差分隐私的形式化定义如下:对于任何两个相邻的数据集 D D D 和 D ′ D' D′,如果一个算法 A \mathcal{A} A 满足以下条件:
P ( A ( D ) ∈ S ) ≤ e ϵ P ( A ( D ′ ) ∈ S ) P(\mathcal{A}(D) \in S) \leq e^\epsilon P(\mathcal{A}(D') \in S) P(A(D)∈S)≤eϵP(A(D′)∈S)
此中, ϵ \epsilon ϵ 是隐私参数,称为隐私预算。 ϵ \epsilon ϵ 越小,隐私保护越强。
差分隐私实现代码示例
Abadi, M., Chu, A., Goodfellow, I., et al. (2016). Deep Learning with Differential Privacy. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security.
Bonawitz, K., et al. (2019). Towards Federated Learning at Scale: System Design. In Proceedings of the 2nd SysML Conference.
Gentry, C. (2009). Fully Homomorphic Encryption Using Ideal Lattices. In STOC '09 Proceedings of the 41st Annual ACM Symposium on Theory of Computing.