# Bayes Security: A Not So Average Metric

arXiv: https://arxiv.org/abs/2011.03396 · HTML: https://mlsanity.com/paper/2011.03396/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Unifying Re-Identification, Attribute Inference, and Data Reconstruction Risks in Differential Privacy](https://mlsanity.com/paper/2507.06969/) (2025)
- [Beyond the Calibration Point: Mechanism Comparison in Differential Privacy](https://mlsanity.com/paper/2406.08918/) (2024)
- [The Fundamental Limits of Least-Privilege Learning](https://mlsanity.com/paper/2402.12235/) (2024)
- [Closed-Form Bounds for DP-SGD against Record-level Inference](https://mlsanity.com/paper/2402.14397/) (2024)
- [Understanding Disclosure Risk in Differential Privacy with Applications to Noise Calibration and Auditing (Extended Version)](https://mlsanity.com/paper/2603.12142/) (2026)
- [Evaluating Membership Inference Attacks in heterogeneous-data setups](https://mlsanity.com/paper/2502.18986/) (2025)

## Abstract (arXiv)

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.