Multiplication triples from entangled quantum resources
An efficient paradigm for multi-party computation (MPC) are protocols structured around access to shared pre-processed computational resources. In this model, certain forms of correlated randomness are distributed to the participants prior to their computation. The shared randomness is then consumed in a computation phase that involves public communication with efficient round complexity, and the computation is secure in this second phase provided the initial correlations were distributed securely. Usually the latter requires some strong setup assumptions, such as a trusted dealer and private channels. We present a novel approach for generating these correlations from entangled quantum graph states and yield information-theoretic privacy guarantees that hold against a malicious adversary, with limited assumptions. Our primary contribution is a tripartite resource state and measurement-based protocol for extracting a binary multiplication triple, a special form of shared randomness that enables the private multiplication of a bit conjunction. Here, we employ a third party as a Referee and demand only an honest pair among the three parties. The role of this Referee is weaker than that of a Dealer, as the Referee learns nothing about the underlying shared randomness that is disseminated. We prove perfect privacy for our protocol, assuming access to an ideal copy of the resource state, an assumption that is based on the existence of graph state verification protocols. Finally, we demonstrate its application as a primitive for more complex Boolean functionalities such as 1-out-of-2 oblivious transfer (OT) and MPC for an arbitrary $N$-party Boolean function, assuming access to the proper broadcasting channel.