An Accurate Evaluation of Maurer’s Universal Test

  • Jean -Sébastien Coron
  • David Naccache
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1556)


Maurer’s universal test is a very common randomness test, capable of detecting a wide gamut of statistical defects. The algorithm is simple (a few Java code lines), flexible (a variety of parameter combinations can be chosen by the tester) and fast. Although the test is based on sound probabilistic grounds, one of its crucial parts uses the heuristic approximation:
$$ c\left( {L, K} \right) \cong 0.7 - \frac{{0.8}} {L} + \left( {1.6 + \frac{{12.8}} {L}} \right)K^{ - {4 \mathord{\left/ {\vphantom {4 L}} \right. \kern-\nulldelimiterspace} L}} $$

In this work we compute the precise value of c(L, K) and show that the inaccuracy due to the heuristic estimate can make the test 2.67 times more permissive than what is theoretically admitted. Moreover, we establish a new asymptotic relation between the test parameter and the source’s entropy.


Accurate Evaluation Binary Sequence Stationary Source Memory Source Asymptotic Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    R. Ash, Information theory, Dover publications, New-York, 1965.zbMATHGoogle Scholar
  2. 2.
    D. Knuth, The art of computer programming, Seminumerical algorithms, vol. 2, Addison-Wesley publishing company, Reading, pp. 2–160, 1969.Google Scholar
  3. 3.
    R. Langley, Practical statistics, Dover publications, New-York, 1968.Google Scholar
  4. 4.
    G. Marsaglia, Monkey tests for random number generators, Computers & mathematics with applications, vol. 9, pp. 1–10, 1993.CrossRefMathSciNetGoogle Scholar
  5. 5.
    U. Maurer, A universal statistical test for random bit generators, Journal of cryptology, vol. 5, no. 2, pp. 89–105, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C. Shannon, A mathematical theory of communication, The Bell system technical journal, vol. 27, pp. 379–423, 623–656, July–October, 1948.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jean -Sébastien Coron
    • 1
  • David Naccache
    • 2
  1. 1.Ecole Normale SupérieureParisFrance
  2. 2.Gemplus Card InternationalIssy-les-MoulineauxFrance

Personalised recommendations