International Conference on Theory and Practice of Natural Computing

Theory and Practice of Natural Computing pp 71-82 | Cite as

Evolutionary Approach for Finding Correlation Immune Boolean Functions of Order t with Minimal Hamming Weight

  • Stjepan Picek
  • Sylvain Guilley
  • Claude Carlet
  • Domagoj Jakobovic
  • Julian F. Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9477)


The role of Boolean functions is prominent in several areas like cryptography, sequences and coding theory. Therefore, various methods to construct Boolean functions with desired properties are of direct interest. When concentrating on Boolean functions and their role in cryptography, we observe that new motivations and hence new properties have emerged during the years. It is important to note that there are still many design criteria left unexplored and this is where Evolutionary Computation can play a distinct role. One combination of design criteria that has appeared recently is finding Boolean functions that have various orders of correlation immunity and minimal Hamming weight. Surprisingly, most of the more traditionally used methods for Boolean function generation are inadequate in this domain. In this paper, we concentrate on a detailed exploration of several evolutionary algorithms and their applicability for this problem. Our results show that such algorithms are a viable choice when evolving Boolean functions with minimal Hamming weight and certain order of correlation immunity. This approach is also successful in obtaining Boolean functions with several values that were known previously to be theoretically optimal, but no one succeeded in finding actual Boolean functions with such values.


Boolean functions Cryptography Correlation immunity Hamming weight Evolutionary algorithms 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Stjepan Picek
    • 1
  • Sylvain Guilley
    • 2
    • 3
  • Claude Carlet
    • 4
    • 5
  • Domagoj Jakobovic
    • 6
  • Julian F. Miller
    • 7
  1. 1.ESAT/COSIC and IMindsKU LeuvenLeuven-heverleeBelgium
  2. 2.TELECOM-ParisTechParis Cedex 13France
  3. 3.Secure-IC S.A.S.Cesson-SévignéFrance
  4. 4.LAGA, UMR 7539, CNRS, Department of MathematicsUniversity of Paris 8Saint-Denis CedexFrance
  5. 5.LAGA, UMR 7539, CNRS, Department of MathematicsUniversity of Paris 13VilletaneuseFrance
  6. 6.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia
  7. 7.Department of ElectronicsUniversity of YorkYorkUK

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