Currently, most quantization based data hiding al- gorithms are built assuming specific distributions of at- tacks, such as additive white Gaussian noise (AWGN), uniform noise, and so on. In this paper, we prove that the worst case additive attack for quantization based data hiding is a 3-\delta function. We derive the expression for the probability of error (P_e) in terms of distortion compensation factor, \alpha, and the attack distribution. By maximizing P_e with respect to the attack distribution, we get the optimal placement of the 3-\delta function. We then experimentally verify that the 3-\delta function is in- deed the worst case attack for quantization based data hiding.