The disclosure proposes a novel method for generating public polynomials. The method simplifies key exchange processes, reduces the time required for key exchange and reduces the bandwidth required for data transmission from a server to a client. Secondly, the method keeps the calculation processes at both sides synchronized through a novel data exchange solution, particularly through handshaking signals, to ensure that the server and the client are always in the same key exchange process. In addition, the method further reduces a transmission bandwidth by sending information of the client twice. A state synchronization mechanism of the client and the server is proposed in the disclosure to ensure that Trivium modules at both sides are in the same state at the beginning of each key exchange, thereby avoiding reinitializing the modules and improving the operation efficiency of the whole system.