson, T., Brynielsson, L.: An overview of distinguishing attacks on stream ciphers. Cryptogr. Commun. 1(1), 71–94 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hermelin, M., Cho, J., Nyberg, K.: Multidimensional extension of Matsui’s Algorithm 2. In: Fast Software Encryption—FSE 2009. Lecture Notes in Computer Science, vol. 5665, pp. 209–227. Springer (2009)

  24. Hermelin, M., Nyberg, K.: Advanced Linear Cryptanalysis of Block and Stream Ciphers, vol. 7, chap. Linear Cryptanalysis Using Multiple Linear Approximations, pp. 25–54. IOS Press (2011)

  25. Johansson, T., Jönsson, F.: Fast correlation attacks based on turbo code techniques. In: Advances in Cryptology—CRYPTO’99. Lecture Notes in Computer Science, vol. 1666, pp. 181–197. Springer-Verlag (1999)

  26. Johansson, T., Jönsson, F.: Improved fast correlation attack on stream ciphers via convolutional codes. In: Advances in Cryptology—EUROCRYPT’99. Lecture Notes in Computer Science, vol. 1592, pp. 347–362. Springer-Verlag (1999)

  27. Johansson, T., Jönsson, F.: Fast correlation attacks through reconstruction of linear polynomials. In: Advances in Cryptology—CRYPTO’00. Lecture Notes in Computer Science, vol. 1880, pp. 300–315. Springer-Verlag (2000)

  28. Johansson, T., Meier, W., Muller, F.: Cryptanalysis of Achterbahn. In: Fast Software Encryption—FSE 2006, Lecture Notes in Computer Science, vol. 4047, pp. 1–14. Springer (2006)

  29. Joux, A.: Algorithmic Cryptanalysis. Chapman & Hall/CRC (2009)

  30. Junod, P., Vaudenay, S.: Optimal key ranking procedures in a statistical cryptanalysis. In: Fast Software Encryption—FSE 2003. Lecture Notes in Computer Science, vol. 2887, pp. 235–246. Springer-Verlag (2003)

  31. Lu, Y., Vaudenay, S.: Faster correlation attack on Bluetooth keystream generator E0. In: Advances in Cryptology—CRYPTO 2004. Lecture Notes in Computer Science, vol. 3152, pp. 407–425. Springer-Verlag (2004)

  32. Matsui, M.: The first experimental cryptanalysis of the data encryption standard. In: Advances in Cryptology—CRYPTO’94. Lecture Notes in Computer Science, vol. 839. Springer-Verlag (1995)

  33. Meier, W., Staffelbach, O.: Fast correlation attacks on stream ciphers. In: Advances in Cryptology—EUROCRYPT’88. Lecture Notes in Computer Science, vol. 330, pp. 301–314. Springer-Verlag (1988)

  34. Meier, W., Staffelbach, O.: Fast correlation attack on certain stream ciphers. J. Cryptol. 1(3), 159–176 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  35. Naya-Plasencia, M.: Cryptanalysis of Achterbahn-128/80. In: Fast Software Encryption—FSE 2007. Lecture Notes in Computer Science, vol. 4593, pp. 73–86. Springer (2007)

  36. Naya-Plasencia, M.: Cryptanalysis of Achterbahn-128/80 with a new keystream limitation. In: WEWoRC 2007—Second Western European Workshop in Research in Cryptology. Lecture Notes in Computer Science, vol. 4945, pp. 142–152. Springer (2008)

  37. Siegenthaler, T.: Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Trans. Inf. Theory 30(5), 776–780 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  38. Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. C-34(1), 81–84 (1985)

    Article  Google Scholar 

  39. Zhang, M.: Maximum correlation analysis of nonlinear combining functions in stream ciphers. J. Cryptol. 13(3), 301–313 (2000)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. INRIA project-team SECRET, B.P. 105, 78153, Le Chesnay cedex, France

    Anne Canteaut

  2. Laboratoire PRISM, Université de Versailles St-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035, Versailles Cedex, France

    María Naya-Plasencia

Authors
  1. Anne Canteaut
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  2. María Naya-Plasencia
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Correspondence to Anne Canteaut.

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Canteaut, A., Naya-Plasencia, M. Correlation attacks on combination generators. Cryptogr. Commun. 4, 147–171 (2012). https://doi.org/10.1007/s12095-012-0069-3

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  • DOI: https://doi.org/10.1007/s12095-012-0069-3

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