New fundamental properties on a secret-key cryptosystem under guessing secrecy criteria

In this paper we consider a secret-key cryptosystem with a wiretapper who tries to guess the plaintext corresponding to a transmitted ciphertext. We discuss several criteria of secrecy based on the probability of successful guess of a plaintext or a key from a ciphertext. We characterize fundamental properties of a secret-key cryptosystem satisfying such criteria. In particular, we show that in any secret-key cryptosystem the probability of the successful guess of a plaintext is always greater than or equal to that of a key under certain conditions. In addition, we point out the existence of a secret-key cryptosystem such that partial information of a plaintext is leaking even if the guessing secrecy criterion introduced by Alimomeni and Safavi-Naini is satisfied.