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A New Approach for FCSRs

  • Franc̨ois Arnault
  • Thierry Berger
  • Cédric Lauradoux
  • Marine Minier
  • Benjamin Pousse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5867)

Abstract

The Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. FCSRs have good statistical properties and they provide a built-in non-linearity. However, two attacks have shown that the current representations of FCSRs can introduce weaknesses in the cipher. We propose a new “ring” representation of FCSRs based upon matrix definition which generalizes the Galois and Fibonacci representations. Our approach preserves the statistical properties and circumvents the weaknesses of the Fibonacci and Galois representations. Moreover, the ring representation leads to automata with a quicker diffusion characteristic and better implementation results. As an application, we describe a new version of F-FCSR stream ciphers.

Keywords

Stream cipher FCSRs ℓ-sequence ring FCSRs 

References

  1. 1.
    Klapper, A., Goresky, M.: 2-adic shift registers. In: Anderson, R. (ed.) FSE 1993. LNCS, vol. 809, pp. 174–178. Springer, Heidelberg (1994)Google Scholar
  2. 2.
    Klapper, A., Goresky, M.: Feedback shift registers, 2-adic span and combiners with memory. Journal of Cryptology 10(2), 111–147 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Klapper, A.: A survey of feedback with carry shift registers. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 56–71. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Fischer, S., Meier, W., Stegemann, D.: Equivalent Representations of the F-FCSR Keystream Generator. In: ECRYPT Network of Excellence - SASC Workshop, pp. 87–94 (2008), http://www.ecrypt.eu.org/stvl/sasc2008/
  5. 5.
    Hell, M., Johansson, T.: Breaking the F-FCSR-H stream cipher in real time. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 557–569. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Arnault, F., Berger, T.P.: F-FCSR: Design of a new class of stream ciphers. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 83–97. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Arnault, F., Berger, T.P., Lauradoux, C.: Update on F-FCSR Stream Cipher. ECRYPT - Network of Excellence in Cryptology (Call for stream Cipher Primitives - Phase 2 2006) (2006), http://www.ecrypt.eu.org/stream/
  8. 8.
    Roggeman, Y.: Varying feedback shift registers. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 670–679. Springer, Heidelberg (1990)Google Scholar
  9. 9.
    Jansen, C.J., Helleseth, T., Kholosha, A.: Cascade jump controlled sequence generator and pomaranch stream cipher (version 2). eSTREAM, ECRYPT Stream Cipher Project, Report 2006/006 (2006), http://www.ecrypt.eu.org/stream
  10. 10.
    Mrugalski, G., Rajski, J., Tyszer, J.: Ring generators - new devices for embedded test applications. IEEE Trans. on CAD of Integrated Circuits and Systems 23(9), 1306–1320 (2004)CrossRefGoogle Scholar
  11. 11.
    Jansen, C.J., Helleseth, T., Kholosha, A.: Pomaranch version 3. eSTREAM, ECRYPT Stream Cipher Project (2006), http://www.ecrypt.eu.org/stream
  12. 12.
    Koblitz, N.: p-adic numbers, p-adic analysis and Zeta-Functions. Springer, Heidelberg (1997)Google Scholar
  13. 13.
    Goresky, M., Klapper, A.: Fibonacci and Galois representations of feedback-with-carry shift registers. IEEE Transactions on Information Theory 48(11), 2826–2836 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Arnault, F., Berger, T.P.: Design and Properties of a New Pseudorandom Generator Based on a Filtered FCSR Automaton. IEEE Transaction on Computers 54(11), 1374–1383 (2005)CrossRefGoogle Scholar
  15. 15.
    Lauradoux, C., Röck, A.: Parallel generation of ℓ-sequences. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds.) SETA 2008. LNCS, vol. 5203, pp. 299–312. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Arnault, F., Berger, T.P., Minier, M.: Some Results on FCSR Automata With Applications to the Security of FCSR-Based Pseudorandom Generators. IEEE Transactions on Information Theory 54(2), 836–840 (2008)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Goldberg, I., Wagner, D.: Architectural considerations for cryptanalytic hardware. Technical report, Secrets of Encryption Research, Wiretap Politics & Chip Design (1996)Google Scholar
  18. 18.
    Joux, A., Delaunay, P.: Galois LFSR, embedded devices and side channel weaknesses. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol. 4329, pp. 436–451. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Röck, A.: Stream ciphers using a random update function: Study of the entropy of the inner state. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 258–275. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Hong, J., Kim, W.H.: TMD-Tradeoff and State Entropy Loss Considerations of Streamcipher MICKEY. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 169–182. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Franc̨ois Arnault
    • 1
  • Thierry Berger
    • 1
  • Cédric Lauradoux
    • 2
  • Marine Minier
    • 3
  • Benjamin Pousse
    • 1
  1. 1.XLIM (UMR CNRS 6172)Université de LimogesLimoges CedexFrance
  2. 2.Information Security GroupUCL / INGI / GSILouvain-la-NeuveBelgium
  3. 3.CITI Laboratory - INSA de LyonLyon UniversityVilleurbanne CedexFrance

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