Paper 2022/1566

Characterisation of Bijectivity Preserving Componentwise Modification of S-Boxes

Kaisa Nyberg, Aalto University
Abstract

Various systematic modifications of vectorial Boolean functions have been used for finding new previously unknown classes of S-boxes with good or even optimal differential uniformity and nonlinearity. Recently, a new method was proposed for modification a component of a bijective vectorial Boolean function by using a linear function. It was shown that the modified function remains bijective under the assumption that the inverse of the function admits a linear structure. A previously known construction of such a modification based on bijective Gold functions in odd dimension is a special case of this type of modification. In this paper, we show that the existence of a linear structure is necessary. Further, we consider replacement of a component of a bijective vectorial Boolean function in the general case. We prove that a permutation on $\mathbb{F}_2^n$ remains bijective if and only if the replacement is done by composing the permutation with an unbalanced Feistel transformation where the round function is any Boolean function on $\mathbb{F}_2^{n-1}$.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
Boolean functions cryptographic S-boxes linear structures Feistel network
Contact author(s)
kaisa nyberg @ aalto fi
History
2022-11-10: approved
2022-11-10: received
See all versions
Short URL
https://ia.cr/2022/1566
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/1566,
      author = {Kaisa Nyberg},
      title = {Characterisation of Bijectivity Preserving Componentwise Modification of S-Boxes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/1566},
      year = {2022},
      url = {https://eprint.iacr.org/2022/1566}
}
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