Skip to main content
SpringerLink
Log in

On Stern’s Attack Against Secret Truncated Linear Congruential Generators

  • Conference paper
Information Security and Privacy (ACISP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3574))

Included in the following conference series:

Abstract

In 1987, Stern showed how the parameters for secret truncated linear congruential generators could be derived in polynomial time. Here, we present a modification to that algorithm which makes it simpler, more robust, and require less data. We then present a more careful analysis of the algorithm, and establish some limits of its applicability. Thus, secret truncated linear congruential generators may not necessarily be insecure for properly chosen parameters. Unfortunately, as in the original algorithm, all the results remain heuristic, however we present results of numerical experiments which support our conclusions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ajtai, M., Kumar, R., Sivakumar, D.: A sieve algorithm for the shortest lattice vector problem. In: Proc. 33rd ACM Symp. on Theory of Comput., pp. 601–610. ACM, New York (2001)

    Google Scholar 

  2. Boyar, J.: ‘Inferring sequences produced by pseudo-random number generators. J. ACM 36, 129–141 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Boyar, J.: Inferring sequences produces by a linear congruential generator missing low–order bits. J. Cryptology 1, 177–184 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  4. Frieze, A.M., Hastad, J., Kannan, R., Lagarias, J.C., Shamir, A.: Reconstructing truncated integer variables satisfying linear congruences. SIAM J. Comp. 17, 262–280 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Joux, A., Stern, J.: Lattice reduction: A toolbox for the cryptanalyst. J. Cryptology 11, 161–185 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Konyagin, S.V., Shparlinski, I.: Character sums with exponential functions and their applications. Cambridge Univ. Press, Cambridge (1999)

    Book  MATH  Google Scholar 

  7. Knuth, D.E.: Deciphering a linear congruential encryption. IEEE Trans. Inf. Theory 31, 49–52 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  8. Knuth, D.E.: The art of computer Programming: Seminumerical algorithms, vol. 2. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  9. Krawczyk, H.: How to predict congruential generators. J. Algorithms 13, 527–545 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kurlberg, P., Pomerance, C.: On the period of the linear congruential and power generators. Acta Arith. (to appear)

    Google Scholar 

  11. Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Mathematische Ann. 261, 513–534 (1982)

    Google Scholar 

  12. Magma Computer Algebra Package, http://magma.maths.usyd.edu.au/magma/

  13. Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. 84, 957–1041 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  14. Niederreiter, H.: Random number generation and Quasi–Monte Carlo methods. SIAM Press, Philadelphia (1992)

    MATH  Google Scholar 

  15. Schnorr, C.P.: A hierarchy of polynomial time basis reduction algorithms. Theor. Comp. Sci. 53, 201–224 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Stern, J.: Secret linear congruential generators are not cryptographically secure. In: Proc. 28th IEEE Symp. on Found. of Comp. Sci., pp. 421–426. IEEE, Los Alamitos (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, NSW 2109, Australia

    Scott Contini & Igor E. Shparlinski

Authors
  1. Scott Contini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Igor E. Shparlinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, Qld 4001, Brisbane, Australia

    Colin Boyd

  2. Information Security Institute, Queensland University of Technology, GPO Box 2434, QLD 4001, Brisbane, Australia

    Juan Manuel González Nieto

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Contini, S., Shparlinski, I.E. (2005). On Stern’s Attack Against Secret Truncated Linear Congruential Generators. In: Boyd, C., González Nieto, J.M. (eds) Information Security and Privacy. ACISP 2005. Lecture Notes in Computer Science, vol 3574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11506157_5

Download citation

  • DOI: https://doi.org/10.1007/11506157_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26547-4

  • Online ISBN: 978-3-540-31684-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation