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Weightwise almost perfectly balanced functions: secondary constructions for all n and better weightwise nonlinearities
Gini, Agnese; Meaux, Pierrick
2022In Weightwise Almost Perfectly Balanced Functions: Secondary Constructions for All n and Better Weightwise Nonlinearities
Peer reviewed
 

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Keywords :
FLIP cipher; Boolean functions; Weightwise (almost) perfectly balanced function; Weightwise nonlinearity
Abstract :
[en] The design of FLIP stream cipher presented at Eurocrypt 2016 motivates the study of Boolean functions with good cryptographic criteria when restricted to subsets of F n 2 . Since the security of FLIP relies on properties of functions restricted to subsets of constant Hamming weight, called slices, several studies investigate functions with good properties on the slices, i.e. weightwise properties. A major challenge is to build functions balanced on each slice, from which we get the notion of Weightwise Almost Perfectly Balanced (WAPB) functions. Although various constructions of WAPB functions have been exhibited since 2017, building WAPB functions with high weightwise nonlinearities remains a difficult task. Lower bounds on the weightwise nonlinearities of WAPB functions are known for very few families, and exact values were computed only for functions in at most 16 variables. In this article, we introduce and study two new secondary constructions of WAPB functions. This new strategy allows us to bound the weightwise nonlinearities from those of the parent functions, enabling us to produce WAPB functions with high weightwise nonlinearities. As a practical application, we build several novel WAPB functions in up to 16 variables by taking parent functions from two different known families. Moreover, combining these outputs, we also produce the 16-variable WAPB function with the highest weightwise nonlinearities known so far.
Disciplines :
Mathematics
Computer science
Author, co-author :
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
External co-authors :
no
Language :
English
Title :
Weightwise almost perfectly balanced functions: secondary constructions for all n and better weightwise nonlinearities
Publication date :
2022
Event name :
Progress in Cryptology - {INDOCRYPT} 2022 - 23rd International Conference in Cryptology in India
Event date :
December 11-14, 2022
Audience :
International
Main work title :
Weightwise Almost Perfectly Balanced Functions: Secondary Constructions for All n and Better Weightwise Nonlinearities
Publisher :
springer
Pages :
492--514
Peer reviewed :
Peer reviewed
Commentary :
Paper accepted at INDOCRYPT2022
Available on ORBilu :
since 25 October 2022

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