Unconditionally secure distributed oblivious polynomial evaluation

Abstract

Oblivious polynomial evaluation (OPE) was first introduced by Naor and Pinkas in 1999. An OPE protocol involves a receiver, R who holds a value, α and a sender, S with a private polynomial, f(x). OPE allows R to compute fα without revealing either α or f(x). Since its inception, OPE has been established as an important building block in many distributed applications. In this article we investigate a method of achieving unconditionally secure distributed OPE (DOPE) in which the function of the sender is distributed amongst a set of n servers. Specifically, we introduce a model for DOPE based on the model for distributed oblivious transfer (DOT) described by Blundo et al. in 2002. We then describe a protocol that achieves the security defined by our model. Our DOPE protocol is efficient and achieves a high level of security. Furthermore, our proposed protocol can also be used as a DOT protocol with little to no modification.