关于密码体制的完善保密性

On perfect secrecy of cryptosystem

从信息论的角度对密码体制的完善保密性进行了研究,通过比较明文空间、密文空间及密钥空间的各种熵和互信息量之间的关系得到了一般密码体制达到完善保密的一些充分与必要条件。此外,对每个密钥被等概使用的密码体制达到完善保密的条件进行了研究,得到了这类体制达到完善保密的1个充分必要条件。研究结果表明:一个密码体制要达到完善保密它的密钥空间的熵应不小于密文空间的熵;明文空间与密文空间的互信息量应该为零;密文空间互信息和密钥空间之间的互信息有关。

The perfect secrecy of cryptosystem was studied on the base of information theory, and a special cryptosystem whose every key is used in equally probability was studied. By analysing the entropy relationship among the spaces of paintext, cipertext and key, some necessary and sufficient conditions for the perfect secrecy of cryptosystem were obtained. The results show that when the cryptosystem is perfect secrecy which the spaces of key is not less than that of the space of cipertext which the relation information among the spaces of paintext and cipertext should be zero. The results develop the communication theory of secrecy system and help to design and understand the cryptosystem.