International Journal of Information Security

, Volume 14, Issue 1, pp 73–84

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

  • Rafael Tonicelli
  • Anderson C. A. Nascimento
  • Rafael Dowsley
  • Jörn Müller-Quade
  • Hideki Imai
  • Goichiro Hanaoka
  • Akira Otsuka
Regular Contribution

DOI: 10.1007/s10207-014-0247-8

Cite this article as:
Tonicelli, R., Nascimento, A.C.A., Dowsley, R. et al. Int. J. Inf. Secur. (2015) 14: 73. doi:10.1007/s10207-014-0247-8

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.

Keywords

Information-theoretic cryptography Cryptographic primitives Oblivious polynomial evaluation Commodity-based model 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rafael Tonicelli
    • 1
  • Anderson C. A. Nascimento
    • 1
  • Rafael Dowsley
    • 2
  • Jörn Müller-Quade
    • 2
  • Hideki Imai
    • 3
  • Goichiro Hanaoka
    • 3
  • Akira Otsuka
    • 3
  1. 1.Department of Electrical EngineeringUniversity of BrasiliaBrasília Brazil
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.National Institute of Advanced Industrial Science and Technology (AIST)Tokyo Japan