| Reference : Weightwise perfectly balanced functions and nonlinearity |
| Scientific congresses, symposiums and conference proceedings : Paper published in a book | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Computer science | |||
| Security, Reliability and Trust | |||
| http://hdl.handle.net/10993/53434 | |||
| Weightwise perfectly balanced functions and nonlinearity | |
| English | |
Gini, Agnese  [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > PI Coron >] | |
| Meaux, Pierrick [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > PI Coron >] | |
| 2022 | |
| Codes, Cryptology and Information Security | |
| Springer | |
| 338--359 | |
| Yes | |
| 978-3-031-33016-2 | |
| Codes, Cryptology and Information Security: 4th International Conference | |
| from 29-05-2023 to 31-05-2023 | |
| Rabat | |
| Morocco | |
| [en] WPB functions ; Boolean functions ; Mathematical Crypto ; Nonlinearity | |
| [en] In this article we realize a general study on the nonlinearity of weightwise perfectly balanced (WPB)
<br />functions. First, we derive upper and lower bounds on the nonlinearity from this class of functions for all n. Then, <br />we give a general construction that allows us to provably provide WPB functions with nonlinearity as low as <br />2 <br />n/2−1 <br />and WPB functions with high nonlinearity, at least 2 <br />n−1 − 2 <br />n/2 <br />. We provide concrete examples in 8 and <br />16 variables with high nonlinearity given by this construction. In 8 variables we experimentally obtain functions <br />reaching a nonlinearity of 116 which corresponds to the upper bound of Dobbertin’s conjecture, and it improves <br />upon the maximal nonlinearity of WPB functions recently obtained with genetic algorithms. Finally, we study the <br />distribution of nonlinearity over the set of WPB functions. We examine the exact distribution for n = 4 and provide <br />an algorithm to estimate the distributions for n = 8 and 16, together with the results of our experimental studies for <br />n = 8 and 16. | |
| http://hdl.handle.net/10993/53434 | |
| also: http://hdl.handle.net/10993/55685 | |
| 10.1007/978-3-031-33017-9_21 | |
| https://eprint.iacr.org/2022/1777.pdf |
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