Worst Case Attack on Quantization Based Data Hiding

Currently, most quantization based data hiding algorithms are built assuming specific distributions of attacks, 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 indeed the worst case attack for quantization based data hiding