The main goal of this tutorial is to review the theory and design the worst case additive attack (WCAA) for ∣M∣-ary quantization-based data-hiding methods using as performance criteria the error probability and the maximum achievable rate of reliable communications. Our analysis focuses on the practical scheme known as distortion compensation dither modulation (DC-DM). From the mathematical point of view, the problem of the worst case attack (WCA) design using probability of error as a cost function is formulated as the maximization of the average probability of error subject to the introduced distortion for a given decoding rule. When mutual information is selected as a cost function, a solution to the minimization problem should provide such an attacking noise probability density function (pdf) that will maximally decrease the rate of reliable communications for an arbitrary decoder structure. The obtained results demonstrate that, within the class of additive attacks, the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the additive white Gaussian or uniform noise attacks.