Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier

Chiesa, Alessandro; Ma, Fermi; Spooner, Nicholas; Zhandry, Mark

doi:10.1109/focs52979.2021.00014

Cited by 13 publications

(10 citation statements)

References 10 publications

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“…4 Now let's state a result first proven in [MW05] and restated in many later works (e.g., [CMSZ22]).…”

Section: Jordan's Lemma and Alternating Projectionsmentioning

confidence: 89%

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

Ananth¹,

Hu²,

Yuen³

2023

Preprint

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Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge.These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by this, we present the first black-box separation of quantum money and cryptographic primitives. Specifically, we show that collision-resistant hash functions cannot be used as a black-box to construct publickey quantum money schemes where the banknote verification makes classical queries to the hash function. Our result involves a novel combination of state synthesis techniques from quantum complexity theory and simulation techniques, including Zhandry's compressed oracle technique.

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“…4 Now let's state a result first proven in [MW05] and restated in many later works (e.g., [CMSZ22]).…”

Section: Jordan's Lemma and Alternating Projectionsmentioning

confidence: 89%

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

Ananth¹,

Hu²,

Yuen³

2023

Preprint

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“…At the end of the interaction, the prover and verifier could then engage in a succinct interactive argument (of knowledge) for a (classical) NP statement that "the verifier would have accepted the committed messages underlying σ 2 and σ 4 ". One could potentially employ Kilian's succinct interactive argument of knowledge for NP which was recently shown to be post-quantum secure under the post-quantum LWE assumption [CMSZ21].…”

Section: From a Verifier-succinct Measurement Protocol To Succinct Ar...mentioning

confidence: 99%

“…However, there is one remaining problem: the argument-of-knowledge property of Kilian's protocol proved by [CMSZ21] is insufficiently composable to be used in our compiler. They demonstrate an extractor for Kilian's protocol that takes any quantum cheating prover that convinces the verifier and extracts a witness from them.…”

Section: From a Verifier-succinct Measurement Protocol To Succinct Ar...mentioning

confidence: 99%

“…Our main tool for these compilers are post-quantum succinct arguments of knowledge for NP [CMSZ21,LMS21]. Specifically, the security guarantees proved in [CMSZ21] are insufficient for the compilers, because the post-quantum extraction algorithm from [CMSZ21] is not sufficiently composable since their extractor might significantly disturb the prover's state. Instead, we make use of a composable variant of the [CMSZ21] extractor due to [LMS21] called "state-preserving succinct arguments of knowledge," 24 which we now define.…”

Section: The Fully Succinct Protocolmentioning

confidence: 99%

“…Specifically, the security guarantees proved in [CMSZ21] are insufficient for the compilers, because the post-quantum extraction algorithm from [CMSZ21] is not sufficiently composable since their extractor might significantly disturb the prover's state. Instead, we make use of a composable variant of the [CMSZ21] extractor due to [LMS21] called "state-preserving succinct arguments of knowledge," 24 which we now define. 9.1 State-Preserving Succinct Arguments of Knowledge Definition 9.1.…”

Section: The Fully Succinct Protocolmentioning

confidence: 99%

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Succinct Classical Verification of Quantum Computation

Bartusek

Kalai

Lombardi

et al. 2022

Lecture Notes in Computer Science

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We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the security parameter). Our protocol is secure assuming the post-quantum security of indistinguishability obfuscation (iO) and Learning with Errors (LWE). This is the first succinct argument for quantum computation in the plain model ; prior work (Chia-Chung-Yamakawa, TCC '20) requires both a long common reference string and non-black-box use of a hash function modeled as a random oracle.At a technical level, we revisit the framework for constructing classically verifiable quantum computation (Mahadev, FOCS '18). We give a self-contained, modular proof of security for Mahadev's protocol, which we believe is of independent interest. Our proof readily generalizes to a setting in which the verifier's first message (which consists of many public keys) is compressed. Next, we formalize this notion of compressed public keys; we view the object as a generalization of constrained/programmable PRFs and instantiate it based on indistinguishability obfuscation.Finally, we compile the above protocol into a fully succinct argument using a (sufficiently composable) succinct argument of knowledge for NP. Using our framework, we achieve several additional results, including• Succinct arguments for QMA (given multiple copies of the witness),• Succinct non-interactive arguments for BQP (or QMA) in the quantum random oracle model, and• Succinct batch arguments for BQP (or QMA) assuming post-quantum LWE (without iO).

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Watermarking PRFs Against Quantum Adversaries

Kitagawa

Nishimaki

2022

Advances in Cryptology – EUROCRYPT 2022

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Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier

Cited by 13 publications

References 10 publications

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

Succinct Classical Verification of Quantum Computation

Watermarking PRFs Against Quantum Adversaries

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