Index Assignment Optimized for Partial Encryption

In this work, we consider the partial encryption of the bitstream of entropy-coded outputs of a scalar quantizer. More specifically, the sequence of most significant bits (MSB) is separately compressed and the resulting bitstream is encrypted, while the remaining information is compressed but not encrypted. Motivated by the observation that the mapping which assigns binary indexes to quantizer outputs controls the quality of the reconstruction at the eavesdropper and the size of the portion to be encrypted, we address the problem of optimal index assignment design. Ideally, the goal is to maximize the eavesdropper’s distortion and minimize the length of the compressed MSB stream. Since these two objectives are conflicting, we formulate the problem as the maximization of a weighted sum of the distortion at the eavesdropper and the probability of the MSB being 0. We show that the problem can be cast as a maximum weighted graph matching problem, which is solvable in polynomial time. Experimental results assess the effectiveness of the proposed index assignment.