Authentication methods in public cloud computing play considerably in preventing unauthorized access to data that had been saved in the public cloud. The aims of reviewing related works in this paper are to collect strong points and identify the weaknesses of the existing works on current authentication methods in public cloud computing from behavior authentication side. The investigation shows that there are many multi-factor authentication methods for obtaining authentication in public cloud computing. The top three methods are password with a smartcard, password with SMS or Mobile, and finally password with biometric. Many researchers have suggested authentication model in public cloud computing using these methods. However, all these methods have suffered from many drawbacks and threats. In this paper, we find that the accuracy of the current Multi-factor authentication in public cloud computing is deficient in dealing with the stolen of password attacks. In a related context, the best method to improve authentication accuracy is to obtain intelligent authentication operations by adapting learning mechanisms for behavior recognition that can provide mitigation to threats, automatically.