Searching secrets rationally

We study quantitative information flow, from the perspective of an analyst who is interested in maximizing its expected gain in the process of discovering a secret, or settling a hypothesis, represented by an unobservable <i>X</i>, after observing some <i>Y</i> related to <i>X</i>. In our framework, inspired by Bayesian decision theory, discovering the secret has an associated reward, while the investigation of the set of possibilities prompted by the observation has a cost. We characterize the optimal strategy for the analyst and the corresponding expected gain (payoff) in a variety of situations. We argue about the importance of <i>advantage</i>, defined as the increment in expected gain after the observation if the analyst acts optimally, and representing the value of the information conveyed by <i>Y</i>. We also argue that the proposed strategy is more effective than others, based on probability coverage. Applications to cryptographic systems and to familial DNA searching are examined.