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Generating cryptographically strong Boolean functions using partial information

Authors
  • Šimovcová, Marta1
  • Stanek, Martin2
  • 1 Slovak University of Technology, Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Ilkovičova 3, Bratislava, 812 19, Slovakia , Bratislava
  • 2 Comenius University Mlynská dolina, Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Bratislava, 842 48, Slovakia , Bratislava
Type
Published Article
Journal
Periodica Mathematica Hungarica
Publisher
Kluwer Academic Publishers
Publication Date
Sep 01, 2004
Volume
49
Issue
1
Pages
119–130
Identifiers
DOI: 10.1023/B:MAHU.0000040543.22350.a0
Source
Springer Nature
Keywords
License
Yellow

Abstract

In our paper we study the usage of partially defined Boolean functions (PDBFs) for generating cryptographically strong Boolean functions. A PDBF can be considered as a Boolean function with some undefined (unknown) values, i.e. its values are from the set 0,1,?. We generalize certain cryptographic properties to PDBFs, such as balancedness, nonlinearity and propagation characteristics. It is shown that usual relationships among properties hold for these generalizations as well. We apply these results to methods for generating cryptographically strong Boolean functions. We focus on greedy approach and test it in various settings. The paper compares obtained results with other methods.

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