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Axioms 2019, 8(2), 40; https://doi.org/10.3390/axioms8020040

A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions

1
Department of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran 16785-136, Iran
2
Steyr School of Management, University of Applied Sciences Upper Austria, 4400 Steyr, Austria
3
Department of Biomedical Computer Science and Mechatronics, UMIT, 6060 Hall in Tyrol, Austria
4
College of Artificial Intelligence, Nankai University, Tianjin 300071, China
5
Predictive Medicine and Data Analytics Lab, Department of Signal Processing, Tampere University of Technology, 33100 Tampere, Finland
6
Predictive Society and Data Analytics Lab, Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland
*
Author to whom correspondence should be addressed.
Received: 7 January 2019 / Revised: 15 March 2019 / Accepted: 26 March 2019 / Published: 3 April 2019
PDF [253 KB, uploaded 9 April 2019]
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Abstract

In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desired Walsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
Keywords: boolean functions; Walsh spectrum; Cayley graphs; algebraic immunity; non-linearity boolean functions; Walsh spectrum; Cayley graphs; algebraic immunity; non-linearity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ghorbani, M.; Dehmer, M.; Taghvayi-Yazdelli, V.; Emmert-Streib, F. A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions. Axioms 2019, 8, 40.

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