Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IACR Communications in Cryptology

Quantum Black-Box Separations: Succinct Non-Interactive Arguments from Falsifiable Assumptions

Gorjan Alagic, Dana Dachman-Soled, Manasi Shingane, Patrick Struck

Published Jan 8, 2026• 0 citations
Publisher

Abstract

In their seminal work, Gentry and Wichs (STOC'11) established an impossibility result for the task of constructing an adaptively-sound SNARG via black-box reduction from a falsifiable assumption. An exciting set of recent SNARG constructions demonstrated that, if one adopts a weaker but still quite meaningful notion of adaptive soundness, then impossibility no longer holds (Waters-Wu, Waters-Zhandry, Mathialagan-Peters-Vaikunthanathan ePrint'24). These fascinating new results raise an intriguing possibility: is there a way to remove this slight weakening of adaptive soundness, thereby completely circumventing the Gentry-Wichs impossibility? A natural route to closing this gap would be to use a quantum black-box reduction, i.e., a reduction that can query the SNARG adversary on superpositions of inputs. This would take advantage of the fact that Gentry-Wichs only consider classical reductions. In this work, we show that this approach cannot succeed. Specifically, we extend the Gentry-Wichs impossibility result to quantum black-box reductions, and thereby establish an important limit on the power of such reductions.

DOI
10.62056/ayfhp2w9p

Related papers

Separating Non-Interactive Classical Verification of Quantum Computation from Falsifiable Assumptions

Mohammed Barhoush, Tomoyuki Morimae, Ryo Nishimaki +1 more

Mahadev [SIAM J. Comput. 2022] introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors (LWE) assumption, achieving a 4-message interactive scheme. This breakthrough naturally raised the question of whether fewer messages are possible in the plain model. Despite its importance, this question has remained unresolved. In this work, we prove that there is no quantum black-box reduction of non-interactive classical verification of quantum computation of $\textsf{QMA}$ to any falsifiable assumption. Here, "non-interactive" means that after an instance-independent setup, the protocol consists of a single message. This constitutes a strong negative result given that falsifiable assumptions cover almost all standard assumptions used in cryptography, including LWE. Our separation holds under the existence of a $\textsf{QMA} \text{-} \textsf{QCMA}$ gap problem. Essentially, these problems require a slightly stronger assumption than $\textsf{QMA}\neq \textsf{QCMA}$. To support the existence of such problems, we present a construction relative to a quantum unitary oracle.

quant-pharXiv:2602.18034•Feb 23, 2026•0 citations

Separating Quantum Indistinguishability Obfuscation from Falsifiable Assumptions

Mohammed Barhoush, Tomoyuki Morimae, Ramis Movassagh

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:2608.25195•Aug 27, 2026•0 citations

A Black-Box Approach to Post-Quantum Zero-Knowledge in Constant Rounds

Nai-Hui Chia, Kai-Min Chung, Takashi Yamakawa

In a recent seminal work, Bitansky and Shmueli (STOC '20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counterparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called $ε$-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box $ε$-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC '96) though the proof of $ε$-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box $ε$-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifier's internal state in an appropriate sense.

arXiv:2011.02670•Nov 5, 2020•1 citation

Limits to black-box amplification in QMA

Scott Aaronson, Phillip Harris, Freek Witteveen

We study the limitations of black-box amplification in the quantum complexity class Q M A . Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result (Jeffery and Witteveen, 2025) shows that completeness can in fact be amplified to be doubly exponentially close to 1. We prove that this is optimal for black-box procedures: we provide a quantum oracle relative to which no Q M A verification procedure using polynomial resources can achieve completeness closer to 1 than doubly exponential, or a soundness which is super-exponentially small. This is proven by making the oracle separation from (Aaronson, 2009) between Q M A and Q M A 1 quantitative, using techniques from complex approximation theory.

arXiv:2509.21131•Quantum•Oct 6, 2026•0 citations

A tale of SNARKs: quantum resilience, knowledge extractability and data privacy

Anca Nitulescu

The contributions detailed in this thesis focus on the design and the analysis of Succinct non-interactive arguments of knowledge, known as SNARKs. SNARKs enable a party with large computational resources to prove to a weaker party that a particular statement is true in an efficient way without further interaction and under a minimal communication requirement. Our results deal with three different aspects of SNARK protocols: the postquantum security of SNARKs, the composability of SNARKs with other cryptographic primitives and the confidentiality of the inputs in the computations verified by SNARKs. First, we propose a new framework that allows the instantiation of a quantumresilient SNARK scheme from lattice assumptions. We also study the notion of extractability that is part of the soundness definition for SNARKs. We remark some limitations of this definition and we address this problem, by introducing and studying a new notion, O-SNARKs. Finally, to achieve data privacy in delegated computation, we study the possibility of constructing SNARKs that enables verification of computations over encrypted data.

•Apr 1, 2019•0 citations

On Quantum Simulation-Soundness

Behzad Abdolmaleki, Céline Chevalier, Ehsan Ebrahimi +2 more

Non-interactive zero-knowledge (NIZK) proof systems are a cornerstone of modern cryptography, but their security has received little attention in the quantum settings. Motivated by improving our understanding of this fundamental primitive against quantum adversaries, we propose a new definition of security against quantum adversary. Specifically, we define the notion of quantum simulation soundness (SS-NIZK), that allows the adversary to access the simulator in superposition. We show a separation between post-quantum and quantum security of SS-NIZK, and prove that Sahai’s construction for SS-NIZK (in the CRS model) can be made quantumly-simulation-sound. As an immediate application of our new notion, we prove the security of the Naor-Yung paradigm in the quantum settings, with respect to a strong quantum IND-CCA security notion. This provides the quantum analogue of the classical dual key approach to prove the security of encryption schemes. Along the way, we introduce a new notion of quantum-query advantage functions, which may be used as a general framework to show classical/quantum separation for other cryptographic primitives, and it may be of independent interest.

IACR Communications in Cryptology•Jan 13, 2025•0 citations
In their seminal work, Gentry and Wichs (STOC'11) established an impossibility result for the task of constructing an adaptively-sound SNARG via black-box reduction from a falsifiable assumption. An exciting set of recent SNARG constructions demonstrated that, if one adopts a weaker but still quite meaningful notion of adaptive soundness, then impossibility no longer holds (Waters-Wu, Waters-Zhandry, Mathialagan-Peters-Vaikunthanathan ePrint'24). These fascinating new results raise an intriguing possibility: is there a way to remove this slight weakening of adaptive soundness, thereby completely circumventing the Gentry-Wichs impossibility? A natural route to closing this gap would be to use a quantum black-box reduction, i.e., a reduction that can query the SNARG adversary on superpositions of inputs. This would take advantage of the fact that Gentry-Wichs only consider classical reductions. In this work, we show that this approach cannot succeed. Specifically, we extend the Gentry-Wichs impossibility result to quantum black-box reductions, and thereby establish an important limit on the power of such reductions.
Mahadev [SIAM J. Comput. 2022] introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors (LWE) assumption, achieving a 4-message interactive scheme. This breakthrough naturally raised the question of whether fewer messages are possible in the plain model. Despite its importance, this question has remained unresolved. In this work, we prove that there is no quantum black-box reduction of non-interactive classical verification of quantum computation of QMA\textsf{QMA}QMA to any falsifiable assumption. Here, "non-interactive" means that after an instance-independent setup, the protocol consists of a single message. This constitutes a strong negative result given that falsifiable assumptions cover almost all standard assumptions used in cryptography, including LWE. Our separation holds under the existence of a QMA-QCMA\textsf{QMA} \text{-} \textsf{QCMA}QMA-QCMA gap problem. Essentially, these problems require a slightly stronger assumption than QMA≠QCMA\textsf{QMA}\neq \textsf{QCMA}QMA=QCMA. To support the existence of such problems, we present a construction relative to a quantum unitary oracle.
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.
In a recent seminal work, Bitansky and Shmueli (STOC '20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counterparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called εεε-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box εεε-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC '96) though the proof of εεε-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box εεε-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifier's internal state in an appropriate sense.
We study the limitations of black-box amplification in the quantum complexity class Q M A . Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result (Jeffery and Witteveen, 2025) shows that completeness can in fact be amplified to be doubly exponentially close to 1. We prove that this is optimal for black-box procedures: we provide a quantum oracle relative to which no Q M A verification procedure using polynomial resources can achieve completeness closer to 1 than doubly exponential, or a soundness which is super-exponentially small. This is proven by making the oracle separation from (Aaronson, 2009) between Q M A and Q M A 1 quantitative, using techniques from complex approximation theory.
The contributions detailed in this thesis focus on the design and the analysis of Succinct non-interactive arguments of knowledge, known as SNARKs. SNARKs enable a party with large computational resources to prove to a weaker party that a particular statement is true in an efficient way without further interaction and under a minimal communication requirement. Our results deal with three different aspects of SNARK protocols: the postquantum security of SNARKs, the composability of SNARKs with other cryptographic primitives and the confidentiality of the inputs in the computations verified by SNARKs. First, we propose a new framework that allows the instantiation of a quantumresilient SNARK scheme from lattice assumptions. We also study the notion of extractability that is part of the soundness definition for SNARKs. We remark some limitations of this definition and we address this problem, by introducing and studying a new notion, O-SNARKs. Finally, to achieve data privacy in delegated computation, we study the possibility of constructing SNARKs that enables verification of computations over encrypted data.
Non-interactive zero-knowledge (NIZK) proof systems are a cornerstone of modern cryptography, but their security has received little attention in the quantum settings. Motivated by improving our understanding of this fundamental primitive against quantum adversaries, we propose a new definition of security against quantum adversary. Specifically, we define the notion of quantum simulation soundness (SS-NIZK), that allows the adversary to access the simulator in superposition. We show a separation between post-quantum and quantum security of SS-NIZK, and prove that Sahai’s construction for SS-NIZK (in the CRS model) can be made quantumly-simulation-sound. As an immediate application of our new notion, we prove the security of the Naor-Yung paradigm in the quantum settings, with respect to a strong quantum IND-CCA security notion. This provides the quantum analogue of the classical dual key approach to prove the security of encryption schemes. Along the way, we introduce a new notion of quantum-query advantage functions, which may be used as a general framework to show classical/quantum separation for other cryptographic primitives, and it may be of independent interest.