Abstract: Perfect secrecy of cryptosystem is one of the important methods weighing the security of secrecy system.Based on the deep analysis of the relationship among plaintext size, ciphertext size, key size and the key probability of perfect secrecy of cryptosystem, two necessary conditions for special perfect secrecy cryptosystem were presented and proved. hhis paper suggested an approach to build perfect secrecy cryptosystem and summarized four correlated restriclions. By researching a question about the existence of a sort of special perfect secrecy cryptosystem which does not be solved, this paper gave the conclusion and correlative proof; furthermore, this paper got a group of relationship of parameter among plaintext size, ciphertext size, and key size, and proved that perfect secrecy cryptosystem can not be built in this way. The results contract the conditions to build perfect secrecy cryptosystem and develop communication theory of Shannon's secrecy system and arc helpful for designing secure cryptosystem.

Key words: Cryptography, Cryptosystem, Perfect secrecy, Computational security, Equivalent keys