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

arXiv:2609.35633

Succinct Arguments for QMA from Collapsing Hash Functions

James Bartusek, Giulio Malavolta

quant-phcs.CRSubmitted Sep 28, 2026• Announced Sep 29, 2026• 0 citations
arXivHTMLPDF

Abstract

We prove the existence of succinct arguments for QMA, assuming only the existence of collapsing hash functions. This is the first scheme that relies only on unstructured ``Minicrypt'' assumptions, which are not known to imply public-key encryption. Our main technical contribution is a quantum-succinct \emph{claw-state generation} protocol that allows us to bootstrap a small number of quantum correlations into an arbitrarily large number of claw-state correlations, using classical communication only. This improves upon the work of [Zhang, STOC 2021], having better round complexity, a proof in the standard model, and being overall much simpler. This yields a quantum-succinct blind delegation of quantum computation protocol from one-way functions, which we plug into the communication-compression compiler of [Bartusek, Liu, and Malavolta, EUROCRYPT 2026] to obtain succinct arguments for QMA.

Related papers

A Modular Approach to Succinct Arguments for QMA

James Bartusek, Jiahui Liu, Giulio Malavolta

Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any $T$-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.

quant-pharXiv:2606.10408•Lecture notes in computer science•Jun 5, 2026•0 citations

Succinct Arguments for QMA in the Quantum Random Oracle Model

Alessandro Chiesa, Zihan Hu

Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.

quant-pharXiv:2609.37429•Sep 30, 2026•0 citations

Succinct Arguments for QMA from Standard Assumptions via Compiled Nonlocal Games

Tony Metger, Anand Natarajan, Tina Zhang

We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTo ‘22) also constructed a succinct classical argument system for Q M A. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP * = R E in Quantum complexity.

arXiv:2404.19754•Annual Symposium on Foundations of Computer Science•Oct 27, 2024•10 citations

Quantum Cryptomania with Classical Communication without One-Way Functions

Mohammed Barhoush, Amit Behera

In classical cryptography, one-way functions are necessary for most of cryptography. In the quantum world, however, Kretschmer at {TQC'21} and subsequent works have demonstrated that quantum versions of various primitives in minicrypt, such as signatures and private-key encryption, do not require quantum-computable one-way functions (\textsf{qOWF}s). However, the question of the necessity of \textsf{qOWF}s for primitives in Cryptomania like public-key encryption with classical public keys and ciphertexts (\textsf{qPKE}) has remained open. We provide a comprehensive picture of the relationship between \textsf{qPKE} and \textsf{qOWF}. First, our main result is a black-box separation between \textsf{qOWF}s and \textsf{qPKE}. In particular, we show that relative to a unitary, real, and self-inverse oracle, there exists a \textsf{qPKE} scheme (with classical keys and ciphertexts), but \textsf{qOWF}s do not exist. Further, our oracles admit a point-function obfuscation construction, thus ruling out black-box construction of \textsf{qOWF} from point function obfuscations. On the positive side, we construct \textsf{qPKE} from quantum indistinguishability obfuscation for quantum circuits with classical obfuscated descriptions and efficiently verifiable one-way puzzles, which is known to be a potentially weaker assumption than \textsf{qOWF}s, due to an existing black-box separation. Our construction is the quantum analog of the classical construction of \textsf{PKE} from one-way functions and indistinguishability obfuscation in the quantum computation with classical communication (QCCC) setting.

quant-pharXiv:2610.32145•Oct 26, 2026•0 citations

A Quantum Approach For Reducing Communications in Classical Secure Computations with Long Outputs

Jiayu Zhang

How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a basic primitive and example, we first consider the following problem which we call secure function sampling with long outputs: suppose $f:\{0,1\}^n\rightarrow \{0,1\}^m$ is a public, efficient classical function, where $m$ is big; Alice would like to sample $x$ from its domain and sends $f(x)$ to Bob; what Bob knows should be no more than $f(x)$ even if it behaves maliciously. Classical cryptography, like FHE and succinct arguments [Gen09,Kil92,HW15], allows us to achieve this task within communication complexity $O(n+m)$; could we achieve this task with communication complexity independent of $m$? In this work, we first design a quantum cryptographic protocol that achieves secure function sampling with approximate security, within $O(n)$ communication (omitting the dependency on the security parameter and error tolerance). We also prove the classical impossibility using techniques in [HW15], which means that our protocol indeed achieves a type of quantum advantage. Building on the secure function sampling protocol, we further construct protocols for general secure two-party computations [Yao86,GB01] with approximate security, with communication complexity only depending on the input length and the targeted security. In terms of the assumptions, we construct protocols for these problems assuming only the existence of collapsing hash functions [Unr16]; what's more, we also construct a classical-channel protocol for these problems additionally assuming the existence of noisy trapdoor claw-free functions [BCMVV,BKVV].

arXiv:2310.05213•Oct 8, 2023•0 citations

Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier

Alessandro Chiesa, Fermi Ma, Nicholas Spooner +1 more

We prove that Kilian's four-message succinct argument system is post-quantum secure in the standard model when instantiated with any probabilistically checkable proof and any collapsing hash function (which in turn exist based on the post-quantum hardness of Learning with Errors). This yields the first post-quantum succinct argument system from any falsifiable assumption. At the heart of our proof is a new quantum rewinding procedure that enables a reduction to repeatedly query a quantum adversary for accepting transcripts as many times as desired. Prior techniques were limited to a constant number of accepting transcripts.

arXiv:2103.08140•Annual Symposium on Foundations of Computer Science•Feb 1, 2022•30 citations
We prove the existence of succinct arguments for QMA, assuming only the existence of collapsing hash functions. This is the first scheme that relies only on unstructured ``Minicrypt'' assumptions, which are not known to imply public-key encryption.
Our main technical contribution is a quantum-succinct \emph{claw-state generation} protocol that allows us to bootstrap a small number of quantum correlations into an arbitrarily large number of claw-state correlations, using classical communication only. This improves upon the work of [Zhang, STOC 2021], having better round complexity, a proof in the standard model, and being overall much simpler. This yields a quantum-succinct blind delegation of quantum computation protocol from one-way functions, which we plug into the communication-compression compiler of [Bartusek, Liu, and Malavolta, EUROCRYPT 2026] to obtain succinct arguments for QMA.
Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any TTT-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.
Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTo ‘22) also constructed a succinct classical argument system for Q M A. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP * = R E in Quantum complexity.
In classical cryptography, one-way functions are necessary for most of cryptography. In the quantum world, however, Kretschmer at {TQC'21} and subsequent works have demonstrated that quantum versions of various primitives in minicrypt, such as signatures and private-key encryption, do not require quantum-computable one-way functions (\textsf{qOWF}s). However, the question of the necessity of \textsf{qOWF}s for primitives in Cryptomania like public-key encryption with classical public keys and ciphertexts (\textsf{qPKE}) has remained open. We provide a comprehensive picture of the relationship between \textsf{qPKE} and \textsf{qOWF}. First, our main result is a black-box separation between \textsf{qOWF}s and \textsf{qPKE}. In particular, we show that relative to a unitary, real, and self-inverse oracle, there exists a \textsf{qPKE} scheme (with classical keys and ciphertexts), but \textsf{qOWF}s do not exist. Further, our oracles admit a point-function obfuscation construction, thus ruling out black-box construction of \textsf{qOWF} from point function obfuscations. On the positive side, we construct \textsf{qPKE} from quantum indistinguishability obfuscation for quantum circuits with classical obfuscated descriptions and efficiently verifiable one-way puzzles, which is known to be a potentially weaker assumption than \textsf{qOWF}s, due to an existing black-box separation. Our construction is the quantum analog of the classical construction of \textsf{PKE} from one-way functions and indistinguishability obfuscation in the quantum computation with classical communication (QCCC) setting.
How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a basic primitive and example, we first consider the following problem which we call secure function sampling with long outputs: suppose f:{0,1}n→{0,1}mf:\{0,1\}^n\rightarrow \{0,1\}^mf:{0,1}n→{0,1}m is a public, efficient classical function, where mmm is big; Alice would like to sample xxx from its domain and sends f(x)f(x)f(x) to Bob; what Bob knows should be no more than f(x)f(x)f(x) even if it behaves maliciously. Classical cryptography, like FHE and succinct arguments [Gen09,Kil92,HW15], allows us to achieve this task within communication complexity O(n+m)O(n+m)O(n+m); could we achieve this task with communication complexity independent of mmm? In this work, we first design a quantum cryptographic protocol that achieves secure function sampling with approximate security, within O(n)O(n)O(n) communication (omitting the dependency on the security parameter and error tolerance). We also prove the classical impossibility using techniques in [HW15], which means that our protocol indeed achieves a type of quantum advantage. Building on the secure function sampling protocol, we further construct protocols for general secure two-party computations [Yao86,GB01] with approximate security, with communication complexity only depending on the input length and the targeted security. In terms of the assumptions, we construct protocols for these problems assuming only the existence of collapsing hash functions [Unr16]; what's more, we also construct a classical-channel protocol for these problems additionally assuming the existence of noisy trapdoor claw-free functions [BCMVV,BKVV].
We prove that Kilian's four-message succinct argument system is post-quantum secure in the standard model when instantiated with any probabilistically checkable proof and any collapsing hash function (which in turn exist based on the post-quantum hardness of Learning with Errors). This yields the first post-quantum succinct argument system from any falsifiable assumption. At the heart of our proof is a new quantum rewinding procedure that enables a reduction to repeatedly query a quantum adversary for accepting transcripts as many times as desired. Prior techniques were limited to a constant number of accepting transcripts.