Abstract: Proven security theory of public key cryptography algorithm clears the defination of the security of cryptography; Establish a basic definition, general cryptography research method based on the reduction to prove; Through strict proof，it combines the safety of the system and the known computational problem or cryptography. Proven security theory research pushs forward the standardization of the password system, a lot of standardization organization puts cryptosystem security certification as one of the password systems essential security properties, it requires new submission criteria of cryptography algorithm to be able to pass the security certificate, currently USES cryptography standards comply with this safety standards. It is proved that CFL is Provable Security with its private key being unrecoverable, and with EUFCMA under some conditions.

Key words: provable security, public key encryption, atomic primitives, random oracle model, CFL (Chen, Fan, and Lü)

摘要： 摘要公钥密码算法的可证明安全性理论，明确了密码体制的安全定义；建立起一种基本定义、基于归约证明的通用密码学研究方法；通过严格的证明把体制的安全性与已知的计算性难题或密码学关联起来.可证明安全性理论的研究推进了密码体制的标准化进程，很多标准化组织将密码体制的安全证明作为密码体制必备的安全属性，要求新提交的密码学标准中的算法能通过安全性证明，目前采用的密码学标准都遵从这种安全规范.在此基础上，证明了CFL是密钥不可恢复可证明安全的，同时证明了当CFL基于SM2，Hash函数满足随机语言机时，其为EUFCMA安全的.

关键词: 可证明安全性, 公钥加密, 极微本原, 随机预言机, CFL (Chen, Fan, and Lü)