Paper 2025/2077

Malicious Homomorphic Secret Sharing with Applications to DV-NIZK and More

Abstract

Homomorphic Secret Sharing (CRYPTO 2016) allows a secret to be shared among two or more parties in such a way that the parties can locally evaluate a class of functions on their shares. Homomorphic secret sharing (HSS) schemes and their underlying techniques have facilitated a wide range of applications. To account for the fact that parties generating or evaluating the shares might act maliciously, variants of HSS schemes that allow detection of such malicious behavior have been introduced. However, all prior approaches of malicious HSS that capture the class of $\mathsf{NC}1$ circuits either crucially rely on a random oracle or require an non-reusable setup. In this work, we initiate the study of malicious public-key $2$-party HSS in the standard model with reusable setup, where any malicious behavior during share generation and share evaluation can be detected. Towards constructing malicious HSS, we introduce the notion of homomorphic secret sharing with robust linear reconstruction (RLR-HSS) and show that this notion readily implies malicious HSS. We outline challenges in instantiating RLR-HSS due to the error present in all current HSS constructions not relying on SHE/FHE, and show how to overcome these using derandomization techniques by Dwork et al. (EUROCRYPT 2004). Finally, we show applications of malicious HSS to compact designated verifier non-interactive zero knowledge arguments and maliciously secure $2$-party computation in the standard model (supporting the same function class as the underlying malicious HSS).