On the concept of a $\varepsilon$-perfect cipher

The generalizations of the perfect cipher concept are discussed. A cipher is called $\varepsilon$-perfect if the maximum absolute value of the difference between the posterior and prior probabilities of a plaintext does not exceed $\varepsilon$. Two constructions of $\varepsilon$-perfect ciphers for a multitude of plaintexts with a minor limitation of their frequency characteristics are studied. The notion of $\varepsilon$-perfect cipher is one of the possible approximations to the notion of a perfect cipher. For studied constructions of ciphers, it is shown that, in comparison with the other such approximations, $\varepsilon$-perfectness and its analogues have much better proximity to perfectness.