Correlated Randomness Reduction in Domain-Restricted Secure Two-Party Computation

Secure two-party computation is a cryptographic tool that enables two parties to compute a function jointly without revealing their inputs. It is known that any function can be realized in the correlated randomness (CR) model, where a trusted dealer distributes input-independent CR to the parties beforehand. Sometimes we can construct more efficient secure two-party protocol for a function g than that for a function f, where g is a restriction of f. However, it is not known in which case we can construct more efficient protocol for domain-restricted function.