Information-Theoretically Secure Oblivious Polynomial Evaluation in the Commodity-Based Model

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

Paper 2009/270

Information-Theoretically Secure Oblivious Polynomial Evaluation in the Commodity-Based Model

Rafael Tonicelli, Rafael Dowsley, Goichiro Hanaoka, Hideki Imai, Jörn Müller-Quade, Akira Otsuka, and Anderson C. A. Nascimento

Abstract

Oblivious polynomial evaluation (OPE) consists of a two-party protocol where a sender inputs a polynomial $P$ , and a receiver inputs a single value $i$ . At the end of the protocol, the sender learns nothing and the receiver learns $P (i)$ . This paper deals with the problem of oblivious polynomial evaluation under an information-theoretical perspective, which is based on recent definitions of Unconditional Security developed by Crépeau et al. (EUROCRYPT 2006). In this paper, we propose an information-theoretical 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. Some applications of the proposed model are provided, such as solutions for the ``Millionaire Problem'' and the ``Oblivious Equality Testing Problem''. We also present a natural generalization to OPE called oblivious linear functional evaluation.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): rdowsley @ cs ucsd edu
History: 2013-02-28: last of 3 revisions; 2009-06-09: received; See all versions
Short URL: https://ia.cr/2009/270
License: CC BY

BibTeX

@misc{cryptoeprint:2009/270,
      author = {Rafael Tonicelli and Rafael Dowsley and Goichiro Hanaoka and Hideki Imai and Jörn Müller-Quade and Akira Otsuka and Anderson C.  A.  Nascimento},
      title = {Information-Theoretically Secure Oblivious Polynomial Evaluation in the Commodity-Based Model},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/270},
      year = {2009},
      url = {https://eprint.iacr.org/2009/270}
}