In the searchable encryption services, data owners wish to store different data ciphertexts and keyword indexes on different servers, so as to avoid centralized search of servers and infer the ciphertext information. A multi-server multi-keyword multi-user searchable encryption scheme under public channel is proposed by combining multi-user searchable encryption and multi-server features. This scheme allows data owners and users use the cloud servers' public keys to generate ciphertext indexes and search trapdoors, thereby satisfying the transmission under public channel and reducing the communication cost. The analysis results show that the proposal has lower communication cost. In the random oracle model, the proposed scheme is ciphertext index indistinguishable under the adaptive selection of keyword attacks in the decisional Diffie-Hellman problem.