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Designs, Codes and Cryptography

Erschienen in:

10.11.2018

Weightwise perfectly balanced functions with high weightwise nonlinearity profile

verfasst von: Jian Liu, Sihem Mesnager

Erschienen in: Designs, Codes and Cryptography | Ausgabe 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.

Vorheriger Artikel Nearly optimal robust secret sharing

Nächster Artikel Optimal binary constant weight codes and affine linear groups over finite fields

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Titel: Weightwise perfectly balanced functions with high weightwise nonlinearity profile
verfasst von: Jian Liu
Sihem Mesnager
Publikationsdatum: 10.11.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 8/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0579-x

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