Construction of weightwise almost perfectly balanced Boolean functions on an arbitrary number of variables

The recent FLIP cipher is an encryption scheme described by Méaux et al. at EUROCRYPT 2016. In the FLIP cipher, the input to the Boolean function used as a filter function has constant Hamming weight equal to the weight of the secret key. Weightwise perfectly balanced Boolean functions, which can be...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2022-01, Vol.307, p.102-114
Main Authors: Guo, Xiaoqi, Su, Sihong
Format: Article
Language:English
Subjects:
[formula omitted]-Hamming weight
Algorithms
Boolean
Boolean algebra
Boolean functions
Codes
Encryption
FLIP cipher
Mathematical analysis
Weightwise (almost) perfectly balancedness
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Summary:The recent FLIP cipher is an encryption scheme described by Méaux et al. at EUROCRYPT 2016. In the FLIP cipher, the input to the Boolean function used as a filter function has constant Hamming weight equal to the weight of the secret key. Weightwise perfectly balanced Boolean functions, which can be used in the FLIP cipher, only exist on 2m variables, while weightwise almost perfectly balanced Boolean functions can exist on an arbitrary number of variables. In this paper, we first introduce a class of quadratic Boolean functions on n variables, where n is a positive integer. We then propose a construction of weightwise almost perfectly balanced Boolean functions on n variables by modifying the support of the quadratic Boolean functions.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.10.011