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Composable Oblivious Extended Permutations

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Foundations and Practice of Security (FPS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8930))

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Abstract

An extended permutation is a function \(f:\{1,\ldots ,m\}\rightarrow \{1,\ldots ,n\}\), used to map an \(n\)-element vector \(\varvec{a}\) to an \(m\)-element vector \(\varvec{b}\) by \(b_i=a_{f(i)}\). An oblivious extended permutation allows this mapping to be done while preserving the privacy of \(\varvec{a}\), \(\varvec{b}\) and \(f\) in a secure multiparty computation protocol. Oblivious extended permutations have several uses, with private function evaluation (PFE) being the theoretically most prominent one.

In this paper, we propose a new technique for oblivious evaluation of extended permutations. Our construction is at least as efficient as the existing techniques, conceptually simpler, and has wider applicability. Our technique allows the party providing the description of \(f\) to be absent during the computation phase of the protocol. Moreover, that party does not even have to exist — we show how to compute the private representation of \(f\) from private data that may itself be computed from the inputs of parties. In other words, our oblivious extended permutations can be freely composed with other privacy-preserving operations in a multiparty computation.

Supported by the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 284731 “Usable and Efficient Secure Multiparty Computation (UaESMC)”, by Estonian Research Council through grant no. IUT27-1, and by European Regional Development Fund through the Estonian Center of Excellence in Computer Science (EXCS).

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Authors and Affiliations

  1. Cybernetica AS, Tallinn, Estonia

    Peeter Laud & Jan Willemson

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  1. Peeter Laud
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  2. Jan Willemson
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Correspondence to Peeter Laud .

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Editors and Affiliations

  1. TELECOM Bretagne, Cesson Sévigné, France

    Frédéric Cuppens

  2. TELECOM SudParis, Evry, France

    Joaquin Garcia-Alfaro

  3. Dalhousie University, Halifax, Nova Scotia, Canada

    Nur Zincir Heywood

  4. University of Calgary, Calgary, Canada

    Philip W. L. Fong

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Laud, P., Willemson, J. (2015). Composable Oblivious Extended Permutations. In: Cuppens, F., Garcia-Alfaro, J., Zincir Heywood, N., Fong, P. (eds) Foundations and Practice of Security. FPS 2014. Lecture Notes in Computer Science(), vol 8930. Springer, Cham. https://doi.org/10.1007/978-3-319-17040-4_19

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  • DOI: https://doi.org/10.1007/978-3-319-17040-4_19

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