Constant-Size Zero-Knowledge Set Membership Proofs Secure Resource-Constrained Networks ∞ Research

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Briefing

The core research problem is the prohibitive computational cost of verifying data integrity in resource-constrained environments like blockchain-based sensor networks. This paper introduces a novel OR-aggregation protocol that utilizes the OR-composition of Sigma protocols to create a zero-knowledge set membership proof system. This foundational breakthrough achieves a proof size and verification time that remain constant, irrespective of the size of the verified set, which is the single most important implication for the future of blockchain architecture as it enables truly scalable, private data verification across vast, low-power IoT networks.

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Context

Prior to this work, efficient set membership proofs, crucial for privacy-preserving data validation, relied on structures like Merkle trees or complex zero-knowledge systems. These established methods incurred computational costs and proof sizes that scaled logarithmically or linearly with the set size. This limitation resulted in significant on-chain data overhead, rendering these techniques impractical for the limited processing power and bandwidth of large-scale, decentralized sensor networks and other resource-constrained devices.

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Analysis

The paper’s core mechanism is the OR-aggregation of Schnorr-based Sigma protocols. A Sigma protocol allows a prover to demonstrate knowledge of a secret without revealing it. The “OR-aggregation” logically combines multiple such proofs into a single, compact proof, demonstrating that the secret element belongs to at least one of the set members without disclosing which one. This differs fundamentally from previous approaches by shifting the complexity from the size of the set to the constant-size structure of the aggregated proof, leveraging elliptic curve properties to maintain succinctness and security under the discrete logarithm assumption.

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Parameters

Proof Size ∞ Constant, independent of the set size (|S|). This contrasts with logarithmic or linear scaling in prior art.
Verification Time ∞ Constant, independent of the set size (|S|). Achieves O(1) complexity for verification.
Cryptographic Basis ∞ Discrete Logarithm Assumption. Security is proven under this established computational hardness assumption.

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Outlook

This research establishes a new primitive for verifiable computation, immediately opening avenues for practical, privacy-preserving data management in decentralized IoT ecosystems. In the next 3-5 years, this constant-cost proof mechanism will be integrated into layer-1 and layer-2 protocols, enabling resource-constrained devices to participate in decentralized governance and data sharing with provable integrity. This will unlock the potential for truly global, high-volume blockchain applications beyond traditional finance.

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Verdict

The OR-aggregation protocol fundamentally redefines the efficiency frontier for zero-knowledge set membership, making constant-cost data integrity verification a foundational reality for all resource-constrained decentralized systems.

Zero-knowledge set membership, OR-aggregation protocol, Sigma protocols, constant proof size, constant verification time, resource-constrained devices, blockchain sensor networks, IoT ecosystems, elliptic curve cryptography, discrete logarithm assumption, Schnorr identification scheme, cryptographic primitive, privacy preservation, scalable verification, on-chain data reduction Signal Acquired from ∞ arxiv.org