Compilation of Function Representations for Secure Computing Paradigms.

This paper introduces M-Circuits, a program representation which generalizes arithmetic and binary circuits. This new representation is motivated by the way modern multi-party computation (MPC) systems based on linear secret sharing schemes actually operate. We then show how this representation also allows one to construct zero knowledge proof (ZKP) systems based on the MPC-in-the-head paradigm. The use of the M-Circuit program abstraction then allows for a number of program-specific optimizations to be applied generically. It also allows to separate complexity and security optimizations for program compilation from those for application protocols (MPC or ZKP).