Information Theoretical Limit of Operation Forensics
Abstract—While more and more forensic techniques have been proposed to detect the processing history of multimedia content, one starts to wonder if there exists a fundamental limit on the capability of forensics. In other words, besides keeping on searching what investigators can do, it is also important to find out the limit of their capability and what they cannot do. In this work, we explore the fundamental limit of operation forensics by proposing an information theoretical framework. Specifically, we consider a general forensic system of estimating operations’ hypotheses based on extracted features from the multimedia content. In this system, forensicability is defined as the maximum forensic information that features contain about operations. Then, due to its conceptual similarity with mutual information in information theory, forensicability is measured as the mutual information between features and operations’ hypotheses. Such a measurement gives the error probability lower bound of all practical estimators which use these features to detect the operations’ hypotheses. Furthermore, it can determine the maximum number of hypotheses that we can theoretically detect. To demonstrate the effectiveness of our proposed information theoretical framework, we apply this framework on a forensic example of detecting the number of JPEG compressions based on DCT coefficient histograms. We conclude that, under typical settings of forensic analysis, the maximum number of JPEG compressions that we can detect using DCT coefficient histogram features is 4. Furthermore, we obtain the optimal strategies for investigators and forgers based on the fundamental measurement of forensicability.