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Prikl. Diskr. Mat., 2016, Number 3(33), Pages 93–97 (Mi pdm556)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Foundations of Informatics and Programming

On generic complexity of the discrete logarithm problem

A. N. Rybalov

Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

Abstract: Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behaviour of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are generically hard problems. In this paper, we consider generic complexity of the classical discrete logarithm problem. We fit this problem in the frameworks of generic complexity and prove that its natural subproblem is generically hard provided that the discrete logarithm problem is hard in the worst case.

Keywords: generic complexity, discrete logarithm problem, probabilistic algorithm.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-41-04312


DOI: https://doi.org/10.17223/20710410/33/8

Full text: PDF file (562 kB)
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Bibliographic databases:

UDC: 510.52

Citation: A. N. Rybalov, “On generic complexity of the discrete logarithm problem”, Prikl. Diskr. Mat., 2016, no. 3(33), 93–97

Citation in format AMSBIB
\Bibitem{Ryb16}
\by A.~N.~Rybalov
\paper On generic complexity of the discrete logarithm problem
\jour Prikl. Diskr. Mat.
\yr 2016
\issue 3(33)
\pages 93--97
\mathnet{http://mi.mathnet.ru/pdm556}
\crossref{https://doi.org/10.17223/20710410/33/8}


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  • http://mi.mathnet.ru/eng/pdm/y2016/i3/p93

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Rybalov, “O genericheskoi slozhnosti problemy izvlecheniya kornya v gruppakh vychetov”, PDM, 2017, no. 38, 95–100  mathnet  crossref
    2. A. N. Rybalov, “Generic amplification of recursively enumerable sets”, Algebra and Logic, 57:4 (2018), 289–294  mathnet  crossref  crossref  isi
    3. A. Rybalov, “On a generic turing reducibility of computably enumerable sets”, Xii International Scientific and Technical Conference Applied Mechanics and Systems Dynamics, Journal of Physics Conference Series, 1210, IOP Publishing Ltd, 2019, 012122  crossref  isi  scopus
  • Прикладная дискретная математика
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