Paper 2025/1463

Leakage-Resilient Circuits against $\mathsf{NC^1}$, Revisited

Abstract

In this study, we revisit leakage-resilient circuits (LRCs) against $\mathsf{NC}^1$-leakage and propose new constructions that minimize the reliance on leak-free hardware. Specifically, we first present a stateless LRC scheme that is resilient to $\mathsf{NC}^1$-leakage, and then extend it to a leakage-tolerant circuit with auxiliary input (AI-LTC). By integrating this with a 2-adaptive leakage-resilient encoding scheme, we achieve a stateful LRC scheme that uses a secure hardware component. In comparison to the state-of-the-art constructions against $\mathsf{NC}^1$-leakage by Miles and Viola (STOC 2013), both the encoder during the leak-free phase in our stateless LRC and the secure hardware component in our stateful LRC are typically much smaller, as their sizes are independent of the original circuit size. Additionally, we provide a non-black-box instantiation of stateful LRC, resulting in a smaller compiled circuit. The security of all our constructions is based on the very mild worst-case assumption $\mathsf{NC}^1 \subsetneq \oplus\mathsf{L}/\mathsf{poly}$, which is strictly weaker than the assumption $\mathsf{NC}^1 \subsetneq \mathsf{L}$ used by Miles and Viola. Furthermore, we propose a generic conversion from AI-LTCs to non-interactive zero-knowledge proofs with offline simulation (oNIZK) for all $\mathsf{NP}$ in the fine-grained setting. Our instantiation derived from it has small common reference strings, perfect soundness, zero-knowledge against adversaries in $\mathsf{NC}^1$ under $\mathsf{NC}^1 \subsetneq \oplus\mathsf{L}/\mathsf{poly}$, and minimal verification complexity. Finally, we show that any fine-grained oNIZK cannot simultaneously achieve perfect soundness and verifiable common reference strings, thereby ruling out the possibility of constructing stateful LRCs without secure hardware by eliminating the trusted setup of our AI-LTC.