Derivation of Error Distribution in Least Squares Steganalysis

This paper considers the least squares method (LSM) for estimation of the length of payload embedded by least-significant bit replacement in digital images. Errors in this estimate have already been investigated empirically, showing a slight negative bias and substantially heavy tails (extreme outliers). In this paper, (approximations for) the estimator distribution over cover images are derived: this requires analysis of the cover image assumption of the LSM algorithm and a new model for cover images which quantifies deviations from this assumption. The theory explains both the heavy tails and the negative bias in terms of cover-specific observable properties, and suggests improved detectors. It also allows the steganalyst to compute precisely, for the first time, a p-value for testing the hypothesis that a hidden payload is present. This is the first derivation of steganalysis estimator performance