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Algebra Discrete Math., 2015, Volume 20, Issue 1, Pages 152–170 (Mi adm537)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

On algebraic graph theory and non-bijective multivariate maps in cryptography

Vasyl Ustimenko

Maria Curie-Sklodowska University, Lublin

Abstract: Special family of non-bijective multivariate maps $F_n$ of ${Z_m}^n$ into itself is constructed for $n = 2, 3, …$ and composite $m$. The map $F_n$ is injective on $\Omega_n=\{x|x_1+x_2 + …x_n \in {Z_m}^* \}$ and solution of the equation $F_n(x)=b, x\in \Omega_n$ can be reduced to the solution of equation $z^r=\alpha$, $z \in {Z_m}^*$, $(r, \phi(m))=1$. The “hidden RSA cryptosystem” is proposed.
Similar construction is suggested for the case $\Omega_n={{Z_m}^*}^n$.

Keywords: multivariate cryptography, linguistic graphs, hidden Eulerian equation, hidden discrete logarithm problem.

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Received: 30.09.2015
Revised: 30.09.2015
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Citation: Vasyl Ustimenko, “On algebraic graph theory and non-bijective multivariate maps in cryptography”, Algebra Discrete Math., 20:1 (2015), 152–170

Citation in format AMSBIB
\Bibitem{Ust15}
\by Vasyl~Ustimenko
\paper On algebraic graph theory and non-bijective multivariate maps in cryptography
\jour Algebra Discrete Math.
\yr 2015
\vol 20
\issue 1
\pages 152--170
\mathnet{http://mi.mathnet.ru/adm537}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431957}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700012}


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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. Vasyl Ustimenko, “On new multivariate cryptosystems with nonlinearity gap”, Algebra Discrete Math., 23:2 (2017), 331–348  mathnet
    2. V. Ustymenko, A. Wroblewska, U. Romanczuk-Polubiec, E. Zhupa, M. Polak, “On the implementation of new symmetric ciphers based on non-bijective multivariate maps”, Proceedings of the 2018 Federated Conference on Computer Science and Information Systems (FedCSIS), eds. M. Ganzha, L. Maciaszek, M. Paprzycki, IEEE, 2018, 397–405  crossref  isi  scopus
  • Algebra and Discrete Mathematics
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