On Verification of Restricted Extended Affine Equivalence of Vectorial Boolean Functions

  • Ferruh Özbudak
  • Ahmet Sınak
  • Oğuz YaylaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


Vectorial Boolean functions are used as substitution boxes in cryptosystems. Designing inequivalent functions resistant to known attacks is one of the challenges in cryptography. In doing this, finding a fast technique for determining whether two given functions are equivalent is a significant problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this paper. We update the verification procedures of the REA-equivalence types given in the recent work of Budaghyan and Kazymyrov (2012). In particular, we solve the system of linear equations simultaneously in the verification procedures to get better complexity. We also present the explicit number of operations of the verification procedures of these REA-equivalence types. Moreover, we construct two new REA-equivalence types and present the verification procedures of these types with their complexities.


Vectorial Boolean functions EA-equivalence REA-equivalence 



We first thank the referees for providing detailed comments and suggestions. The second author is partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK). The third author is supported by TÜBİTAK under the National Postdoctoral Research Scholarship No 2219.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  4. 4.Department of Mathematics and Computer SciencesNecmettin Erbakan UniversityKonyaTurkey

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