Classical Obfuscation of Quantum Circuits via Publicly-Verifiable QFHE
James Bartusek, Aparna Gupte, Saachi Mutreja, Omri Shmueli
TL;DR
The work tackles the challenge of obfuscating quantum circuits with classical tools. It introduces a framework where a compact, publicly-verifiable quantum fully-homomorphic encryption scheme enables obfuscation of pseudo-deterministic quantum circuits via a verify-then-decrypt paradigm, all in the classical oracle model. A key technical advance is the first publicly-verifiable Pauli functional commitment with classical keys, supported by one-shot signatures, which enables public verification of quantum evaluations and underpins a compiler from privately-verifiable QFHE to publicly-verifiable QFHE and ultimately to obfuscation. The approach further achieves post-quantum succinct ideal obfuscation by combining FHE with SNARK-based succinct proofs, yielding a succinct, public-obfuscated program with blindness and public verifiability for BQP computations. This results in the first succinct randomized encoding of pseudo-deterministic quantum computation and provides a practical pathway to classical obfuscation of expressive quantum circuits under quantum hardness assumptions.
Abstract
A classical obfuscator for quantum circuits is a classical program that, given the classical description of a quantum circuit $Q$, outputs the classical description of a functionally equivalent quantum circuit $\hat{Q}$ that hides as much as possible about $Q$. Previously, the only known feasibility result for classical obfuscation of quantum circuits (Bartusek and Malavolta, ITCS 2022) was limited to circuits that always reject. On the other hand, if the obfuscator is allowed to compile the quantum circuit $Q$ into a quantum state $|\hat{Q}\rangle$, there exist feasibility results for obfuscating all pseudo-deterministic quantum circuits (Bartusek, Kitagawa, Nishimaki and Yamakawa, STOC 2023, Bartusek, Brakerski and Vaikuntanathan, STOC 2024), and all unitaries (Huang and Tang, FOCS 2025). We show that (relative to a classical oracle) there exists a classical obfuscator for all pseudo-deterministic quantum circuits. We do this by giving the first construction of a compact quantum fully-homomorphic encryption (QFHE) scheme that supports public verification of (pseudo-deterministic) quantum evaluation, relative to a classical oracle. To construct our QFHE scheme, we improve on the approach of Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023), which required ciphertexts that are both quantum and non-compact due to the use of quantum coset states and their publicly-verifiable properties. We introduce new techniques for analyzing coset states that can be generated ''on the fly'', by proving new cryptographic properties of the one-shot signature scheme of Shmueli and Zhandry (CRYPTO 2025). Our techniques allow us to produce QFHE ciphertexts that are purely classical, compact, and publicly-verifiable. This also yields the first classical verification of quantum computation protocol for BQP that simultaneously satisfies blindness and public-verifiability.