Biblio
We consider transmissions of secure messages over a burst erasure wiretap channel under decoding delay constraint. For block codes we introduce and study delay optimal secure burst erasure correcting (DO-SBE) codes that provide perfect security and recover a burst of erasures of a limited length with minimum possible delay. Our explicit constructions of DO-SBE block codes achieve maximum secrecy rate. We also consider a model of a burst erasure wiretap channel for the streaming setup, where in any sliding window of a given size, in a stream of encoded source packets, the eavesdropper is able to observe packets in an interval of a given size. For that model we obtain an information theoretic upper bound on the secrecy rate for delay optimal streaming codes. We show that our block codes can be used for construction of delay optimal burst erasure correcting streaming codes which provide perfect security and meet the upper bound for a certain class of code parameters.
It is investigated how to achieve semantic security for the wiretap channel. A new type of functions called biregular irreducible (BRI) functions, similar to universal hash functions, is introduced. BRI functions provide a universal method of establishing secrecy. It is proved that the known secrecy rates of any discrete and Gaussian wiretap channel are achievable with semantic security by modular wiretap codes constructed from a BRI function and an error-correcting code. A characterization of BRI functions in terms of edge-disjoint biregular graphs on a common vertex set is derived. This is used to study examples of BRI functions and to construct new ones.
This paper presents the recent progress in studying the algorithmic computability of capacity expressions of secure communication systems. Several communication scenarios are discussed and reviewed including the classical wiretap channel, the wiretap channel with an active jammer, and the problem of secret key generation.