Abstract: Nowadays, identity-based encryption (IBE) has become a new research direction of public key encryption, and security is the most important factor for constructing an IBE scheme. When designing a public encryption scheme, security goals are usually considered by the standard of attack models. And then, the definition of security combines both security goal and attack models. After analyzing the proposed IBE schemes, the authors present the formalized definition of IBE security and provide the comparison with security of traditional public key encryption. They also summarize the various mathematical assumptions on which the security relies and study the relations among assumptions. Furthermore, transformation rules among securities and transformation methods to reach higher security are described, and it is pointed out that these transformation methods all use some test in the construction, i.e., they give some additional disposal of ciphertext or factor construction in the encryption phase; meanwhile, they can verify the validity of ciphertext in the decryption phase. Later, also contrasted are the IBE schemes on the security and efficiency, which indicates that the transformation to reach higher security will reduce efficiency. Finally, the disadvantages of IBE, future research directions and open problems are summarized.