On the Existence of Three Round Zero-Knowledge Proofs

Fleischhacker, Nils; Goyal, Vipul; Jain, Abhishek

doi:10.1007/978-3-319-78372-7_1

Cited by 17 publications

(5 citation statements)

References 41 publications

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“…This is another example of theoretical separation between ZK and ǫ-ZK. On the other hand, Fleischhacker, Goyal, and Jain [FGJ18] showed that there does not exist 3-round ǫ-ZK proof for NP even with non-black-box simulation under some computational assumptions, which is the same lower bound as that for ZK proofs if we allow non-black-box simulation.…”

Section: Related Workmentioning

confidence: 99%

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

Chia¹,

Chung²,

Yamakawa³

2020

Preprint

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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 ǫ-zero-knowledge. Concretely, we construct the following protocols:• We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box ǫ-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 ǫ-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 ǫ-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.

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Section: Related Workmentioning

confidence: 99%

“…ǫ-ZK was originally called ǫ-knowledge, but some later works[BKP18,FGJ18] call it ǫ-ZK. We use ǫ-ZK to clarify that this is a variant of ZK.4 Actually,[BKP19] shows that even weaker notion called weak ZK suffices for witness indistinguishability and witness hiding.…”

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confidence: 99%

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

Chia¹,

Chung²,

Yamakawa³

2020

Preprint

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“…Kalai, Rothblum, and Rothblum [KRR17] proved that there does not exist constant-round public-coin ZK proofs for NP even with non-uniform simulation under certain assumptions on obfuscation. Fleischhacker, Goyal, and Jain [FGJ18] proved that there does not exist three-round ZK proofs for NP even with non-uniform simulation under the same assumptions. Though these results are shown in the classical setting, it might be possible to extend them to the quantum setting by assuming similar assumptions against quantum adversaries.…”

Section: More Related Workmentioning

confidence: 99%

On the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds

Chia,

Chung,

Liu

et al. 2021

Preprint

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We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for NP. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for NP unless NP ⊆ BQP. As constant-round black-box zero-knowledge arguments for NP exist in the classical setting, our main result points out a fundamental difference between post-quantum and classical zero-knowledge protocols. Combining previous results, we conclude that unless NP ⊆ BQP, constant-round post-quantum zeroknowledge protocols for NP exist if and only if we use non-black-box techniques or relax certain security requirements such as relaxing standard zero-knowledge to ǫ-zero-knowledge. Additionally, we also prove that three-round and public-coin constant-round post-quantum black-box ǫ-zero-knowledge arguments for NP do not exist unless NP ⊆ BQP.

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“…ZK proofs cannot be directly used for VMPC since we require a 3-round public-coin protocol to comply with our minimal interaction setting and this is infeasible, cf. [39,32], while we cannot utilize a subversionsound NIZK either, cf. [7], since in this case, we can at best obtain witness indistinguishability which is insufficient for proving the simulation-based privacy needed for VMPC.…”

Section: Technical Overview and Contributionsmentioning

confidence: 99%

Crowd Verifiable Zero-Knowledge and End-to-End Verifiable Multiparty Computation

Baldimtsi

Kiayias

Zacharias

et al. 2020

Advances in Cryptology – ASIACRYPT 2020

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Auditing a secure multiparty computation (MPC) protocol entails the validation of the protocol transcript by a third party that is otherwise untrusted. In this work we introduce the concept of end-to-end verifiable MPC (VMPC), that requires the validation to provide a correctness guarantee even in the setting that all servers, trusted setup primitives and all the client systems utilized by the input-providing users of the MPC protocol are subverted by an adversary. To instantiate VMPC, we introduce a new concept in the setting of zero-knowlegde protocols that we term crowd verifiable zero-knowledge (CVZK). A CVZK protocol enables a prover to convince a set of verifiers about a certain statement, even though each one individually contributes a small amount of entropy for verification and some of them are adversarially controlled. Given CVZK, we present a VMPC protocol that is based on discretelogarithm related assumptions. At the high level of adversity that VMPC is meant to withstand, it is infeasible to ensure perfect correctness, thus we investigate the classes of functions and verifiability relations that are feasible in our framework, and present a number of possible applications the underlying functions of which can be implemented via VMPC.

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On the Existence of Three Round Zero-Knowledge Proofs

Cited by 17 publications

References 41 publications

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

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

On the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds

Crowd Verifiable Zero-Knowledge and End-to-End Verifiable Multiparty Computation

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