Derivation of Error Distribution in Least Squares Steganalysis

Abstract

We consider the Least Squares Method (LSM) for estimation of length of payload embedded by Least Significant Bit (LSB) 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 work we derive (approximations for) the estimator distribution over cover images: 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, 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. To our knowledge this is the first derivation of steganalysis estimator performance.