A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions

A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions

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 pre...

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Main Authors: Modjtaba Ghorbani, Matthias Dehmer, Vahid Taghvayi-Yazdelli, Frank Emmert-Streib
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Axioms
Subjects:
boolean functions
Walsh spectrum
Cayley graphs
algebraic immunity
non-linearity
Online Access:https://www.mdpi.com/2075-1680/8/2/40
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spelling doaj-7a4012ef1f8649f889f2677701d29c9f2020-11-25T00:48:20ZengMDPI AGAxioms2075-16802019-04-01824010.3390/axioms8020040axioms8020040A Graph Theoretic Approach to Construct Desired Cryptographic Boolean FunctionsModjtaba Ghorbani0Matthias Dehmer1Vahid Taghvayi-Yazdelli2Frank Emmert-Streib3Department of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran 16785-136, IranSteyr School of Management, University of Applied Sciences Upper Austria, 4400 Steyr, AustriaDepartment of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran 16785-136, IranPredictive Medicine and Data Analytics Lab, Department of Signal Processing, Tampere University of Technology, 33100 Tampere, FinlandIn 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.https://www.mdpi.com/2075-1680/8/2/40boolean functionsWalsh spectrumCayley graphsalgebraic immunitynon-linearity
collection DOAJ
language English
format Article
sources DOAJ
author Modjtaba Ghorbani
Matthias Dehmer
Vahid Taghvayi-Yazdelli
Frank Emmert-Streib
spellingShingle Modjtaba Ghorbani
Matthias Dehmer
Vahid Taghvayi-Yazdelli
Frank Emmert-Streib
A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
Axioms
boolean functions
Walsh spectrum
Cayley graphs
algebraic immunity
non-linearity
author_facet Modjtaba Ghorbani
Matthias Dehmer
Vahid Taghvayi-Yazdelli
Frank Emmert-Streib
author_sort Modjtaba Ghorbani
title A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
title_short A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
title_full A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
title_fullStr A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
title_full_unstemmed A Graph Theoretic Approach to Construct Desired Cryptographic Boolean Functions
title_sort graph theoretic approach to construct desired cryptographic boolean functions
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2019-04-01
description 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.
topic boolean functions
Walsh spectrum
Cayley graphs
algebraic immunity
non-linearity
url https://www.mdpi.com/2075-1680/8/2/40
work_keys_str_mv AT modjtabaghorbani agraphtheoreticapproachtoconstructdesiredcryptographicbooleanfunctions
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