Paper 2025/1491 Original: eprint.iacr.org/2025/1491 ↗

Homomorphic Secret Sharing with Verifiable Evaluation

Abstract

A homomorphic secret sharing (HSS) scheme allows a client to delegate a computation to a group of untrusted servers while achieving input privacy as long as at least one server is honest. In recent years, many HSS schemes have been constructed that have, in turn, found numerous applications to cryptography. Prior work on HSS focuses on the setting where the servers are semi-honest. In this work we study HSS in the setting of malicious evaluators. We propose the notion of HSS with verifiable evaluation (ve-HSS) that guarantees correctness of output even when all the servers are corrupted. ve-HSS retains all the attractive features of HSS and adds the new feature of succinct public verification of output. We present black-box constructions of ve-HSS by devising generic transformations for semi-honest HSS schemes (with negligible error). This provides a new non-interactive method for verifiable and private outsourcing of computation.