In order to build a multi-key secure multi-party computation ( SMC) protocol with high performance,the key homomorphic properties of Gentry-Sahai-Waters ( GSW13) fully-homomorphic encryption ( FHE) scheme is in- vestigated.Afterwards,a general multi-key SMC protocol with simple structure,which needs only 3 rounds of inter- actions,is proposed on the basis of leveled GSW13.In the semi-honesty and semi-malicious setting as well as in the common random string model,the security of the protocol relies on the learning with errors ( LWE) problem and a variant of LWE.Then,the difficulty in solving the variant is analyzed,and a formalized security proof in semi- malicious setting is given.The proposed SMC protocol naturally constitutes a leveled multi-key FHE scheme in the same setting.Comparative analysis results show that the proposed protocol is superior to the existing schemes in terms of overall performance.