Link discovery is a process of identifying association(s) among different entities included in a complex network structure. These association(s) may represent any interaction among entities, for example between people or even bank accounts. The need for link discovery arises in many applications including law enforcement, counter-terrorism, social network analysis, intrusion detection, and fraud detection. Given the sensitive nature of information that can be revealedfrom link discovery, privacy is a major concern from the perspective of both individuals and organizations. For example, in the context of financial fraud detection, linking transactions may reveal sensitive information about other individuals not involved in any fraud. It is known that link discovery can be done in a privacy-preserving manner by securely finding the transitive closure of a graph.We propose two very efficient techniques to find the transitive closure securely. The two protocols have varying levels of security and performance We analyze the performance and usability of the proposed approach in terms of both analytical and experimental results.