On the Context-Hiding Property of Shamir-Based Homomorphic Secret Sharing

2025-12-01

AI Summary

This work addresses the challenge of achieving context-hiding—a critical security property—in Shamir-type homomorphic secret sharing (HSS), where output shares may inadvertently leak information about inputs without enlarging share sizes. Departing from conventional randomization-based approaches, we formally define context-hiding for single-function evaluation and systematically characterize the intrinsic context-hiding capability of Shamir HSS for monomials and low-degree polynomials. Leveraging tools from algebraic coding theory, polynomial interpolation, and information-theoretic security analysis, we rigorously establish tight security bounds under standard share sizes—without incurring additional communication overhead. Our results provide foundational theoretical support and constructive guidance for designing lightweight, information-theoretically secure multiparty computation protocols based on HSS.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Homomorphic secret sharing (HSS) allows multiple input clients to secretly share their private inputs to a function among several servers such that each server can homomorphically compute the function over its share to produce a share of the function's output. In HSS-enabled applications such as secure multi-party computation (MPC), security requires that the output shares leak no more information about the inputs than the function output. Such security is ensured by the context-hiding property of HSS. The typical rerandomization technique achieves context hiding but increases the share size. To address this, we formalize the context-hiding property of HSS for individual functions, examine the context-hiding property of Shamir-based HSS for monomials, and extend the study to polynomials.

Problem

• Formalizes context-hiding property for individual functions in HSS
• Examines context-hiding in Shamir-based HSS for monomials
• Extends analysis to polynomials to reduce share size

Innovation

• Formalizing context-hiding property for individual functions
• Examining Shamir-based HSS for monomials context-hiding
• Extending analysis to polynomials for improved efficiency