Error-Detecting in Monotone Span Programs with Application to Communication Efficient Multi-Party Computation

Recent improvements in the state-of-the-art of MPC for nonfull-threshold access structures introduced the idea of using a collisionresistant hash functions and redundancy in the secret-sharing scheme to construct a communication-efficient MPC protocol which is computationallysecure against malicious adversaries, with abort. The prior work is based on replicated secret-sharing; in this work we extend this methodology to any multiplicative LSSS implementing a Q2 access structure. To do so we need to establish a folklore property of error detection for such LSSS and their associated Monotone Span Programs. In doing so we obtain communication-efficient online and offline protocols for MPC in the pre-processing model.

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