Recent research in quantitative theories for information-hiding topics, such as Anonymity and Secure Information Flow, tend to converge towards the idea of modeling the system as a noisy channel in the information-theoretic sense. The notion of information leakage, or vulnerability of the system, has been related in some approaches to the concept of mutual information of the channel. A recent work of Smith has shown, however, that if the attack consists in one single try, then the mutual information and other concepts based on Shannon entropy are not suitable, and he has proposed to use Rényi's min-entropy instead. In this paper, we consider and compare two different possibilities of defining the leakage, based on the Bayes risk, a concept related to Rényi min-entropy. Information-hiding refers to a large class of problems including Secure Information Flow and Anonymity. There has been a growing interest in developing quantitative theories for this class of problems, because it has been recognized that non quantitative (i.e. possibilistic) approaches are in general too coarse, in the sense that they tend to consider as equivalent systems that have very different degrees of protection. Concepts from Information Theory have revealed quite convenient in this domain. In particular, the notion of noisy channel has been used to model protocols for information-hiding, and the flow of information in programs. The idea is that the input of the channel represents the information to be kept secret, and the output represents the observable. The noise of the channel is generated by the efforts of the protocol to hide the link between the secrets and the observable, often achieved by using randomized mechanisms.
Moreover, the idea of quantitative leakage in the context of protocols has been investigated in REF .
Quantitative Notions of Leakage for One-try Attacks
MFPS
Electr. Notes Theor. Comput. Sci.
Computer Science