IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
Further Results on Autocorrelation of Vectorial Boolean Functions
Zeyao LINiu JIANGZepeng ZHUO
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JOURNAL FREE ACCESS

2023 Volume E106.A Issue 10 Pages 1305-1310

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Abstract

In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $\sum_{u\in \mathbb{F}_2^n,v\in \mathbb{F}_2^m}\mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.

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© 2023 The Institute of Electronics, Information and Communication Engineers
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