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Peer-to-Peer Networking and Applications

Efficient non-interactive zero-knowledge proofs for quantum range verification in blockchain

B. Sriman, S. Ganesh Kumar

Published Jun 1, 2024• 2 citations
Publisher
DOI
10.1007/s12083-024-01715-w

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Lattice-based non-interactive zero-knowledge proof has been widely used in one-way communication and can be effectively applied to resist quantum attacks. However, lattice-based non-interactive zero-knowledge proof schemes have long faced and paid more attention to some efficiency issues, such as proof size and verification time. In this paper, we propose the non-interactive zero-knowledge proof schemes from RLWE-based key exchange by making use of the Hash function and public-key encryption. We then show how to apply the proposed schemes to achieve the fixed proof size and rapid public verification. Compared with previous approaches, our schemes can realize better effectiveness in proof size and verification time. In addition, the proposed schemes are secure from completeness, soundness, and zero-knowledge.
We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge (ZK) and 3) certified-everlasting zero-knowledge (CE-ZK). The CE-ZK property allows a verifier of a quantum proof to revoke the proof in a way that can be checked (certified) by the prover. Conditioned on successful certification, the verifier's state can be efficiently simulated with only the statement, in a statistically indistinguishable way. Our contributions regarding these certified-everlasting NIZKs (CE-NIZKs) are as follows: - We identify a barrier to obtaining CE-NIZKs in the CRS model via generalizations of known interactive ZK proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK using non-black-box use of NIZK for NP satisfying certain properties, along with OWFs. As a result, we obtain CE-NIZKs for NP in the CRS model, based on polynomial hardness of the learning with errors (LWE) assumption. - In addition, we observe that the aforementioned barrier does not apply to the shared EPR model. We leverage this to construct CE-NIZK for NP in this model based on any statistical binding hidden bits generator, which is known from LWE. The only quantum computation here involves single-qubit measurements of the EPR pairs.
A verifiable random function (VRF in short) is a powerful pseudo-random function that provides a non-interactively public verifiable proof for the correctness of its output. Recently, VRFs have found essential applications in blockchain design, such as random beacons and proof-of-stake consensus protocols. To our knowledge, the first generation of blockchain systems used inherently inefficient proof-of-work consensuses, and the research community tried to achieve the same properties by proposing proof-of-stake schemes where resource-intensive proof-of-work is emulated by cryptographic constructions. Unfortunately, those most discussed proof-of-stake consensuses (e.g., Algorand and Ouroborous family) are not future-proof because the building blocks are secure only under the classical hard assumptions; in particular, their designs ignore the advent of quantum computing and its implications. In this paper, we propose a generic compiler to obtain the post-quantum VRF from the simple VRF solution using symmetric-key primitives (e.g., non-interactive zero-knowledge system) with an intrinsic property of quantum-secure. Our novel solution is realized via two efficient zero-knowledge systems ZKBoo and ZKB++, respectively, to validate the compiler correctness. Our proof-of-concept implementation indicates that even today, the overheads introduced by our solution are acceptable in real-world deployments. We also demonstrate potential applications of a quantum-secure VRF, such as quantum-secure decentralized random beacon and lottery-based proof of stake consensus blockchain protocol.