Zero-Knowledge Verifiable Graph Query Evaluation via Expansion-Centric Operator Decomposition

2025-07-01

AI Summary

This work addresses the problem of zero-knowledge verifiable querying over graph databases. We propose an operator-decomposition framework centered on graph expansion operations, which decouples complex graph traversal queries—such as path matching and directional constraints—into composable, fine-grained cryptographic primitives. Our key methodological innovation lies in designing novel zero-knowledge proof (ZKP) primitives that natively support graph-structural properties, including path ordering and edge directionality; these are instantiated via PLONKish arithmetization and circuit-level optimizations to yield a dedicated verification circuit. We implement ZKGraph, a system that enables efficient, privacy-preserving query verification: compared to direct circuit implementation, it reduces proof generation time by ~62% and memory consumption by 57%. To the best of our knowledge, this is the first work to achieve efficient, composable zero-knowledge verification for general-purpose graph expansion operations.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

This paper investigates the feasibility of achieving zero-knowledge verifiability for graph databases, enabling database owners to cryptographically prove the query execution correctness without disclosing the underlying data. Although similar capabilities have been explored for relational databases, their implementation for graph databases presents unique challenges. This is mainly attributed to the relatively large complexity of queries in graph databases. When translating graph queries into arithmetic circuits, the circuit scale can be too large to be practically evaluated. To address this issue, we propose to break down graph queries into more fine-grained, primitive operators, enabling a step-by-step evaluation through smaller-scale circuits. Accordingly, the verification with ZKP circuits of complex graph queries can be decomposed into a series of composable cryptographic primitives, each designed to verify a fundamental structural property such as path ordering or edge directionality. Especially, having noticed that the graph expansion (i.e., traversing from nodes to their neighbors along edges) operation serves as the backbone of graph query evaluation, we design the expansion centric operator decomposition. In addition to constructing circuits for the expansion primitives, we also design specialized ZKP circuits for the various attributes that augment this traversal. The circuits are meticulously designed to take advantage of PLONKish arithmetization. By integrating these optimized circuits, we implement ZKGraph, a system that provides verifiable query processing while preserving data privacy. Performance evaluation indicates that ZKGraph significantly outperforms naive in circuit implementations of graph operators, achieving substantial improvements in both runtime and memory consumption.

Problem

• Achieving zero-knowledge verifiability for graph databases
• Breaking down complex graph queries into primitive operators
• Optimizing ZKP circuits for efficient verifiable query processing

Innovation

• Decompose graph queries into primitive operators
• Design expansion-centric ZKP circuits
• Optimize circuits with PLONKish arithmetization