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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 8/2019

10-11-2018

Weightwise perfectly balanced functions with high weightwise nonlinearity profile

Authors: Jian Liu, Sihem Mesnager

Published in: Designs, Codes and Cryptography | Issue 8/2019

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Abstract

Boolean functions satisfying good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher (Méaux et al.: in Lecture Notes in Computer Science, vol. 9665, pp. 311–343, Springer, Berlin, 2016). In this paper, we propose a large class of weightwise perfectly balanced (WPB) functions, which is 2-rotation symmetric. This new class of WPB functions is not extended affinely equivalent to the known constructions. We also discuss the weightwise nonlinearity profile of these functions, and present general lower bounds on k-weightwise nonlinearity, where k is a power of 2. Moreover, we exhibit a subclass of the family. By a recursive lower bound, we show that these subclass of WPB functions have very high weightwise nonlinearity profile.
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Metadata
Title
Weightwise perfectly balanced functions with high weightwise nonlinearity profile
Authors
Jian Liu
Sihem Mesnager
Publication date
10-11-2018
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 8/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-018-0579-x

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