skip to main content
article
Free Access

Initializing generalized feedback shift register pseudorandom number generators

Published:10 August 1986Publication History
Skip Abstract Section

Abstract

The generalized feedback shift register pseudorandom number generators proposed by Lewis and Payne provide a very attractive method of random number generation. Unfortunately, the published initialization procedure can be extremely time consuming. This paper considers an alternative method of initialization based on a natural polynomial representation for the terms of a feedback shift register sequence that results in substantial improvements in the initialization process.

References

  1. 1 ARVILLIAS, A. C., AND MARITSAS, D.G. Partitioning the period of a class of m-sequences and application to pseudorandom number generation. J. ACM 25, 4 (Oct. 1978), 675-686. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2 BECKMAN, R. J., AND JOHNSON, M. E. A ranking procedure for partial discriminant analysis. J. Am. Stat. Assoc. 76 (1981), 671-675.Google ScholarGoogle ScholarCross RefCross Ref
  3. 3 BRIGHT, H. S., AND ENISON, R. L. Quasi-random number sequences for a long-period TLP generator with remarks on application to cryptography. ACM Comput. Surv. I1, 4 (Dec. 1979), 357-370. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4 I'~EMBREE, G. B. Random number generation on micro-computers. Tech. Rep. Montana State Univ. Statistical Center, Bozeman, Montana.Google ScholarGoogle Scholar
  5. 5 LATAWIEC, K.J. New method of generation of shifted linear pseudorandom binary sequences. Proc. IEE 121'(1974), 905-906.Google ScholarGoogle Scholar
  6. 6 LEWIS, T. G., AND PAYNE, W. H. Generalized feedback shift register pseudorandom number algorithm. J. ACM 20, 3 (July 1973), 456-468. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7 MARITSAS, D. G., ARVILLIAS, A. C., AND BOUNAS, A.C. Phase-shift analysis of linear feedback shift register structures generating pseudorandom sequences. IEEE Trans. Comput. C-27, (1978), 660-669.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8 MARSAGLIA, G. Random numbers fall mainly in the planes. Proc. Nat. Acad. Sci. 61 (1968), 25-28.Google ScholarGoogle ScholarCross RefCross Ref
  9. 9 PAYNE, W. H., AND MCMILLEN, K. L. Orderly enumeration of nonsingular binary matrices applied to text encryption. Commun. ACM 21, 4 (Apr. 1978), 259-263. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10 SIMMONS, G.J. Symmetric and asymmetric encryption. ACM Comput. Surv. 11, 4 (Dec. 1979) 305-330. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11 TAUSWORTHE, R. C. Random numbers generated by linear recurrence modulo two. Math. Comput. 19 (1965), 201-209.Google ScholarGoogle ScholarCross RefCross Ref
  12. 12 TOOTILL, J. P. R., ROaiNSON, W. D., AND ADAMS, A.G. The runs up-and-down performance of Tausworthe pseudo-random number generators. J. ACM 18, 3 (July 1971), 381-399. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13 TOOTILL, J. P. R., ROBINSON, W. D., AND EAGLE, O.J. An asymptotically random Tausworthe sequence. J. ACM 20, 3 (July 1973), 469-481. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14 WEISS, M.S. Modifications of the Kolmogorov-Smirnov statistic for use with correlated data. J. Am. Stat. Assoc. 73 (1978), 872-875.Google ScholarGoogle ScholarCross RefCross Ref
  15. 15 WHITTLESEY, J. R.B. On the multidimensional uniformity of pseudorandom number generators. Commun. ACM 12, 5 (May 1969), 247. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. 16 ZIERLER, N. Linear recurring sequences. J. SIAM 7 (1959), 31-48.Google ScholarGoogle Scholar
  17. 17 ZIERLER, N., AND BRILLHART, J. On primitive trinomials (rood 2). Inf. Control 13 (1968), 541-554.Google ScholarGoogle ScholarCross RefCross Ref
  18. 18 ZIERLER, N., AND BRILLHART, J. On primitive trinomials (mod 2), If. Inf. Control 14 (1969), 566-569.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Initializing generalized feedback shift register pseudorandom number generators

    Recommendations

    Reviews

    Andrew Donald Booth

    Feedback shift register techniques are useful in both hardware and software forms. They have found particular application in the efficient generation of code sequences for correlation sonar and related oceanographic devices. The authors consider the software variety and are concerned with initialization techniques. The SETR procedure of Lewis and Payne [1] is shown to be inefficient, and a new algorithm INIT is described and analyzed. A practical trial on a VAX 11/780 shows that, in the case considered, INIT took 1.3 seconds against 27 seconds for SETR. On an ALTOS microcomputer the corresponding times were five seconds and 210 seconds. This is a useful new technique.

    Access critical reviews of Computing literature here

    Become a reviewer for Computing Reviews.

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    • Published in

      cover image Journal of the ACM
      Journal of the ACM  Volume 33, Issue 4
      Oct. 1986
      189 pages
      ISSN:0004-5411
      EISSN:1557-735X
      DOI:10.1145/6490
      Issue’s Table of Contents

      Copyright © 1986 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 10 August 1986
      Published in jacm Volume 33, Issue 4

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • article

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader
    About Cookies On This Site

    We use cookies to ensure that we give you the best experience on our website.

    Learn more

    Got it!