As the use of multimedia editing tools increases, people become questioning the authenticity of multimedia content. This is specially a big concern for authorities, such as law enforcement, news reporter and government, who constantly use multimedia evidence to make critical decisions. To verify the authenticity of multimedia content, many forensic techniques have been proposed to identify the processing history of multimedia content under question. However, as new technologies emerge and more complicated scenarios are considered, the limitation of multimedia forensics has been gradually realized by forensic researchers. It is the inevitable trend in multimedia forensics to explore the fundamental limits. In this dissertation, we propose several theoretical frameworks to study the fundamental limits in various forensic problems.

Specifically, we begin by developing empirical forensic techniques to deal with the limitation of existing techniques due to the emergence of new technology, compressive sensing. Then, we go one step further to explore the fundamental limit of forensic performance. Two types of forensic problems have been examined. In operation forensics, we propose an information theoretical framework and define forensicability as the maximum information features contain about hypotheses of processing histories. Based on this framework, we have found the maximum number of JPEG compressions one can detect. In order forensics, an information theoretical criterion is proposed to determine when we can and cannot detect the order of manipulation operations that have been applied on multimedia content.

Additionally, we have examined the fundamental tradeoffs in multimedia antiforensics, where attacking techniques are developed by forgers to conceal manipulation fingerprints and confuse forensic investigations. In this field, we have defined concealability as the effectiveness of anti-forensics concealing manipulation fingerprints. Then, a tradeoff between concealability, rate and distortion is proposed and characterized for compression anti-forensics, which provides us valuable insights of how forgers may behave under their best strategy.