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Zap. Nauchn. Sem. POMI, 2012, Volume 399, Pages 65–87 (Mi znsl5221)  

Circuit complexity of linear functions: gate elimination and feeble security

A. P. Davydowa, S. I. Nikolenkob

a St. Petersburg Academic University — Nanotechnology Research and Education Centre of the Russian Academy of Sciences (the Academic University), St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: In this work, we consider provably secure cryptographic constructions in the context of circuit complexity. Based on the ideas of provably secure trapdoor functions previously developed in (Hirsch, Nikolenko, 2009; Melanich, 2009), we present a new linear construction of a provably secure trapdoor function with order of security $5/4$. Besides, we present an in-depth general study of the gate elimination method for the case of linear functions. We also give a non-constructive proof of nonlinear lower bounds on the circuit complexity of linear Boolean functions and upper bounds on circuit implementations of linear Boolean functions, obtaining specific constants.

Key words and phrases: feeble security, circuit complexity, trapdoor functions, provable security.

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English version:
Journal of Mathematical Sciences (New York), 2013, 188:1, 35–46

Bibliographic databases:

UDC: 519.6
Received: 31.01.2012

Citation: A. P. Davydow, S. I. Nikolenko, “Circuit complexity of linear functions: gate elimination and feeble security”, Computational complexity theory. Part X, Zap. Nauchn. Sem. POMI, 399, POMI, St. Petersburg, 2012, 65–87; J. Math. Sci. (N. Y.), 188:1 (2013), 35–46

Citation in format AMSBIB
\Bibitem{DavNik12}
\by A.~P.~Davydow, S.~I.~Nikolenko
\paper Circuit complexity of linear functions: gate elimination and feeble security
\inbook Computational complexity theory. Part~X
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 399
\pages 65--87
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5221}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2945000}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 1
\pages 35--46
\crossref{https://doi.org/10.1007/s10958-012-1104-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871935818}


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