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Weak Equivalents for Nonlinear Filtering Functions

  • Amparo Fúster-Sabater
  • Pino Caballero-Gil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8584)

Abstract

The application of a nonlinear filtering function to a Linear Feedback Shift Register (LFSR) is a general technique for designing pseudorandom sequence generators with cryptographic application. In this paper, we investigate the equivalence between different nonlinear filtering functions applied to distinct LFSRs. It is a well known fact that given a binary sequence generated from a pair (nonlinear filtering function, LFSR), the same sequence can be generated from any other LFSR of the same length by using another filtering function. However, until now no solution has been found for the problem of computing such an equivalent. This paper analyzes the specific case in which the reciprocal LFSR of a given register is used to generate an equivalent of the original nonlinear filtering function. The main advantage of the contribution is that weaker equivalents can be computed for any nonlinear filter, in the sense that such equivalents could be used to cryptanalyze apparently secure generators. Consequently, to evaluate the cryptographic resistance of a sequence generator, the weakest equivalent cipher should be determined and not only a particular instance.

Keywords

Nonlinear filtering function pseudorandom sequence LFSR stream cipher cryptography 

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References

  1. 1.
    Biryukov, A., Shamir, A.: Cryptanalytic time/Memory/Data tradeoffs for stream ciphers. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 1–13. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    eSTREAM: the ECRYPT Stream Cipher Project, http://www.ecrypt.eu.org/stream/
  4. 4.
    Faugere, J.-C., Ars, G.: An Algebraic Cryptanalysis of Nonlinear Filter Generators using Grobner bases (2003), http://www.inria.fr/rrrt/rr-4739.html
  5. 5.
    Filiol, E.: Decimation attack of stream ciphers. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 31–42. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Fúster-Sabater, A., Caballero-Gil, P.: On the linear complexity of nonlinearly filtered pn-sequences. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 80–90. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  7. 7.
    Games, R.A., Rushanan, J.J.: Blind synchronization of m-sequences with even span. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 168–180. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and Interactability. Freeman and Company (1979)Google Scholar
  9. 9.
    Golic, J.D., Clark, A., Dawson, E.: Generalized inversion attack on nonlinear filter generators. IEEE Transactions on Computers 49(10), 1100–1109 (2000)CrossRefGoogle Scholar
  10. 10.
    Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)Google Scholar
  11. 11.
    Hell, M., Johansson, T., Meier, W.: Grain - A Stream Cipher for Constrained Environments (2005), http://www.ecrypt.eu.org/stream/p3ciphers/grain/Grain_p3.pdf
  12. 12.
    Key, E.L.: An analysis of the structure and complexity of nonlinear binary sequence generators. IEEE Transactions on Information Theory 22(6), 732–736 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Lohlein, B.: Design and analysis of cryptographic secure keystream generators for stream cipher encryption. PhD thesis, Faculty of Electrical and Information Engineering, University of Hagen, Germany (2001)Google Scholar
  14. 14.
    Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory IT-15(1), 122–127 (1969)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Meier, W., Staffelbach, O.J.: Fast correlation attacks on stream ciphers. Journal of Cryptology 1(3), 159–176 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Pasalic, E.: On guess and determine cryptanalysis of LFSR-based stream ciphers. IEEE Transactions on Information Theory 55(7), 3398–3406 (2009)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Rønjom, S., Cid, C.: Nonlinear equivalence of stream ciphers. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 40–54. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Rueppel, R.A.: Analysis and Design of Stream Ciphers. Springer (1986)Google Scholar
  19. 19.
    Schneider, M.: Methods of generating binary pseudo-random sequences for stream cipher encryption. PhD thesis, Faculty of Electrical Engineering, University of Hagen, Germany (1999)Google Scholar
  20. 20.
    Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Transactions on Computers 100(1), 81–85 (1985)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Amparo Fúster-Sabater
    • 1
  • Pino Caballero-Gil
    • 2
  1. 1.Institute of Physical and Information Technologies (CSIC)MadridSpain
  2. 2.University of La LagunaLa LagunaSpain

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