Paper 2025/449

Concretely Efficient Correlated Oblivious Permutation

Abstract

Oblivious permutation (OP) enables two parties, a sender with a private data vector $x$ and a receiver with a private permutation π, to securely obtain the shares of π(x). OP has been used to construct many important MPC primitives and applications such as secret shuffle, oblivious sorting, private set operations, secure database analysis, and privacy-preserving machine learning. Due to its high complexity, OP has become a performance bottleneck in several practical applications, and many efforts have been devoted to enhancing its concrete efficiency. Chase et al. (Asiacrypt'20) proposed an offline-online OP paradigm leveraging a pre-computable resource termed Share Translation. While this paradigm significantly reduces online costs, the substantial offline cost of generating Share Translation remains an area for further investigation. In this work, we redefine the pre-computable resource as a cryptographic primitive known as Correlated Oblivious Permutation (COP) and conduct in-depth analyses and optimizations of the two COP generation solutions: network-based solution and matrix-based solution. The optimizations for the network-based solution halve the communication/computation cost of constructing a switch (the basic unit of the permutation network) and reduce the number of switches in the permutation network. The optimizations for the matrix-based solution halve the communication cost of small-size COP generation and reduce the cost of large-size COP generation with in-outside permutation decomposition. We implement our two COP generation protocols and conduct comprehensive evaluations. Taking commonly used 128-bit input data as an example, our network-based and matrix-based solutions are up to 1.7x and 1.6x faster than baseline protocols, respectively. We further facilitate the state-of-the-art (SOTA) PSU protocols with our optimized COP, achieving over 25% reduction in communication cost and 35% decrease in execution time. This shows that our COP optimizations bring significant improvements for real-world MPC primitives.