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Diskretnaya Matematika, 2016, Volume 28, Issue 2, Pages 117–126
DOI: https://doi.org/10.4213/dm1374 (Mi dm1374) 		 
On $1$-stable perfectly balanced Boolean functions

S. V. Smyshlyaev

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DOI: https://doi.org/10.4213/dm1374
Abstract: The paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the $1$-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is $1$-stable.
Keywords: perfectly balanced functions, barriers of Boolean functions, correlation-immunity, cryptography.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00226 А
16-01-00470 А
This work was supported by the Russian Fund for Basic Research, grant nos. 16-01-00226-a and 16-01-00470-a).
Received: 19.04.2016
English version:
Discrete Mathematics and Applications, 2017, Volume 27, Issue 2, Pages 109–115
DOI: https://doi.org/10.1515/dma-2017-0013
Bibliographic databases:
Document Type: Article
UDC: 519.716.322+519.719.2
Language: Russian
Citation: S. V. Smyshlyaev, “On $1$-stable perfectly balanced Boolean functions”, Diskr. Mat., 28:2 (2016), 117–126; Discrete Math. Appl., 27:2 (2017), 109–115
Citation in format AMSBIB
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\pages 117--126
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\jour Discrete Math. Appl.
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  • https://www.mathnet.ru/eng/dm/v28/i2/p117
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    		Дискретная математика
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