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-δ function. We derive the expression for the probability of error (Pe) in terms of distortion compensation factor, α, and the attack distribution. By maximizing Pe with respect to the attack distribution, we get the optimal placement of the 3-δ function. We then experimentally verify that the 3-δ function is indeed the worst case attack for quantization based data hiding.
Ning Liu, K. P. Subbalakshmi