Software Implementation of Linear Feedback Shift Registers over Extended Fields

  • O. Delgado-Mohatar
  • A. Fúster-Sabater
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 189)


Linear Feedback Shift Registers are currently used as generators of pseudorandom sequences with multiple applications from communication systems to cryptography. In this work, design and software implementation of LFSRs defined over extended fields GF(2 n ) instead of over the binary field GF(2) are analyzed. The key idea is to take profit of the underlying structure of the processor over which the application is executed. The study has been carried out for diverse extended fields and different architectures. Numerical results prove that extended fields provide speedup factors up to 10.15. The benefits of these fields are clear for LFSR applications included cryptographic applications.


software implementation extended field LFSR security 


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  1. 1.
    Corchado, E., Herrero, A.: Neural visualization of network traffic data for intrusion detection. Appl. Soft Comput. 11(2), 2042–2056 (2011)CrossRefGoogle Scholar
  2. 2.
    eSTREAM, the ECRYPT Stream Cipher Project, The eSTREAM Portfolio in 2012,
  3. 3.
    Dragomir, O., Stefanov, T.P., Bertels, K.: Loop Unrolling and Shifting for Reconfigurable Architectures. In: Proceedings of the 18th International Conference on Field Programmable Logic and Applications, FPL 2008 (September 2008)Google Scholar
  4. 4.
    Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)Google Scholar
  5. 5.
    Greenan, K., Miller, E., Schwarz, T.: Optimizing Galois field arithmetic for diverse processor architectures and applications. In: Miller, E., Williamson, C. (eds.) Proc. of MASCOTS, pp. 257–266. IEEE Computer Society (2008)Google Scholar
  6. 6.
    Herrero, A., Zurutuza, U., Corchado, E.: A Neural-Visualization IDS for Noneynet Data. Int. J. Neural Syst. 22(2) (2012)Google Scholar
  7. 7.
    Huang, J.C., Leng, T.: Generalized Loop-Unrolling: A Method for Program Speedup. In: Application-Specific Software Engineering and Technology, IEEE Workshop on Field Programmable Logic, pp. 244–249 (1999)Google Scholar
  8. 8.
    Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, New York (1997)MATHGoogle Scholar
  9. 9.
    Paar, C.: Efficient VLSI Architectures for Bit-Parallel Computation in Galois Fields. PhD thesis, Institute for Experimental Mathematics. University of Essen, Germany (1994)Google Scholar
  10. 10.
    Panda, M., Abraham, A., Das, S., Patra, M.R.: Network intrusion detection system: a machine learning approach. Intelligent Decision Technologies 5(4), 347–356 (2011)Google Scholar
  11. 11.
    Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants, Discrete Mathematics and Its Applications. CRC Press, Taylor & Francis Group, Boca Raton, FL (2012)Google Scholar
  12. 12.
    Plank, J.S.: Optimizing Cauchy Reed-Solomon Codes for Fault-Tolerant Storage Applications. Tech. Rep. CS-05-569. University of Tennessee (December 2005)Google Scholar
  13. 13.
    Tsabana, B., Vishne, U.: Efficient Linear Feedback Shift Registers with Maximal Period. Finite Fields and their Applications 8(2), 256–267 (2002)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Universidad Internacional de Castilla y León (UNICYL)BurgosSpain
  2. 2.Information Security Institute, C.S.I.C.MadridSpain

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