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Information-theoretically secure oblivious polynomial evaluation in the commodity-based model

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Abstract

Oblivious polynomial evaluation (OPE) consists of a two-party protocol where a sender inputs a polynomial \(p(x)\) and a receiver inputs a single value \(x_{0}\). At the end of the protocol, the sender learns nothing and the receiver learns \(p(x_{0})\). This paper deals with the problem of oblivious polynomial evaluation under an information-theoretic perspective, which is based on the definitions of unconditional security developed by Crépeau et al. (Information-theoretic conditions for two-party secure function evaluation. EUROCRYPT 2006, LNCS 4004. Springer, Berlin, Heidelberg, pp 538–554, 2006). In this paper, we propose an information-theoretic model for oblivious polynomial evaluation relying on pre-distributed data and prove very general lower bounds on the size of the pre-distributed data, as well as the size of the communications in any protocol. It is demonstrated that these bounds are tight by obtaining a round-optimal OPE protocol, which meets the lower bounds simultaneously. We present a natural generalization to OPE called oblivious linear functional evaluation.

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Notes

  1. In the computational security setting, OT can be based on various assumptions [3, 11–13, 16, 20, 27, 28, 30].

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Brasilia, Campus Darcy Ribeiro, Brasília , 70910-900, Brazil

    Rafael Tonicelli & Anderson C. A. Nascimento

  2. Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Am Fasanengarten 5, 76128 , Karlsruhe, Germany

    Rafael Dowsley & Jörn Müller-Quade

  3. National Institute of Advanced Industrial Science and Technology (AIST), 1-18-13, Sotokanda, Chyioda-ku, Tokyo , 101-0021, Japan

    Hideki Imai, Goichiro Hanaoka & Akira Otsuka

Authors
  1. Rafael Tonicelli
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  2. Anderson C. A. Nascimento
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  3. Rafael Dowsley
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  4. Jörn Müller-Quade
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  5. Hideki Imai
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  6. Goichiro Hanaoka
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  7. Akira Otsuka
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Corresponding author

Correspondence to Rafael Dowsley.

Additional information

A preliminary, conference version of this work appeared in [17]. We would like to point out that this journal version uses a more strict, simulation-based model of security for the positive results which implies the security of sequential compositions of the protocol. In addition, the proofs of the lower bounds are generalized to cover also protocols with multiple rounds instead of being for one-round protocols only.

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Tonicelli, R., Nascimento, A.C.A., Dowsley, R. et al. Information-theoretically secure oblivious polynomial evaluation in the commodity-based model. Int. J. Inf. Secur. 14, 73–84 (2015). https://doi.org/10.1007/s10207-014-0247-8

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