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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 402, Pages 91–107 (Mi znsl5240)  
A complete one-way function based on a free finite rank $\mathbb Z\times\mathbb Z$-module

S. I. Nikolenkoab, D. S. Tugaryova

a Academic University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: It is known that the subsemimodule membership problem for finite rank free $\mathbb Z\times\mathbb Z$-modules is undecidable. Modifying the undecidability construction, we present a complete one-way function based on finite rank free $\mathbb Z\times\mathbb Z$-modules.
Key words and phrases: one-way functions, average-case complexity, tiling problems.
Received: 16.05.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 3, Pages 307–315
DOI: https://doi.org/10.1007/s10958-013-1397-3
Bibliographic databases:
Document Type: Article
UDC: 510.53
Language: Russian
Citation: S. I. Nikolenko, D. S. Tugaryov, “A complete one-way function based on a free finite rank $\mathbb Z\times\mathbb Z$-module”, Combinatorics and graph theory. Part IV, RuFiDiM'11, Zap. Nauchn. Sem. POMI, 402, POMI, St. Petersburg, 2012, 91–107; J. Math. Sci. (N. Y.), 192:3 (2013), 307–315
Citation in format AMSBIB
\Bibitem{NikTug12}
\by S.~I.~Nikolenko, D.~S.~Tugaryov
\paper A complete one-way function based on a~free finite rank $\mathbb Z\times\mathbb Z$-module
\inbook Combinatorics and graph theory. Part~IV
\bookinfo RuFiDiM'11
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 402
\pages 91--107
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5240}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2981981}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 3
\pages 307--315
\crossref{https://doi.org/10.1007/s10958-013-1397-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884985454}
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