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Designs, Codes and Cryptography

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15-01-2022

A note on “Cryptographically strong permutations from the butterfly structure”

Authors: Nian Li, Zhao Hu, Maosheng Xiong, Xiangyong Zeng

Published in: Designs, Codes and Cryptography | Issue 2/2022

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Abstract

Very recently, a class of cryptographically strong permutations with boomerang uniformity 4 and the best known nonlinearity is constructed from the closed butterfly structure in Li et al. (Des Codes Cryptogr 89(4):737–761, 2021). In this note, we provide two additional results concerning these permutations. We first represent the conditions of these permutation obtained in Li et al. (Des Codes Cryptogr 89(4):737–761, 2021) in a much simpler form, and then show that they are linear equivalent to Gold functions. We also prove a criterion for solving a new type of equations over finite fields, which is useful and may be of independent interest.

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Title: A note on “Cryptographically strong permutations from the butterfly structure”
Authors: Nian Li
Zhao Hu
Maosheng Xiong
Xiangyong Zeng
Publication date: 15-01-2022
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 2/2022
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-021-00974-5

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