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Prikladnaya Diskretnaya Matematika, 2018, Number 40, Pages 34–58
DOI: https://doi.org/10.17223/20710410/40/4
(Mi pdm626)
 

This article is cited in 13 scientific papers (total in 16 papers)

Mathematical Methods of Cryptography

Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography

N. Tokarevaab, A. Gorodilovaab, S. Agievichc, V. Idrisovaab, N. Kolomeecab, A. Kutsenkoa, A. Oblaukhova, G. Shushuevb

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
c Belarusian State University, Minsk, Belarus
References:
Abstract: The mathematical problems, presented at the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016, and their solutions are considered. They are related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, the secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history. The problem is the following: construct $F\colon\mathbb F_2^5\to\mathbb F_2^5$ with maximum possible component algebraic immunity $3$ or prove that it does not exist. Alexey Udovenko from University of Luxembourg has found such a function.
Keywords: cryptography, ciphers, Boolean functions, biometry, blockchain, Olympiad, NSUCRYPTO.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
Russian Foundation for Basic Research 15-07-01328
17-41-543364
The work was supported by Russian Ministry of Science and Education under the 5-100 Excellence Programme, RMC NSU, and by the Russian Foundation for Basic Research (projects no. 15-07-01328, 17-41-543364).
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: English
Citation: N. Tokareva, A. Gorodilova, S. Agievich, V. Idrisova, N. Kolomeec, A. Kutsenko, A. Oblaukhov, G. Shushuev, “Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography”, Prikl. Diskr. Mat., 2018, no. 40, 34–58
Citation in format AMSBIB
\Bibitem{TokGorAgi18}
\by N.~Tokareva, A.~Gorodilova, S.~Agievich, V.~Idrisova, N.~Kolomeec, A.~Kutsenko, A.~Oblaukhov, G.~Shushuev
\paper Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography
\jour Prikl. Diskr. Mat.
\yr 2018
\issue 40
\pages 34--58
\mathnet{http://mi.mathnet.ru/pdm626}
\crossref{https://doi.org/10.17223/20710410/40/4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000438782300004}
\elib{https://elibrary.ru/item.asp?id=35155723}
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  • https://www.mathnet.ru/eng/pdm/y2018/i2/p34
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Прикладная дискретная математика
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