On Removing Interaction from Quantum Proofs

Abstract:An important open question in quantum cryptography is the construction of publicly-verifiable NIZKs for QMA. Classically, one can construct NIZKs for NP in the random oracle model (and sometimes in the standard model) by compiling an honest-verifier ZK (HVZK) $\Sigma$-protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a $\Sigma$-protocol (which they call a $\Xi$-protocol) in which the prover's first message is quantum, and show that HVZK $\Xi$-protocols exist for QMA. However, it is not clear how to compile such protocols into NIZKs in the (Q)ROM, because the Fiat-Shamir transformation seems to be incompatible with quantum messages. In this work we give formal evidence that this is indeed the case: we show that if generic "Fiat-Shamir-like" compilers for quantum protocols exist in the QROM (with small completeness and soundness error) then QMA = BQP.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2609.38387 [quant-ph]

(or arXiv:2609.38387v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.38387 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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