Quantum indistinguishability obfuscation (qIO) aims to make a quantum circuit unintelligible while preserving its functionality. It serves as a foundational primitive for advanced applications, such as witness encryption (WE) for QMA, non-interactive zero-knowledge arguments for QMA, and attribute-based encryption for BQP. Despite its importance, constructing qIO from standard assumptions remains a major open problem. In this work, we prove that the security of WE for QMA cannot be based on any falsifiable cryptographic assumption via a restricted class of quantum black-box reductions. Because qIO for null quantum circuits implies WE for QMA, this also separates null-qIO from falsifiable assumptions. Since almost all standard cryptographic assumptions are falsifiable, our result presents a barrier to basing qIO on standard cryptographic assumptions. The reductions we rule out are restricted: the reduction must query the adversary classically, non-adaptively, at the same security parameter, and only on honestly generated ciphertexts. Moreover, our impossibility applies only to WE with classical ciphertexts, and therefore does not rule out qIO with obfuscators whose output is a quantum state. Ruling out more general reductions, as well as more general forms of WE and qIO, remains open. Our impossibility relies on the existence of a QMA-QCIP[2] gap problem, an average-case assumption postulating a QMA language that cannot be verified with two messages of classical communication.Quantum indistinguishability obfuscation (qIO) aims to make a quantum circuit unintelligible while preserving its functionality. It serves as a foundational primitive for advanced applications, such as witness encryption (WE) for QMA, non-interactive zero-knowledge arguments for QMA, and attribute-based encryption for BQP. Despite its importance, constructing qIO from standard assumptions remains a major open problem. In this work, we prove that the security of WE for QMA cannot be based on any falsifiable cryptographic assumption via a restricted class of quantum black-box reductions. Because qIO for null quantum circuits implies WE for QMA, this also separates null-qIO from falsifiable assumptions. Since almost all standard cryptographic assumptions are falsifiable, our result presents a barrier to basing qIO on standard cryptographic assumptions. The reductions we rule out are restricted: the reduction must query the adversary classically, non-adaptively, at the same security parameter, and only on honestly generated ciphertexts. Moreover, our impossibility applies only to WE with classical ciphertexts, and therefore does not rule out qIO with obfuscators whose output is a quantum state. Ruling out more general reductions, as well as more general forms of WE and qIO, remains open. Our impossibility relies on the existence of a QMA-QCIP[2] gap problem, an average-case assumption postulating a QMA language that cannot be verified with two messages of classical communication.

quant-pharXiv:2608.25195Aug 27, 20260 citations

Indistinguishability Obfuscation of Null Quantum Circuits and Applications

James Bartusek, Giulio Malavolta

We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of ''dual-mode'' classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of ''dual-mode'' classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.

arXiv:2106.06094Jun 11, 20210 citations

Verifiable Quantum Advantage and Computation via Quantum Circuit Obfuscation

Alexandru Gheorghiu, Aparna Gupte, Vojtěch Havlíček +1 more

We construct protocols for classically verifiable quantum advantage and classical verification of $\mathsf{BQP}$ computations using \emph{quantum indistinguishability obfuscation} (qiO). Specifically, given qiO and assuming a slightly stronger version of $\mathsf{BQP}\neq\mathsf{BPP}$ , we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on \emph{peaked random circuit sampling} of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary $\mathsf{BQP}$ computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is \emph{publicly verifiable}. To our knowledge, this is the first publicly verifiable protocol for classical verification of $\mathsf{BQP}$ computations under computational assumptions in the standard model. As qiO is the basis for our results, we propose an approach to constructing qiO by adapting the local-mixing framework of Canetti--Chamon--Mucciolo--Ruckenstein.We construct protocols for classically verifiable quantum advantage and classical verification of $\mathsf{BQP}$ computations using \emph{quantum indistinguishability obfuscation} (qiO). Specifically, given qiO and assuming a slightly stronger version of $\mathsf{BQP}\neq\mathsf{BPP}$, we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on \emph{peaked random circuit sampling} of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary $\mathsf{BQP}$ computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is \emph{publicly verifiable}. To our knowledge, this is the first publicly verifiable protocol for classical verification of $\mathsf{BQP}$ computations under computational assumptions in the standard model. As qiO is the basis for our results, we propose an approach to constructing qiO by adapting the local-mixing framework of Canetti--Chamon--Mucciolo--Ruckenstein.

quant-pharXiv:2609.40289Oct 1, 20260 citations

From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability ObfuscationFrom Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation

Tomoyuki Morimae, Shirakawa, Yuki, Takashi Yamakawa

Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of $\mathsf{NP}$ , is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished by whether the obfuscation algorithm, evaluation algorithm, and description of obfuscated program are classical or quantum. For each variant, we identify quantum cryptographic primitives that can be constructed under the assumption of quantum iO and the infinitely-often quantum worst-case hardness of $\mathsf{NP}$ (i.e., $\mathsf{NP}\not\subseteq\mathsf{\text{i.o.} BQP}$ ). In particular, we construct pseudorandom unitaries, QCCC quantum public-key encryption and (QCCC) quantum symmetric-key encryption, and several primitives implied by them such as one-way state generators, (efficiently-verifiable) one-way puzzles, and EFI pairs, etc. While our main focus is on quantum iO, even in the classical setting, our techniques yield a new and arguably simpler construction of OWFs from classical (imperfect) iO and the infinitely-often worst-case hardness of $\mathsf{NP}$ .Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of $\mathsf{NP}$, is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished by whether the obfuscation algorithm, evaluation algorithm, and description of obfuscated program are classical or quantum. For each variant, we identify quantum cryptographic primitives that can be constructed under the assumption of quantum iO and the infinitely-often quantum worst-case hardness of $\mathsf{NP}$ (i.e., $\mathsf{NP}\not\subseteq\mathsf{\text{i.o.} BQP}$). In particular, we construct pseudorandom unitaries, QCCC quantum public-key encryption and (QCCC) quantum symmetric-key encryption, and several primitives implied by them such as one-way state generators, (efficiently-verifiable) one-way puzzles, and EFI pairs, etc. While our main focus is on quantum iO, even in the classical setting, our techniques yield a new and arguably simpler construction of OWFs from classical (imperfect) iO and the infinitely-often worst-case hardness of $\mathsf{NP}$.

arXiv:2506.19542Leibniz international proceedings in informaticsJun 24, 20250 citations

Classical Obfuscation of Quantum Circuits via Publicly-Verifiable QFHE

James Bartusek, Aparna Gupte, Saachi Mutreja +1 more

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.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.

arXiv:2510.08400Oct 9, 20250 citations

On Removing Interaction from Quantum Proofs

Nicholas Spooner, Max Tromanhauser

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) $Σ$ -protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a $Σ$ -protocol (which they call a $Ξ$ -protocol) in which the prover's first message is quantum, and show that HVZK $Ξ$ -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.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) $Σ$-protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a $Σ$-protocol (which they call a $Ξ$-protocol) in which the prover's first message is quantum, and show that HVZK $Ξ$-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.

quant-pharXiv:2609.38387Oct 1, 20260 citations

We construct protocols for classically verifiable quantum advantage and classical verification of

\mathsf{BQP}

computations using \emph{quantum indistinguishability obfuscation} (qiO). Specifically, given qiO and assuming a slightly stronger version of

\mathsf{BQP}\neq\mathsf{BPP}

, we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on \emph{peaked random circuit sampling} of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary

\mathsf{BQP}

computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is \emph{publicly verifiable}. To our knowledge, this is the first publicly verifiable protocol for classical verification of

\mathsf{BQP}

computations under computational assumptions in the standard model. As qiO is the basis for our results, we propose an approach to constructing qiO by adapting the local-mixing framework of Canetti--Chamon--Mucciolo--Ruckenstein.

From Worst-Case Hardness of

\mathsf{NP}

to Quantum Cryptography via Quantum Indistinguishability Obfuscation

Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of

\mathsf{NP}

, is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished by whether the obfuscation algorithm, evaluation algorithm, and description of obfuscated program are classical or quantum. For each variant, we identify quantum cryptographic primitives that can be constructed under the assumption of quantum iO and the infinitely-often quantum worst-case hardness of

\mathsf{NP}

(i.e.,

\mathsf{NP}\not\subseteq\mathsf{\text{i.o.} BQP}

). In particular, we construct pseudorandom unitaries, QCCC quantum public-key encryption and (QCCC) quantum symmetric-key encryption, and several primitives implied by them such as one-way state generators, (efficiently-verifiable) one-way puzzles, and EFI pairs, etc. While our main focus is on quantum iO, even in the classical setting, our techniques yield a new and arguably simpler construction of OWFs from classical (imperfect) iO and the infinitely-often worst-case hardness of

\mathsf{NP}

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.

Σ

-protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a

Σ

-protocol (which they call a

Ξ

-protocol) in which the prover's first message is quantum, and show that HVZK

Ξ

-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.