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Prikladnaya Diskretnaya Matematika, 2015, Number 2(28), Pages 54–58
DOI: https://doi.org/10.17223/20710410/28/6
(Mi pdm509)
 

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

Mathematical Methods of Cryptography

On generic complexity of the quadratic residuosity problem

A. N. Rybalov

Omsk State University, Omsk, Russia
Full-text PDF (572 kB) Citations (7)
References:
Abstract: Generic-case approach to algorithmic problems was suggested by Myasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior 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. For example, this is the classical discrete logarithm problem. In this talk we consider generic complexity of the quadratic residuosity problem. We fit this problem in the frameworks of generic complexity and prove that its natural subproblem is generically hard provided that the quadratic residuosity problem is hard in the worst case.
Keywords: generic complexity, quadratic residue, probabilistic algorithm.
Bibliographic databases:
Document Type: Article
UDC: 510.52
Language: Russian
Citation: A. N. Rybalov, “On generic complexity of the quadratic residuosity problem”, Prikl. Diskr. Mat., 2015, no. 2(28), 54–58
Citation in format AMSBIB
\Bibitem{Ryb15}
\by A.~N.~Rybalov
\paper On generic complexity of the quadratic residuosity problem
\jour Prikl. Diskr. Mat.
\yr 2015
\issue 2(28)
\pages 54--58
\mathnet{http://mi.mathnet.ru/pdm509}
\crossref{https://doi.org/10.17223/20710410/28/6}
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  • https://www.mathnet.ru/eng/pdm/y2015/i2/p54
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Прикладная дискретная математика
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    Full-text PDF :65
    References:57
     
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