Security system designers favor worst-case security metrics, such as those derived from differential privacy (DP), due to the strong guarantees they provide. On the downside, these guarantees result in a high penalty on the system's performance. In this paper, we study Bayes security, a security metric inspired by the cryptographic advantage. Similarly to DP, Bayes security i) is independent of an adversary's prior knowledge, ii) it captures the worst-case scenario for the two most vulnerable secrets (e.g., data records); and iii) it is easy to compose, facilitating security analyses. Additionally, Bayes security iv) can be consistently estimated in a black-box manner, contrary to DP, which is useful when a formal analysis is not feasible; and v) provides a better utility-security trade-off in high-security regimes because it quantifies the risk for a specific threat model as opposed to threat-agnostic metrics such as DP.

We formulate a theory around Bayes security, and we provide a thorough comparison with respect to well-known metrics, identifying the scenarios where Bayes Security is advantageous for designers.