Additions, Multiplications, and the Interaction In-Between: Optimizing MPC Protocols via Leveled Linear Secret Sharing (Full Version)

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Secure multiparty computation (MPC) enables distrusting parties in a distributed system to compute on their private inputs without compromising their privacy. For many secret-sharing-based approaches, including some of today's most efficient MPC protocols, there is a pattern where two shared values are locally multiplied into some intermediate representation that is immediately and interactively translated back into sharings of the product. The intermediate representation is often still a full-f