Creating an adversary resilient Learned Bloom Filter \cite{learnedindexstructures} with provable guarantees is an open problem \cite{reviriego1}. We define a strong adversarial model for the Learned Bloom Filter. We also construct two adversary resilient variants of the Learned Bloom Filter called the Uptown Bodega Filter and the Downtown Bodega Filter. Our adversarial model extends an existing adversarial model designed for the Classical (i.e not ``Learned'') Bloom Filter by Naor Yogev~\cite{moni1} and considers computationally bounded adversaries that run in probabilistic polynomial time (PPT). We show that if pseudo-random permutations exist, then a secure Learned Bloom Filter may be constructed with $\lambda$ extra bits of memory and at most one extra pseudo-random permutation in the critical path. We further show that, if pseudo-random permutations exist, then a \textit{high utility} Learned Bloom Filter may be constructed with $2\lambda$ extra bits of memory and at most one extra pseudo-random permutation in the critical path. Finally, we construct a hybrid adversarial model for the case where a fraction of the workload is chosen by an adversary. We show realistic scenarios where using the Downtown Bodega Filter gives better performance guarantees compared to alternative approaches in this hybrid model.

翻译：构建具有可证明保证的对抗性鲁棒学习型布隆过滤器 \cite{learnedindexstructures} 是一个开放性问题 \cite{reviriego1}。我们为学习型布隆过滤器定义了一个强对抗模型。我们还构建了两种对抗性鲁棒的学习型布隆过滤器变体，分别称为 Uptown Bodega 过滤器和 Downtown Bodega 过滤器。我们的对抗模型扩展了 Naor 和 Yogev 为经典（即非“学习型”）布隆过滤器设计的现有对抗模型 \cite{moni1}，并考虑了在概率多项式时间（PPT）内运行的计算有界对手。我们证明，若伪随机置换存在，则可通过使用 $\lambda$ 额外比特内存并在关键路径上至多增加一次伪随机置换，构建一个安全的学习型布隆过滤器。我们进一步证明，若伪随机置换存在，则可通过使用 $2\lambda$ 额外比特内存并在关键路径上至多增加一次伪随机置换，构建一个\textit{高效用}学习型布隆过滤器。最后，我们针对部分工作负载由对手选择的情况构建了一个混合对抗模型。我们展示了在此混合模型中，使用 Downtown Bodega 过滤器相比替代方法能提供更好性能保证的现实场景。