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Circuit complexity of linear functions: gate elimination and feeble security

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In this paper, we consider provably secure cryptographic constructions in the context of circuit complexity. Based on the ideas of provably secure trapdoor functions 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 nonconstructive proof of lower bounds on the circuit complexity of linear Boolean functions and upper bounds on circuit implementations of linear Boolean functions, obtaining specific constants. Bibliography: 53 titles.

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Authors and Affiliations

  1. St. Petersburg Academic University, St. Petersburg, Russia

    A. P. Davydow

  2. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    S. I. Nikolenko

Authors
  1. A. P. Davydow
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  2. S. I. Nikolenko
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Correspondence to A. P. Davydow.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 399, 2012, pp. 65–87.

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Davydow, A.P., Nikolenko, S.I. Circuit complexity of linear functions: gate elimination and feeble security. J Math Sci 188, 35–46 (2013). https://doi.org/10.1007/s10958-012-1104-9

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