Circuit Privacy and Novel Protocols for Semi-Honest Three-Party Secure Multiparty Computation with an Honest Majority

In this work, we present a novel protocol class for secure three-party computation with an honest majority. We refer this protocol class as Oblivious Error Correction (OEC). For each multiplication gate, our replicated OEC protocol requires only two domain elements of global communication in the online phase and one element of communication in the offline phase. Also, only parties P2 and P3 are involved in the online phase. This makes our protocols especially interesting for cases where P1 can only communicate to the other parties with high latency. In both protocol's online phases a multiplication gate requires only 3 local multiplications in total. Our protocols are simulation-based secure in the presence of semi-honest adversaries, and achieve privacy but not correctness in the presence of malicious adversaries. Both presented protocols support the client-server model and work for both arithmetic and boolean circuits. Our duplicated OEC protocol can achieve circuit privacy against one or two of the computation nodes if the parties also communicate for every addition gate. The former property may be interesting to achieve a two-input-party computation where P3 only acts as an auxiliary party with no input and should not learn the computed function. The latter property may be interesting to let P2 and/or P3 supply private inputs to a confidential application logic of P1.