An Analysis of Empirical PMF Based Tests for Least Significant Bit Image Steganography

We consider here the class of probability mass-function (PMF) based detectors of least significant bit (LSB) embedded steganography. That is, in this paper we investigate the use of frequency counts of pixel intensities as a statistic for tests detecting the presence of hidden messages. We focus on LSB replacement (though we briefly consider LSB matching) embedding as it is a simple technique where the effect on the true PMF of the resulting image can be understood mathematically. We begin our study by considering the existing tests of Westfeld and Pfitzmann [11] and Dabeer et al. [1]. These tests assume that pixel intensities are random values that are independent and identically distributed (i.i.d.). We generalize these tests by considering PMFs of neighboring pixel intensities. We argue that consideration of higher order of correlations provide only diminishing marginal returns, and thus we can make general statements on the value of PMF based detectors. We measure the performance of our tests by calculation of receiver operating curves (ROC) over a corpus of 350 digital images. We then proceed to compare to a non-PMF based test, in particular the RS tests of Fridrich et al [3]. Although our generalized tests outperform existing PMF based predecessors, they are outperformed by the RS tests. This indicates that using PMFs as a statistic for detecting hidden messages is inherently insufficient.