Secure Computation Against NC1 Leakage Without Secure Hardware

In this work, we construct (stateful) leakage-resilient circuits (LRCs) secure against bounded-output-length leakage functions computable by $\mathsf{NC}^1$ circuits under the mild worst-case assumption $\mathsf{NC}^1 \subsetneq \oplus\mathsf{L}/\mathsf{poly}$, without relying on any leak-free hardware components, thereby resolving the open problem left by Bogdanov, Ishai, and Srinivasan (CRYPTO 2019; Journal of Cryptology, 2021) and Wang (CRYPTO 2025).

Concretely, we first construct a leakage-tolerant circuit with succinct setup (sAI-LTC) secure against 2-adaptive $\mathsf{NC}^1$ leakage, and then generically combine it with a 2-adaptive leakage-resilient composable encoding scheme to obtain the desired LRC.

We further give a direct non-black-box instantiation that optimizes the compiled circuit size at the cost of a slightly larger setup, matching the circuit size of Wang's construction that relies on leak-free hardware while using a more compact setup.

Finally, we show that our sAI-LTC generically implies a fine-grained multi-theorem non-interactive proof system for all $\mathsf{NP}$, with compact common reference strings, perfect soundness, and multi-theorem zero-knowledge with offline simulation against $\mathsf{NC}^1$ adversaries.