F-FCSR: Design of a New Class of Stream Ciphers

  • François Arnault
  • Thierry P. Berger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3557)


In this paper we present a new class of stream ciphers based on a very simple mechanism. The heart of our method is a Feedback with Carry Shift Registers (FCSR) automaton. This automaton is very similar to the classical LFSR generators, except the fact that it performs operations with carries. Its properties are well mastered: proved period, non-degenerated states, good statistical properties, high non-linearity.

The only problem to use such an automaton directly is the fact that the mathematical structure (2-adic fraction) can be retrieved from few bits of its output using an analog of the Berlekamp-Massey algorithm.

To mask this structure, we propose to use a filter on the cells of the FCSR automaton. Due to the high non-linearity of this automaton, the best filter is simply a linear filter, that is a XOR on some internal states. We call such a generator a Filtered FCSR (F-FCSR) generator.

We propose four versions of our generator: the first uses a static filter with a single output at each iteration of the generator (F-FCSR-SF1). A second with an 8 bit output (F-FCSR-SF8). The third and the fourth are similar, but use a dynamic filter depending on the key (F-FCSR-DF1 and F-FCSR-DF8). We give limitations on the use of the static filter versions, in scope of the time/memory/data tradeoff attack.

These stream ciphers are very fast and efficient, especially for hardware implementations.


stream cipher pseudorandom generator feedback with carry shift register 2-adic fractions 


  1. 1.
    Arnault, F., Berger, T., Necer, A.: A new class of stream ciphers combining LFSR and FCSR architectures. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 22–33. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Arnault, F., Berger, T.P., Necer, A.: Feedback with Carry Shift Registers synthesis with the Euclidean Algorithm. IEEE Trans. Inform. Theory 50(5), 910–917 (2004)CrossRefMathSciNetGoogle Scholar
  3. 3.
    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
  4. 4.
    Coppersmith, D., Krawczyk, H., Mansour, Y.: The shrinking generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Courtois, N., Meier, W.: Algebraic attack on stream ciphers with linear feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Faugère, J.C.: A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5). In: Proceedings of International Symposium on Symbolic and Algebraic Computation, ISSAC 2002, Villeneuve d’Ascq, pp. 75–83.Google Scholar
  7. 7.
    Klapper, A., Goresky, M.: 2-adic shift registers, fast software encryption. In: Anderson, R. (ed.) FSE 1993. LNCS, vol. 809, pp. 174–178. Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Klapper, A., Goresky, M.: Cryptanalysis based on 2-adic rational approximation. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 262–273. Springer, Heidelberg (1995)Google Scholar
  9. 9.
    Klapper, A., Goresky, M.: Feedback shift registers, 2-adic span, and combiners with memory. Journal of Cryptology 10, 11–147 (1997)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Klapper, A., Goresky, M.: Fibonacci and Galois representation of feedback with carry shift registers. IEEE Trans. Inform. Theory 48, 2826–2836 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Koblitz, N.: p-adic Numbers, p-adic analysis and Zeta-Functions. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)CrossRefGoogle Scholar
  13. 13.
    A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications,
  14. 14.
    Daemen, J., Rijmen, V.: The Block Cipher Rijndael. In: Schneier, B., Quisquater, J.-J. (eds.) CARDIS 1998. LNCS, vol. 1820, pp. 288–296. Springer, Heidelberg (2000)Google Scholar
  15. 15.
  16. 16.
    Rueppel, R.A.: Correlation immunity and the summation generator. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 260–272. Springer, Heidelberg (1986)Google Scholar
  17. 17.
    Rueppel, R.A.: Linear complexity and random sequences. In: Pichler, F. (ed.) EUROCRYPT 1985. LNCS, vol. 219, pp. 167–188. Springer, Heidelberg (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • François Arnault
    • 1
  • Thierry P. Berger
    • 1
  1. 1.LACOUniversité de LimogesLimoges CEDEXFrance

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