Non-asymptotic estimates for the probability of correct messages recovering in the binary erasure wiretap channel

Abstract

We consider an information transmission system which consists of an irredundant source of binary messages, an ideal main channel between the sender and the legitimate receiver, and an erasure wiretap channel between the sender and the adversary. A known method of random messages coding by binary linear codes is used to ensure reliable information security in the wiretap channel. We obtain the exact expression and non-asymptotic estimates for the probability of correct messages recovering in the wiretap channel. This parameter characterizes practical security of the above mentioned systems. Obtained estimates are applicable to a wide class of binary linear codes with known values of length, dimension and minimal (or dual) distance. They allow us to formulate criteria for choosing codes to construct practically secure and effective systems with ran-dom coding in the binary erasure channel and to set suffi-cient condition of asymptotic perfectness of such systems. The results can be applied for cryptographic applications based on the use of the wiretap channel model.