The main goal of this study consists in the development of the worst case additive attack (WCAA) for quantization-based methods using as design criteria the bit error rate probability and the maximum achievable rate of reliable communications. Our analysis is focused on the practical scheme known as a 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 can be 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 of 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 results show that within the class of additive noise attacks the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the AWGN or the uniform noise attacks.