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Prikl. Diskr. Mat., 2015, Number 2(28), Pages 54–58 (Mi pdm509)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematical Methods of Cryptography

On generic complexity of the quadratic residuosity problem

A. N. Rybalov

Omsk State University, Omsk, Russia

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.

DOI: https://doi.org/10.17223/20710410/28/6

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Bibliographic databases:

UDC: 510.52

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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    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 raspoznavaniya kvadratichnykh vychetov”, PDM. Prilozhenie, 2015, no. 8, 71–73  mathnet  crossref
    2. A. N. Rybalov, “O genericheskoi slozhnosti problemy izvlecheniya kornya v gruppakh vychetov”, PDM, 2017, no. 38, 95–100  mathnet  crossref
    3. A. N. Rybalov, “Generic amplification of recursively enumerable sets”, Algebra and Logic, 57:4 (2018), 289–294  mathnet  crossref  crossref  isi
    4. 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
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