A New Approach to Arguments of Quantum Knowledge

Abstract: We construct a non-interactive zero-knowledge argument system for QMA with the following properties of interest. 1. Transparent setup. Our protocol only requires a uniformly random string (URS) setup. The only prior (publicly-verifiable) NIZK for QMA (Bartusek and Malavolta, ITCS 2022) requires an entire obfuscated program as the common reference string. 2. Extractability. Valid QMA witnesses can be extracted directly from our accepting proofs. That is, we obtain an argument of knowledge, which was previously only known in a secret parameters model (Coladangelo, Vidick, and Zhang, CRYPTO 2020). At the heart of our construction is a novel application of the coset state authentication scheme from (Bartusek, Brakerski, and Vaikuntanathan, STOC 2024) to the setting of QMA verification. Along the way, we establish new properties of the authentication scheme, and design a new type of ZX QMA verifier with ``strong completeness.'' The security of our construction rests on the heuristic use of a post-quantum indistinguishability obfuscator. However, rather than rely on the full-fledged classical oracle model (i.e. ideal obfuscation), we isolate a particular game-based property of the obfuscator that suffices for our proof, which we dub the evasive composability heuristic. Going a step further, we show how to replace the heuristic use of an obfuscator with the heuristic use of a hash function (plus sub-exponentially secure functional encryption). We accomplish this by establishing security of the ideal obfuscation scheme of Jain, Lin, Luo, and Wichs (CRYPTO 2023) in the quantum pseudorandom oracle model, which can be heuristically instantiated with a hash function. This result is of independent interest, and allows us to translate several quantum-cryptographic results that were only known in the classical oracle model to results in the quantum pseudorandom oracle model.