Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography]
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Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 4, Pages 73–97 (Mi mvk136)  

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties

K. N. Pankov

Moscow State Institute of Radio Engineering, Electronics and Automation, Moscow

Abstract: For linear combinations of coordinate functions of random Boolean mapping a local limit theorem for the distribution of subsets of weights of submappings is improved. Also a local limit theorem for subsets of their spectral coefficients is proved. By means of these theorems we obtain upper and lower asymptotic estimates for numbers of correlation-immune and ($n,m,k$)-resilient Boolean mappings. Also we obtain an upper asymptotic estimate of the number of plateaued Boolean mappings.

Key words: random binary mapping, local limit theorem, spectral coefficient, correlation-immune Boolean mapping, resilient Boolean mapping, plateaued Boolean mapping.

DOI: https://doi.org/10.4213/mvk136

Full text: PDF file (472 kB)
References: PDF file   HTML file

UDC: 519.212.2+519.214
Received 22.IV.2013

Citation: K. N. Pankov, “Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties”, Mat. Vopr. Kriptogr., 5:4 (2014), 73–97

Citation in format AMSBIB
\Bibitem{Pan14}
\by K.~N.~Pankov
\paper Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties
\jour Mat. Vopr. Kriptogr.
\yr 2014
\vol 5
\issue 4
\pages 73--97
\mathnet{http://mi.mathnet.ru/mvk136}
\crossref{https://doi.org/10.4213/mvk136}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Gorodilova, “Ot kriptoanaliza shifra k kriptograficheskomu svoistvu bulevoi funktsii”, PDM, 2016, no. 3(33), 16–44  mathnet  crossref
    2. K. N. Pankov, “Utochnennye asimptoticheskie otsenki dlya chisla $(n,m,k)$-ustoichivykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2017, no. 10, 46–49  mathnet  crossref
    3. K. N. Pankov, “Improved asymptotic estimates for the numbers of correlation-immune and $k$-resilient vectorial Boolean functions”, Discrete Math. Appl., 29:3 (2019), 195–213  mathnet  crossref  crossref  mathscinet  isi  elib
    4. K. N. Pankov, “Uluchshennye asimptoticheskie otsenki dlya chisla korrelyatsionno-immunnykh dvoichnykh funktsii i otobrazhenii”, PDM. Prilozhenie, 2018, no. 11, 49–52  mathnet  crossref  elib
    5. K. N. Pankov, “Rekurrentnye formuly dlya chisla $k$-elastichnykh i korrelyatsionno-immunnykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2019, no. 12, 62–66  mathnet  crossref  elib
    6. K. Pankov, “Enumeration of boolean mapping with given cryptographic properties for personal data protection in blockchain data storage”, Proceedings of the 24Th Conference of Open Innovations Association (Fruct), Proceedings Conference of Open Innovations Association Fruct, IEEE, 2019, 300–306  isi
    7. K. N. Pankov, “Uluchshennye otsenki dlya chisla $k$-elastichnykh i korrelyatsionno-immunnykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2021, no. 14, 48–51  mathnet  crossref
  • Математические вопросы криптографии
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