The Filter-Combiner Model for Memoryless Synchronous Stream Ciphers

  • Palash Sarkar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2442)


We introduce a new model - the Filter-Combiner model - for memoryless synchronous stream ciphers. The new model combines the best features of the classical models for memoryless synchronous stream ciphers - the Nonlinear-Combiner model and the Nonlinear-Filter model. In particular, we show that the Filter-Combiner model provides key length optimal resistance to correlation attacks and eliminates weaknesses of the NF model such as the the Anderson leakage and the Inversion Attacks. Further, practical length sequences extracted from the Filter-Combiner model cannot be distinguished from true random sequences based on linear complexity test. We show how to realise the Filter-Combiner model using Boolean functions and cellular automata. In the process we point out an important security advantage of sequences obtained from cellular automata over sequences obtained from LFSRs.


synchronous stream ciphers linear feedback shift registers cellular automata nonlinear filter model nonlinear combiner model filter-combiner model 


  1. 1.
    R. J. Anderson. Searching for the optimum correlation attack. In Fast Software Encryption-FSE 1994, pp 137–143.Google Scholar
  2. 2.
    P. Camion, C. Carlet, P. Charpin, and N. Sendrier. On correlation immune functions. In Advances in Cryptology-CRYPTO’91, pages 86–100. Springer-Verlag, 1992.Google Scholar
  3. 3.
    A. Canteaut and M. Trabbia. Improved fast correlation attacks using parity checks equations of weight 4 and 5. Advances in Cryptology-EUROCRYPT 2000, Lecture Notes in Computer Science, pp 573–588.CrossRefGoogle Scholar
  4. 4.
    V. Chepysov, T. Johansson and B. Smeets. A simple algorithm for fast correlation attacks on stream ciphers, In Fast Software Encryption-FSE 2000, Lecture Notes in Computer Science.Google Scholar
  5. 5.
    C. Ding, G. Xiao, and W. Shan. The Stability Theory of Stream Ciphers. Number 561 in Lecture Notes in Computer Science. Springer-Verlag, 1991.MATHGoogle Scholar
  6. 6.
    M.R. Garey and D.S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco, 1979.MATHGoogle Scholar
  7. 7.
    J. D. Golic. On the Security of Nonlinear Filter Generators. Fast Software Encryption-Cambridge’ 96, D. Gollman, ed., 1996.Google Scholar
  8. 8.
    J. D. Golic, A. Clark and E. Dawson. Generalized inversion attack on nonlinear filter generators. IEEE Transactions on Computers, 49(10):1100–1109 (2000).CrossRefGoogle Scholar
  9. 9.
    R. Lidl and H. Niederreiter. Introduction to finite fields and their applications. Cambridge University Press, revised edition, 1994.Google Scholar
  10. 10.
    S. Maitra and P. Sarkar. Highly nonlinear resilient functions optimizing Siegenthaler’s inequality. Advances in Cryptology-CRYPTO 1999, Lecture Notes in Computer Science, pp 198–215.Google Scholar
  11. 11.
    J.L. Massey. Shift register synthesis and BCH decoding. IEEE Transactions on Information Theory,, 15(1969), 122–127.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1997.Google Scholar
  13. 13.
    J. P. Mesirov and M. M. Sweet. Continued fraction expansions of rational expressions for built-in self-test. Journal of Number Theory, 27, 144–148 (1987).MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    R. A. Rueppel. Analysis and Design of Stream Ciphers Springer-Verlag, 1986.Google Scholar
  15. 15.
    R. A. Rueppel and O. J. Staffelbach. Products of linear recurring sequences with maximum complexity. IEEE Transactions on Information Theory, volume IT-33, number 1, pp. 124–131, 1987.CrossRefGoogle Scholar
  16. 16.
    P. Sarkar. Computing Shifts in 90/150 Cellular Automata Sequences. CACR Technical Report CORR 2001-46, University of Waterloo,
  17. 17.
    P. Sarkar and S. Maitra. Nonlinearity bounds and constructions of resilient Boolean functions. In Advances in Cryptology-CRYPTO 2000, number 1880 in LNCS, pages 515–532. Springer Verlag, 2000.CrossRefGoogle Scholar
  18. 18.
    T. Siegenthaler. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory, IT-30(5):776–780, September 1984.Google Scholar
  19. 19.
    T. Siegenthaler. Decrypting a class of stream ciphers using ciphertext only. IEEE Transactions on Computers, C-34(1):81–85, January 1985.Google Scholar
  20. 20.
    S. Tezuka and M. Fushimi. A method of designing cellular automata as pseudo random number generators for built-in self-test for VLSI. In Finite Fields: Theory, Applications and Algorithms, Contemporary Mathematics, AMS, pages 363–367, 1994.Google Scholar
  21. 21.
    G.-Z. Xiao and J. Massey. A spectral characterization of correlation immune combining functions. IEEE Transactions on Information Theory, 34(3):569–571, May 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Palash Sarkar
    • 1
  1. 1.Cryptology Research Centre Applied Statistics UnitIndian Statistical InstituteKolkataIndia

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