Detection of embeddings in binary Markov chains

The paper is concerned with problems in steganography on the detection of embeddings and statistical estimation of positions at which message bits are embedded. Binary stationary Markov chains with known or unknown matrices of transition probabilities are used as mathematical models of cover sequences (container files). Based on the runs statistics and the likelihood ratio statistic, statistical tests are constructed for detecting the presence of embeddings. For a family of contiguous alternatives, the asymptotic power of statistical tests based on the runs statistics is found. An algorithm of polynomial complexity is developed for the statistical estimation of positions with embedded bits. Results of computer experiments are presented.