An information theoretic framework for order of operations forensics

To verify the authenticity of easily manipulated multimedia content, forensic researchers have proposed many techniques to estimate the processing history of given multimedia content. When multiple operations may be applied on multimedia content, a complete processing history would involve the information of not only what manipulation operations have been applied, but also in what order they were applied. However, there are few works considering the problem of detecting the order of operations. Moreover, due to the interplay among operations, the order of operations may not always be detectable. This leads to a fundamental question of when we can or cannot detect the order of operations. In this paper, we propose an information theoretical framework to answer this question. Specifically, we formulate the problem of detecting the order of operations into a multiple hypotheses testing problem. Then, we propose an information theoretical framework to characterize the relationship between the true hypothesis and the detected hypothesis. Under this framework, we propose a mutual information based criterion to determine the detectability of the order of operations. Furthermore, conditional fingerprints are defined in this framework to understand why the order of operations is not always detectable. The detection of the order of resizing and blurring is examined in this paper, where the order detection scheme has been proposed and the effectiveness of our framework has been demonstrated by simulations.