On the Extremal Source Key Rates for Secure Storage over Graphs

2026-01-12

AI Summary

This study investigates the extremal source-key capacity for secure storage systems over graph structures, where each edge-associated source symbol must be perfectly recoverable by its two incident nodes while remaining information-theoretically secure against all other nodes. By introducing shared source keys and enforcing edge-wise correctness and security constraints, the work analyzes the achievable upper bound on the ratio of source symbol size to key size. Combining information-theoretic security models, graph-theoretic analysis, and explicit coding constructions, the paper fully characterizes the extremal capacities for several graph classes: those achieving unit capacity, graphs enabling secure storage without any secret keys, and generalized extremal graphs under multiple source symbols. Furthermore, it establishes necessary and sufficient graphical conditions for attaining extremal capacity in both single-source and multi-source settings.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• 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 secure storage codes over graphs, where multiple independent source symbols are encoded and stored at graph nodes subject to edge-wise correctness and security constraints. For each edge, a specified subset of source symbols must be recoverable from its two incident nodes, while no information about the remaining sources is revealed. To meet the security requirement, a shared source key may be employed. The ratio between the source symbol size and the source key size defines the source key rate, and the supremum of all achievable rates is referred to as the source key capacity. We study extremal values of the source key capacity in secure storage systems and provide complete graph characterizations for several fundamental settings. For the case where each edge is associated with a single source symbol, we characterize all graphs whose source key capacity equals one. We then generalize this result to the case where each edge is associated with multiple source symbols and identify a broad class of graphs that achieve the corresponding extremal capacity under a mild structural condition. In addition, we characterize all graphs for which secure storage can be achieved without using any source key.

Problem

• secure storage
• source key rate
• graph
• information security
• extremal capacity

Innovation

• secure storage codes
• source key capacity
• graph characterization
• information-theoretic security
• extremal rates