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Distribution of recurrent sequences modulo prime powers

Abstract
  • Richard G. E. Pinch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1025)

Abstract

We study the distribution of linear recurrent sequences modulo p n for prime p when the auxiliary polynomial is irreducible and the period is maximal. We show that such a sequence takes each possible value equally often up to an error of order pn/2.

References

  1. 1.
    M. Ganley (ed.), Cryptography and coding III, IMA conference series (n.s.), vol. 45, Institute of Mathematics and its Applications, Oxford University Press, 1993, Proceedings, 3rd IMA conference on cryptography and coding, Cirencester, December 1991.Google Scholar
  2. 2.
    Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopaedia of Mathematics and its applications, vol. 20, Addison-Wesley, Reading Mass., 1983, 0-201-13519-1, Republished, Cambridge University Press, 1984.Google Scholar
  3. 3.
    -, Introduction to finite fields and their applications, second ed., Cambridge University Press, 1994, First edition 1986.Google Scholar
  4. 4.
    M. Mascagni, S.A. Ciccaro, D.V. Pryor, and M.L. Robinson, A fast, high-quality and reproducible lagged-Fibonacci pseudrandom number generator, Technical report SRC-TR-94-115, Supercomputing Research Center, IDA, Bowie, MD, U.S.A., Feb 1994.Google Scholar
  5. 5.
    Harald Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), no. 6, 957–1041.Google Scholar
  6. 6.
    -, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323–346.Google Scholar
  7. 7.
    R.G.E. Pinch, Recurrent sequences modulo prime powers, In Ganley [1], pp. 297–310.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Richard G. E. Pinch
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK

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