Statistics and Computing

, Volume 5, Issue 4, pp 307–310 | Cite as

Testing for randomness in stream ciphers using the binary derivative

  • Neville Davies
  • Ed Dawson
  • Helen Gustafson
  • A. N. Pettitt


The binary derivative has been used to measure the randomness of a binary string formed by a pseudorandom number generator for use in cipher systems. In this paper we develop statistical properties of the binary derivative and show that certain types of randomness testing in binary derivatives are equivalent to well-established tests for randomness in the original string. A uniform method of testing randomness in binary strings is described based on using the binary derivative. We show that the new tests are faster and more powerful than several of the well-established tests for randomness.


Bernoulli trials binary derivative cryptography pseudorandom sequence stream cipher 


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Copyright information

© Chapman & Hall 1995

Authors and Affiliations

  • Neville Davies
    • 1
  • Ed Dawson
    • 2
  • Helen Gustafson
    • 3
  • A. N. Pettitt
    • 3
  1. 1.Department of Mathematics, Statistics and Operational ResearchThe Nottingham Trent UniversityNottinghamUK
  2. 2.Information Security Research Centre, Queensland University of TechnologyBrisbaneAustralia
  3. 3.School of Mathematics, Queensland University of TechnologyBrisbaneAustralia

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