Two-Stage Optimal Hypotheses Testing for a Model of Stegosystem with an Active Adversary

Abstract

We study the information-theoretic model of stegosystem with an active adversary, where unlike a passive adversary he can not only read but also write. The legitimate sender as well as the adversary can embed or not a message in the sending data. The receiver’s first task is to decide whether the communication is a covertext, data with no hidden message, or a stegotext, modified data with a hidden secret message. In case of stegotext, the receiver’s second task is to decide whether the message was sent by a legitimate sender or from an adversary. For this purpose an authenticated encryption from the legitimate sender is considered. In this paper we suggest two-stage statistical hypothesis testing approach from the receivers point of view. We propose the logarithmically asymptotically optimal testing for this model. As a result the functional dependence of reliabilities of the first and second kind of errors in both stages is constructed. A comparison of overall error probabilities with the situation of one stage hypotheses testing is discussed and the behaviour of functional dependences of reliabilities are illustrated.