Symmetric cryptographic solution to Yao’s millionaires’ problem and an evaluation of secure multiparty computations

Secure multiparty computation has become a central research focus in the international cryptographic community and in the future likely will represent an integral part of computing science. Protocols for Yao’s millionaires’ problem provide the building blocks for many secure multiparty computation protocols, which makes their efficiency critical. Unfortunately, all known protocols for Yao’s millionaires’ problem employ public key cryptography and thus are inefficient. This article constructs a new efficient solution to Yao’s millionaires’ problem based on symmetric cryptography. We first develop an efficient protocol for set-inclusion problems, which has independent interest for secure multiparty computations. The privacy-preserving property of the solution is demonstrated by a well-accepted simulation paradigm. To compare the security levels of different solutions, we propose a new security paradigm that quantitatively captures the security levels of different solutions and can determine which secure multiparty computation solution is preferable. This article thus provides an important supplement to the simulation paradigm. Together with the simulation paradigm, it offers a complete security evaluation benchmark for multiparty computations.