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Non-linear Complexity of the Naor–Reingold Pseudo-random Function

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Information Security and Cryptology - ICISC’99 (ICISC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1787))

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Abstract

We obtain an exponential lower bound on the non-linear complexity of the new pseudo-random function, introduced recently by M. Naor and O. Reingold. This bound is an extension of the lower bound on the linear complexity of this function that has been obtained by F. Griffin and I. E. Shparlinski.

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References

  1. Cusick, T.W., Ding, C., Renvall, A.: Stream Ciphers and Number Theory. Elsevier, Amsterdam (1998)

    MATH  Google Scholar 

  2. Griffin, F., Shparlinski, I.E.: On the linear complexity of the Naor-Reingold pseudo-random function. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 301–308. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Cryptography. CRC Press, Boca Raton (1996)

    Book  Google Scholar 

  4. Naor, M., Reingold, O.: Number-theoretic constructions of effcient pseudo- random functions. In: Proc. 38th IEEE Symp. on Foundations of Comp. Sci (FOCS 1997), Miami Beach, pp. 458–467. IEEE, Los Alamitos (1997)

    Google Scholar 

  5. Niederreiter, H.: Some computable complexity measures for binary sequences. In: Ding, C., Helleseth, T., Niederreiter, H. (eds.) Proc. Intern. Conf. on Sequences and their Applications (SETA 1998), Singapore, pp. 67–78. Springer, London (1999)

    Google Scholar 

  6. Niederreiter, H., Vielhaber, M.: Linear complexity profiles: Hausdorff dimen- sion for almost perfect profiles and measures for general profiles. J. Compl. 13, 353–383 (1996)

    Article  MathSciNet  Google Scholar 

  7. Rueppel, R.A.: Stream ciphers. In: Contemporary Cryptology: The Science of In- formation Integrity, pp. 65–134. IEEE Press, NY (1992)

    Google Scholar 

  8. Shparlinski, I.E.: On the uniformity of distribution of the Naor–Reingold pseudo-random function. Finite Fields and Their Appl (to appear)

    Google Scholar 

  9. Shparlinski, I.E.: On the Naor–Reingold pseudo-random function from elliptic curves, pp. 1–9 (1999) (preprint)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    William D. Banks

  2. Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

    Frances Griffin & Daniel Lieman

  3. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

    Igor E. Shparlinski

Authors
  1. William D. Banks
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  2. Frances Griffin
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  3. Daniel Lieman
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  4. Igor E. Shparlinski
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Yonsei University, Seoul, Korea

    JooSeok Song

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© 2000 Springer-Verlag Berlin Heidelberg

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Banks, W.D., Griffin, F., Lieman, D., Shparlinski, I.E. (2000). Non-linear Complexity of the Naor–Reingold Pseudo-random Function. In: Song, J. (eds) Information Security and Cryptology - ICISC’99. ICISC 1999. Lecture Notes in Computer Science, vol 1787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719994_5

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  • DOI: https://doi.org/10.1007/10719994_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67380-4

  • Online ISBN: 978-3-540-45568-4

  • eBook Packages: Springer Book Archive

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