VeHSS: Two-server Verifiable Homomorphic Secret Sharing Leveraging SIMD Operations

Abstract

Outsourced computation poses challenges in data privacy and computation integrity. Fully homomorphic encryption (FHE) ensures data privacy but incurs high computational overhead. Homomorphic secret sharing (HSS), an alternative with reduced overhead, enables homomorphic evaluations to be distributed across remote servers without interaction. On the downside, neither FHE nor HSS guarantees computation integrity. To address this issue, verifiable homomorphic secret sharing (VHSS) schemes have been proposed to verify computation correctness. However, existing VHSS schemes for polynomials only verify whether the servers perform the same function rather than the intended specified function, and implicitly assume that at least one server is honest. Moreover, the costs of generating verification information are the same as or even more than re-executing the computation. We propose a two-server VHSS scheme leveraging single-instruction multiple data (SIMD) parallel computations. Our scheme verifies computation correctness for specified functions even when both non-colluding servers are malicious under our security model. Moreover, it supports amortized verification on the client side by enabling the precomputation of reusable values for verification, while introducing no additional computational costs on servers. As a byproduct, we also discuss how our method can be applied to FHE to mitigate recent attacks targeting decryption keys.