Probabilistic data structures like hash tables, skip lists, and treaps support efficient operations through randomized hierarchies that enable ''skipping'' elements, achieving sub-linear query complexity on average for perfectly correct responses. They serve as critical components in performance-sensitive systems where correctness is essential and efficiency is highly desirable. While simpler than deterministic alternatives like balanced search trees, these structures traditionally assume that input data are independent of the structure's internal randomness and state -- an assumption questionable in malicious environments -- potentially leading to a significantly increased query complexity. We present adaptive attacks on all three aforementioned structures that, in the case of hash tables and skip lists, cause exponential degradation compared to the input-independent setting. While efficiency-targeting attacks on hash tables are well-studied, our attacks on skip lists and treaps provide new insights into vulnerabilities of skipping-based probabilistic data structures. Next, we propose simple and efficient modifications to the original designs of these data structures to provide provable security against adaptive adversaries. Our approach is formalized through Adaptive Adversary Property Conservation (AAPC), a general security notion that captures deviation from the expected efficiency guarantees in adversarial scenarios. We use this notion to present rigorous robustness proofs for our versions of the data structures. Lastly, we perform experiments whose empirical results closely agree with our analytical results.

Secure Multi-Party Computation (MPC) is continuously becoming more and more practical. Many optimizations have been introduced, making MPC protocols more suitable for solving real-world problems. However, the MPC protocols and optimizations are usually implemented as a standalone proof of concept or in an MPC framework and are tightly coupled with special-purpose circuit formats, such as Bristol Format. This makes it very hard and time-consuming to re-use algorithmic advances and implemented applications in a different context. Developing generic algorithmic optimizations is exceptionally hard because the available MPC tools and formats are not generic and do not provide the necessary infrastructure.