[2603.01986] Accurate, private, secure, federated U-statistics with higher degree

Computer Science > Cryptography and Security arXiv:2603.01986 (cs) [Submitted on 2 Mar 2026] Title:Accurate, private, secure, federated U-statistics with higher degree Authors:Quentin Sinh (MAGNET), Jan Ramon (MAGNET) View a PDF of the paper titled Accurate, private, secure, federated U-statistics with higher degree, by Quentin Sinh (MAGNET) and 1 other authors View PDF Abstract:We study the problem of computing a U-statistic with a kernel function f of degree k $\ge$ 2, i.e., the average of some function f over all k-tuples of instances, in a federated learning setting. Ustatistics of degree 2 include several useful statistics such as Kendall's $\tau$ coefficient, the Area under the Receiver-Operator Curve and the Gini mean difference. Existing methods provide solutions only under the lower-utility local differential privacy model and/or scale poorly in the size of the domain discretization. In this work, we propose a protocol that securely computes U-statistics of degree k $\ge$ 2 under central differential privacy by leveraging Multi Party Computation (MPC). Our method substantially improves accuracy when compared to prior solutions. We provide a detailed theoretical analysis of its accuracy, communication and computational properties. We evaluate its performance empirically, obtaining favorable results, e.g., for Kendall's $\tau$ coefficient, our approach reduces the Mean Squared Error by up to four orders of magnitude over existing baselines. Subjects: Cryptography an...