Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2019, Issue 12, Pages 154–160
DOI: https://doi.org/10.17223/2226308X/12/44
(Mi pdma459)
 

Mathematical Methods of Cryptography

Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system

V. A. Roman'kov

Omsk State University
References:
Abstract: We present an efficient algorithm to compute a discrete logarithm in a finite nilpotent group, or more generally, in a finitely generated nilpotent group. Special cases of a finite $p$-group ($p$ is a prime) and a finitely generated torsion free nilpotent group are considered. Then we show how the derived algorithm can be generalized to an arbitrary finite or finitely generated nilpotent group respectively. We suppose that group is presented by generating elements and defining relators or like a subgroup of a triangular matrix group over a prime finite field (in finite case) or over the ring of integers (in torsion-free case). On the base of the derived algorithm we give a cryptanalysis of some schemes of polylinear cryptography known in the literature.
Keywords: discrete logarithm, nilpotent group, polylinear system, cryptanalysis.
Funding agency Grant number
Russian Foundation for Basic Research 18-41-550001_а
The author is supported by RFBR, project No. 18-41-550001а.
Bibliographic databases:
Document Type: Article
UDC: 003.26
Language: English
Citation: V. A. Roman'kov, “Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 154–160
Citation in format AMSBIB
\Bibitem{Rom19}
\by V.~A.~Roman'kov
\paper Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system
\jour Prikl. Diskr. Mat. Suppl.
\yr 2019
\issue 12
\pages 154--160
\mathnet{http://mi.mathnet.ru/pdma459}
\crossref{https://doi.org/10.17223/2226308X/12/44}
\elib{https://elibrary.ru/item.asp?id=41153913}
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  • https://www.mathnet.ru/eng/pdma/y2019/i12/p154
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