An Algorithm for Constructing a Fastest Galois NLFSR Generating a Given Sequence

  • Jean-Michel Chabloz
  • Shohreh Sharif Mansouri
  • Elena Dubrova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


The problem of efficient implementation of security mechanisms for advanced contactless technologies like RFID is gaining increasing attention. Severe constraints on resources such as area, power consumption, and production cost make the application of traditional cryptographic techniques to these technologies a challenging task. Non-Linear Feedback Shift Register (NLFSR)-based stream ciphers are promising candidates for cryptographic primitives for RFIDs because they have the smallest hardware footprint of all existing cryptographic systems. This paper presents a heuristic algorithm for constructing a fastest Galois NLFSR generating a given sequence. The algorithm takes an NLFSR in the Fibonacci configuration and transforms it to an equivalent Galois NLFSR which has the minimal delay. Our key idea is to find a best position for a given feedback connection without changing the positions of the other feedback connections. We use a technology dependent cost function which approximates the delay of an NLFSR after the technology mapping. The experimental results on 57 NLFSRs used in existing stream ciphers show that, on average, the presented algorithm allows us to decrease the delay by 25.5% as well as to reduce the area by 4.1%.


Critical Path Stream Cipher Technology Mapping Feedback Function Feedback Connection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Cannière, C., Preneel, B.: Trivium. In: Robshaw, M.J.B., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 244–266. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    David, R.: Random Testing of Digital Circuits. Marcel Dekker, New York (1998)Google Scholar
  3. 3.
    Dubrova, E.: A transformation from the Fibonacci to the Galois NLFSRs. IEEE Transactions on Information Theory, 5263–5271 (November 2009)Google Scholar
  4. 4.
    Dubrova, E., Teslenko, M., Tenhunen, H.: On analysis and synthesis of (n,k)-non-linear feedback shift registers. In: Proceedings of Design and Test in Europe Conference (DATE 2008), Munich, Germany, pp. 133–137 (March 2008)Google Scholar
  5. 5.
    Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Review 24(2), 195–221 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gammel, B., Göttfert, R., Kniffler, O.: Achterbahn-128/80: Design and analysis. In: Workshop Record of The State of the Art of Stream Ciphers (SASC 2007), Bochum, Germany, pp. 152–165 (January 2007)Google Scholar
  7. 7.
    Gammel, B.M., Göttfert, R., Kniffler, O.: An NLFSR-based stream cipher. In: Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS 2006), Island of Kos, Greece, pp. 2920–2924 (May 2006)Google Scholar
  8. 8.
    Gill, A.: Linear Sequential Circuits. McGraw-Hill, New York (1966)zbMATHGoogle Scholar
  9. 9.
    Gittins, B., Landman, H.A., O’Neil, S., Kelson, R.: A presentation on VEST hardware performance, chip area measurements, power consumption estimates and benchmarking in relation to the AES, SHA-256 and SHA-512. Cryptology ePrint Archive, Report 415 (2005)Google Scholar
  10. 10.
    Golomb, S.: Shift Register Sequences. Aegean Park Press (1982)Google Scholar
  11. 11.
    Hatayama, K., Nakao, M., Kiyoshige, Y., Natsume, K., Sato, Y., Nagumo, T.: Application of high-quality built-in test to industrial designs. In: Proceedings of International Test Conference (ITC 2002), Baltimore, MD, USA, pp. 1003–1012 (October 2002)Google Scholar
  12. 12.
    Hell, M., Johansson, T., Maximov, A., Meier, W.: The Grain family of stream ciphers. In: Robshaw, M.J.B., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 179–190. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Jansen, C.J.: Investigations On Nonlinear Streamcipher Systems: Construction and Evaluation Methods. Ph.D. Thesis, Technical University of Delft (1989)Google Scholar
  14. 14.
    Juels, A.: RFID security and privacy: a research survey. IEEE Journal on Selected Areas in Communications 24(2), 381–394 (2006)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Linardatos, D., Kalouptsidis, N.: Synthesis of minimal cost nonlinear feedback shift registers. Signal Process 82(2), 157–176 (2002)zbMATHCrossRefGoogle Scholar
  16. 16.
    Mansouri, S.: Re-Designing Grain Stream Cipher for Higher Throughput. M. Sc. Thesis, Royal Institute of Technology (KTH), Sweden (2009)Google Scholar
  17. 17.
    Massey, J.: Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory 15, 122–127 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Massey, J.L., Liu, R.: Equivalence of nonlinear-feedback shift-registers. IEEE Transactions on Information Theory 10, 378–379 (1964)zbMATHCrossRefGoogle Scholar
  19. 19.
    Mrugalski, G., Rajski, J., Tyszer, J.: Ring generators - New devices for embedded test applications. Transactions on Computer-Aided Design of Integrated Circuits and Systems 23(9), 1306–1320 (2004)CrossRefGoogle Scholar
  20. 20.
    Mykkeltveit, J.: Nonlinear recurrences and arithmetic codes. Information and Control 33(3), 193–209 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Robshaw, M.: Stream ciphers. Technical Report TR - 701, RSA Laboratories (July 1994)Google Scholar
  22. 22.
    Robshaw, M.: The estream project. In: Robshaw, M.J.B., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 1–6. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Ronce, C.A.: Feedback Shift Registers. LNCS, vol. 169. Springer, Heidelberg (1984)Google Scholar
  24. 24.
    Schneier, B.: Applied cryptography: protocols, algorithms, and source code in C, 2nd edn. John Wiley & Sons, Inc., New York (1995)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-Michel Chabloz
    • 1
  • Shohreh Sharif Mansouri
    • 1
  • Elena Dubrova
    • 1
  1. 1.Royal Institute of TechnologyKistaSweden

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