|
This article is cited in 1 scientific paper (total in 1 paper)
Distance between vectorial Boolean functions and affine analogues (following the Eighth International Olympiad in Cryptography)
V. G. Ryabov NP «GST», Moscow
Abstract:
We study the Hamming distance from a vectorial Boolean function to a set of affine mappings (the nonlinearity of a vectorial function). New upper bound on the nonlinearity of vectorial functions and lower bound on the nonlinearity of mappings with a given differential uniformity are obtained, which refine the previously known ones. The dependence of the Hamming distance between a vectorial function and an affine mapping on the Walsh – Hadamard coefficients of nonzero linear combinations of coordinates of the vectorial function is found, which makes it possible to give estimates of nonlinearity in terms of these coefficients.
Key words:
vectorial Boolean function, Hamming distance, nonlinearity, differential uniformity, bent function, APN function, Walsh-Hadamard coefficients.
Received 08.X.2023
Citation:
V. G. Ryabov, “Distance between vectorial Boolean functions and affine analogues (following the Eighth International Olympiad in Cryptography)”, Mat. Vopr. Kriptogr., 15:1 (2024), 127–142
Linking options:
https://www.mathnet.ru/eng/mvk466https://doi.org/10.4213/mvk465 https://www.mathnet.ru/eng/mvk/v15/i1/p127
|
Statistics & downloads: |
Abstract page: | 185 | Full-text PDF : | 14 | References: | 55 | First page: | 40 |
|