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Journal of Information Security and Applications

A constant round quantum secure protocol for oblivious polynomial evaluation

Tapaswini Mohanty, Vikas Srivastava, Sihem Mesnager, Sumit Kumar Debnath

Published Aug 4, 2023• 2 citations
Publisher
DOI
10.1016/j.jisa.2023.103560

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The study of secure multiparty computation has yielded powerful feasibility results showing that any efficient functionality can be securely computed in the presence of malicious adversaries. Despite this, there are few problems of specific interest for which we have highly efficient protocols that are secure in the presence of malicious adversaries under full simulation based definitions (following the ideal/real model paradigm). Due to the difficulties of constructing such protocols, many researchers have resorted to weaker definitions of security and weaker adversary models. In this paper, we construct highly efficient protocols for the well-studied problem of oblivious polynomial evaluation. Our protocol is secure under standard cryptographic assumptions for the settings of malicious adversaries, and readily transform to protocols that are secure under universal composability and in the presence of covert adversaries. Our protocol is constant round and requires O(d · s) exponentiations, where d is the degree of the polynomial and s is a statistical security parameter (that should equal about 160 in practice).
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 x0. At the end of the protocol, the sender learns nothing and the receiver learns p(x0). This paper deals with the problem of oblivious polynomial evaluation under an information-theoretic perspective, which is based on recent definitions of Unconditional Security developed by Crépeau et al. [11]. 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.