Multi-party computation is receiving more and more attention as its application in more areas prove promising. In this research, our focus is on secure two-party computation. In particular, we propose non-interactive constructions for securely computing private equality testing and greater-than testing protocols. Our first construction is a private equality testing (PET) protocol. What distinguishes our construction from the state of the art is that it is single-round and secure against malicious adversaries. Our second construction is a private greater-than testing (PGT) protocol (i.e. the Yao's Millionaires problem) which is also single-round but only secure in the semi-honest model. Our protocols are based on the Peikert-Vaikuntanathan-Waters maliciously secure oblivious transfer and a collision resistant hash function.
We formally prove that the PET protocol and the PGT protocol provide computational security. In this research, we developed our protocol for PET and run experiments to test it. The results provide evidence of efficiency of our protocol.