Secure multiparty computation is a research focus in the international cryptographic community and a pivotal privacy preserving technology in cyberspaces. Privacy-Preserving lexicographical string sorting, as a completely new problem of secure multi-party computation, has important practical significance and broad application prospects in information security. It can not only improve the efficiency of secure database query but also solve the millionaires' problem in the case that the numbers to be compared are very large. In this study, to privately determine the lexicographical order of two private strings, an encoding scheme is first proposed to encode private numbers, then based on a homomorphic encryption algorithm supported by cloud computing outsourcing, a simple and efficient protocol is developed. Furthermore, a proof is provided to shoe that this protocol is secure in the semi-honest model, and its correctness is also analyzed. At the same time, the computational complexities and communication complexities of the protocol are analyzed, and the efficiency of the protocol on a PC is demonstrated. Finally, as a fundamental solution, the scheme is applied to solve the millionaires' problem in the case that the numbers to be compared are very large.