Secure multiparty computation (SMC) is a key technology of cyberspace security and privacy preservation, and it is vital to provide secure cloud computing with SMC based on homomorphic encryption schemes. Secure set computing, which has extensive applications, is a fundamental problem in SMC. Existing solutions to secure set computing are mainly constructed between two parties, but less presented on multi-parties. Those schemes are inefficient, and are hardly adequate to cloud computing. This study proposes a new coding scheme and incorporates homomorphic encryption algorithm to construct a protocol for secure set union computing in cloud environment. The proposed scheme is universal and secure against the collusion of participants. The homomorphic encryption adopted can be either additive or multiplicative. The paper also proposes an efficient secure set union computing scheme, incorporating the G?del numbering and ElGamal public key encryption. The proposed schemes can be used to sort multiple sets, and are proved to be secure in the semi-honest model. In addition, with few modifications, the protocol can also securely compute the intersection of multiple sets.