Multi-Party Replicated Secret Sharing over a Ring with Applications to Privacy-Preserving Machine Learning

Aug 3, 2026

Uploaded by Aurora

Secure multi-party computation delivers major performance gains and increasingly supports privacy-preserving machine learning. Secret-sharing-based methods are widely used because they efficiently realize arithmetic operations needed for private neural network inference and training, while offering information-theoretic security. This work develops multi-party protocols for replicated secret sharing over an arbitrary ring in the honest-majority semi-honest setting, enabling general-purpose computation beyond field-based designs. Benchmarks show substantial speedups and competitive performance in machine learning workloads.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Abstract

Introduction

Background: Secret Sharing and PPML

Ring vs. Field Computation

Honest Majority Setting and Limitations

Contributions

Elementary Building Blocks for RSS over Rings

Higher-Level Protocols for Z2^k

Benchmarks and Performance Results

Improvements for Quantized Neural Networks

Multi-Party Replicated Secret Sharing over a Ring with Applications to Privacy-Preserving Machine Learning Alessandro Baccarini University at Buffalo (SUNY) Buffalo, New York, USA [anbaccar@buffalo.edu](anbaccar@buffalo.edu) Marina Blanton University at Buffalo (SUNY) Buffalo, New York, USA [mblanton@buffalo.edu](mblanton@buffalo.edu) Chen Yuan University at Buffalo (SUNY) Buffalo, New York, USA [chyuan@buffalo.edu](chyuan@buffalo.edu) ABSTRACT Secure multi-party computation has seen significant performance advances and increasing use in recent years. Techniques based on secret sharing offer attractive performance and are a popular choice for privacy-preserving machine learning applications. Traditional techniques operate over a field, while designing equivalent techniques for a ring Z2􀀺 can boost performance. In this work, we develop a suite of multi-party protocols for a ring in the honest majority setting starting from elementary operations to more complex with the goal of supporting general-purpose computation. We demonstrate that our techniques are substantially faster than their field-based equivalents when instantiated with a different number of parties and perform on par with or better than state-of-the-art techniques with designs customized for a fixed number of parties. We evaluate our techniques on machine learning applications and show that they offer attractive performance. KEYWORDS secure multi-party computation, replicated secret sharing, privacypreserving machine learning 1 INTRODUCTION Secure multi-party computation has recently seen notable performance improvements that make privacy-preserving computation of increasingly complex functionalities on increasingly large data sets more practical than ever before. Recent significant interest in privacy-preserving machine learning (PPML) has highlighted secret sharing techniques which were often previously overlooked in the literature. Secret sharing (SS) offers superior performance for arithmetic operations such as matrix multiplications over other cryptographic tools, and has been extensively used for privacy-preserving neural network (NN) inference and training [14, 15, 18, 27, 36, 47, 49, 55, 56] . Because SS offers informationtheoretic security, computation can proceed on short integers, aiding efficiency. Traditionally, performance of SS techniques has been measured in terms of two parameters: the number of interactive operations and the number of sequential interactive operations, or rounds. However, for some computations such as matrix multiplication local operations can dominate the overall cost. Traditional techniques such as Shamir SS [54] carry out computation on protected data over a field, most commonly set up as Z􀀿 with prime 􀀿 . This makes frequent use of modulo reduction a necessity, increasing the cost of the computation. To improve performance and directly utilize native instructions of modern processors, researchers turned to computation over ring Z2􀀺 [8, 12, 16, 20] . Unfortunately, Shamir SS – a popular and efficient choice for computation in the honest majority setting – cannot be used for computation over Z2􀀺 , and we must seek alternatives. The honest majority setting, which assumes that only a minority of the parties carrying out the computation can be corrupt, offers great performance with reasonable trust assumptions relative to stronger settings, making a good performance-security trade-off. The techniques we are aware of in this setting which can perform computation over ring Z2􀀺 for some 􀀺 are limited to a fixed number of parties, most commonly to 3 (see, e.g., [8, 14, 15, 41, 47]) and cannot tolerate collusion. This means that the techniques do not easily generalize to a larger number of participants, should there be a need to change the computation setup, e.g., to permit the use of a higher collusion threshold. This is the task we set to address in this work and generalize computation based on replicat

FAQs

Why are replicated secret sharing techniques useful for privacy-preserving machine learning?

Secret sharing enables efficient arithmetic, which is central to operations like matrix multiplications used in private neural network inference and training. It also provides information-theoretic security while allowing computation on protected integers.

What is the motivation for implementing secret sharing over a ring instead of a field?

Field-based designs often require frequent modulo reduction, increasing cost. Ring-based computation can directly leverage processor-native operations and improve efficiency, though some common schemes do not transfer directly to Z2^k.

How does the proposed approach perform compared with field-based equivalents?

The authors report substantial speedups over field-based methods for multiple operations when using three parties (about 10–33x). As the number of parties grows, improvements decrease, yet gains remain for seven parties for certain operations.

Aug 3, 2026

Uploaded by Aurora