Joseph Nelson
Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India.

Chungath Srinivasan
TIFAC-CORE in Cyber Security, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India.

K. V. Lakshmy
TIFAC-CORE in Cyber Security, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India.

DOI https://doi.org/10.33889/IJMEMS.2023.8.5.060

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Abstract

Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 four-variable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions.

Keywords- Primary construction of bent functions, Algorithm to construct bent functions, Boolean functions, Number of bent functions, Auto correlation.

Citation

Nelson, J., Srinivasan, C., & Lakshmy, K. V (2023). An Algorithm for Constructing Support of Bent Functions by Extending a Set. International Journal of Mathematical, Engineering and Management Sciences, 8(5), 1040-1055. https://doi.org/10.33889/IJMEMS.2023.8.5.060.