Distributed Protocols for Oblivious Transfer and Polynomial Evaluation

A secure multiparty computation (MPC) allows several parties to compute a function over their inputs while keeping their inputs private. In its basic setting, the protocol involves only parties that hold inputs. In distributed MPC, there are also external servers who perform a distributed protocol that executes the needed computation, without learning information on the inputs and outputs. Here we propose distributed protocols for several fundamental MPC functionalities. We begin with a Distributed Scalar Product (DSP) protocol for computing scalar products of private vectors. We build upon DSP in designing various protocols for Oblivious Transfer (OT): k-out-of-N OT, Priced OT, and Generalized OT. We also use DSP for Oblivious Polynomial Evaluation (OPE) and Oblivious Multivariate Polynomial Evaluation (OMPE). All those problems involve a sender and a receiver that hold private vectors and they wish to compute their scalar product. However, in each of these problems the receiver must submit a vector of a specified form. Hence, a crucial ingredient in our protocols is a sub-protocol for validating that the receiver’s vector complies with the relevant restrictions, without learning anything else on that vector. Therefore, while previous studies presented distributed protocols for 1-out-of-N OT and OPE, our protocols are the first ones that are secure against malicious receivers. Our distributed protocols for the other OT variants and for OMPE are the first ones that handle such problems. Our protocols offer information-theoretic security, under the assumption that the servers are semi-honest and have an honest majority, and they are very efficient.