Constant-Overhead Secure Computation of Boolean Circuits using Preprocessing

We present a protocol for securely computing a Boolean circuit C in presence of a dishonest and malicious majority. The protocol is unconditionally secure, assuming a preprocessing functionality that is not given the inputs. For a large number of players the work for each player is the same as computing the circuit in the clear, up to a constant factor. Our protocol is the first to obtain these properties for Boolean circuits. On the technical side, we develop new homomorphic authentication schemes based on asymptotically good codes with an additional multiplication property. We also show a new algorithm for verifying the product of Boolean matrices in quadratic time with exponentially small error probability, where previous methods only achieved constant error.

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