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Characteristics of highly nonlinear functions

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Abstract

The highly nonlinear odd-dimensional Boolean-functions have many applications in the cryptographic practice, that is why the research of that function-classes and construction of such functions have a great importance. This study focuses on some types of functions having special characteristics in the class of highly nonlinear odd-dimensional Boolean-functions. Upper bound can be given for the number of non-zero linear structures of such functions and regarding them as mappings some functional-relations can be proved. From the results one can gain two algorithms. By the help of the first one special highly nonlinear odd dimensional Boolean-functions can be constructed by using functions having the same characteristics, the second one renders possible the construction of bent functions of a one-level higher dimension by the use of special highly nonlinear odd-dimensional Boolean-functions. The paper shows a relation between bent functions in even dimensional Boolean-space and odd dimensional highly nonlinear Boolean functions.

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Authors and Affiliations

  1. Budapesti Gazdasági Főiskola Kereskedelmi, Vendéglátóipari és Idegenforgalmi Kar, Informatikai Intézet, 1054 Budapest, V., Alkotmány utca 9-11., Hungary

    Ildikó Licskó

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  1. Ildikó Licskó
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Licskó, I. Characteristics of highly nonlinear functions. Periodica Mathematica Hungarica 47, 135–149 (2003). https://doi.org/10.1023/B:MAHU.0000010817.08940.47

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  • DOI: https://doi.org/10.1023/B:MAHU.0000010817.08940.47

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