On Unconditional ϵ-Security of Private Key Encryption

Motivated by perfect guessing security for private key encryption by Alimomeni and Safavi-Naini (ICITS 2012), we study the relations between various unconditional ∊-security notions, including $\epsilon$-guess security, ∊-min entropic security and ∊-Shannon security. We characterize the relations between these security notions. Our results stem from the essential mathematical properties of the underlying measures (i.e. guessing probability, min entropy and Shannon mutual information). We also prove the lower bound on either key entropy or key size or key min entropy for these models. Our results show that the ∊-security under these models has a large key size or (min) entropy and hence impossible to be efficient.