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

• URL: http://arxiv.org/abs/2512.01604v1
• Date: Mon, 01 Dec 2025 12:23:19 GMT
• Title: On the Context-Hiding Property of Shamir-Based Homomorphic Secret Sharing
• Abstract summary: Homomorphic secret sharing (HSS) allows multiple input clients to secretly share their private inputs to a function among several servers.<n>Security requires that the output shares leak no more information about the inputs than the function output.<n>We formalize the context-hiding property of HSS for individual functions, and extend the study to monomials.
• Score: 8.944044445529766
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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