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

Abstract

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. In this paper, we focus on the size of CR. We prove that we can construct more efficient protocol for a domain-restricted function when there is a “good” structure in CR space of a protocol for the original function, and show a unified way to construct a more efficient protocol in such case. In addition, we show two applications of the above result: The first application shows that some known techniques of reducing CR size for domain-restricted function can be derived in a unified way, and the second application shows that we can construct more efficient protocol than an existing one using our result.