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This work presents RPM, a scalable anonymous communication protocol suite using secure multiparty computation (MPC) with the offline-online model. We generate random, unknown permutation matrices in a secret-shared fashion and achieve improved (online) performance and the lightest communication and computation overhead for the clients compared to the state of art robust anonymous communication protocols. Using square-lattice shuffling, we make our protocol scale well as the number of clients increases. We provide three protocol variants, each targeting different input volumes and MPC frameworks/libraries. Besides, due to the modular design, our protocols can be easily generalized to support more MPC functionalities and security properties as they get developed. We also illustrate how to generalize our protocols to support two-way anonymous communication and secure sorting. We have implemented our protocols using the MP-SPDZ library suit and the benchmark illustrates that our protocols achieve unprecedented online phase performance with practical offline phases. 

Abstract While the practicality of secure multi-party computation (MPC) has been extensively analyzed and improved over the past decade, we are hitting the limits of efficiency with the traditional approaches of representing the computed functionalities as generic arithmetic or Boolean circuits. This work follows the design principle of identifying and constructing fast and provably-secure MPC protocols to evaluate useful high-level algebraic abstractions; thus, improving the efficiency of all applications relying on them. We present Polymath, a constant-round secure computation protocol suite for the secure evaluation of (multi-variate) polynomials of scalars and matrices, functionalities essential to numerous data-processing applications. Using precise natural precomputation and high-degree of parallelism prevalent in the modern computing environments, Polymath can make latency of secure polynomial evaluations of scalars and matrices independent of polynomial degree and matrix dimensions. We implement our protocols over the HoneyBadgerMPC library and apply it to two prominent secure computation tasks: privacy-preserving evaluation of decision trees and privacy-preserving evaluation of Markov processes. For the decision tree evaluation problem, we demonstrate the feasibility of evaluating high-depth decision tree models in a general n -party setting. For the Markov process application, we demonstrate that Poly-math can compute large powers of transition matrices with better online time and less communication.