Geodesic
On possibility to construct algebraic immune S-boxes by choosing coordinate Boolean functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 48-50

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Vectorial Boolean functions, or S-boxes, are the main nonlinear components of symmetric ciphers, and their properties ensure the cipher’s resistance to various types of cryptanalysis. \protect\break S-box can be presented as a set of Boolean functions called coordinate functions. One good way of constructing S-boxes is to carefully choose these coordinate Boolean functions with necessary cryptographic properties. We continue the study of the set of Boolean functions in a small number of variables with optimal algebraic and correlation immunity orders. The possibility of using these functions as coordinate functions of S-box resistant to algebraic cryptanalysis has been verified programmatically. However, these Boolean functions cannot be used to construct a permutation on $\mathbb{Z}^4_2$ as well as S-box with optimal component algebraic immunity using only a single Boolean function and a permutation.
Keywords: symmetric-key encryption, Boolean functions, S-boxes, algebraic immunity, correlation immunity. 
@article{PDMA_2024_17_a11,
     author = {I. S. Khilchuk},
     title = {On possibility to construct algebraic immune {S-boxes} by choosing coordinate {Boolean} functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {48--50},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a11/}
}
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I. S. Khilchuk. On possibility to construct algebraic immune S-boxes by choosing coordinate Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 48-50. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a11/