Combining Evolutionary Computation and Algebraic Constructions to Find Cryptography-Relevant Boolean Functions

  • Stjepan Picek
  • Elena Marchiori
  • Lejla Batina
  • Domagoj Jakobovic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8672)


Boolean functions play a central role in security applications because they constitute one of the basic primitives for modern cryptographic services. In the last decades, research on Boolean functions has been boosted due to the importance of security in many diverse public systems relying on such technology. A main focus is to find Boolean functions with specific properties. An open problem in this context is to find a balanced Boolean function with an 8-bit input and nonlinearity 118. Theoretically, such a function has been shown to exist, but it has not been found yet. In this work we focus on specific classes of Boolean functions, and analyze the landscape of results obtained by integrating algebraic and evolutionary computation (EC) based approaches. Results indicate that combinations of these approaches give better results although not reaching 118 nonlinearity.


Boolean Functions Nonlinearity Evolutionary Computation Bent Functions Cryptographic Properties 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Stjepan Picek
    • 1
    • 2
  • Elena Marchiori
    • 1
  • Lejla Batina
    • 1
  • Domagoj Jakobovic
    • 2
  1. 1.Institute for Computing and Information SciencesRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia

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