Strongly Resilient Non-Interactive Key Predistribution For Hierarchical Networks

Key establishment is the basic necessary tool in the network security, by which pairs in the network can establish shared keys for protecting their pairwise communications. There have been some key agreement or predistribution schemes with the property that the key can be established without the interaction (\cite{Blom84,BSHKY92,S97}). Recently the hierarchical cryptography and the key management for hierarchical networks have been active topics(see \cite{BBG05,GHKRRW08,GS02,HNZI02,HL02,Matt04}. ). Key agreement schemes for hierarchical networks were presented in \cite{Matt04,GHKRRW08} which is based on the Blom key predistribution scheme(Blom KPS, [1]) and pairing. In this paper we introduce generalized Blom-Blundo et al key predistribution schemes. These generalized Blom-Blundo et al key predistribution schemes have the same security functionality as the Blom-Blundo et al KPS. However different and random these KPSs can be used for various parts of the networks for enhancing the resilience. We also presentkey predistribution schemes from a family hyperelliptic curves. These key predistribution schemes from different random curves can be used for various parts of hierarchical networks. Then the non-interactive, identity-based and dynamic key predistributon scheme based on this generalized Blom-Blundo et al KPSs and hyperelliptic curve KPSs for hierarchical networks with the following properties are constructed. 1)$O(A_KU)$ storage at each node in the network where $U$ is the expansion number and $A_K$ is the number of nodes at the $K$-th level of the hierarchical network; 2)Strongly resilience to the compromising of arbitrary many leaf and internal nodes; 3)Information theoretical security without random oracle.

💡 Research Summary

The paper addresses the fundamental problem of key establishment in hierarchical networks by proposing two novel non‑interactive key predistribution schemes (KPSs) that achieve strong resilience, information‑theoretic security, and practical efficiency. The first scheme is a “generalized Blom‑Blundo” construction that extends the classic Blom and Blundo KPSs. Instead of fixing the polynomial degree or matrix dimensions, the authors allow the degree (w) to be chosen adaptively according to network size and security requirements. For each hierarchy level (K) a distinct set of secret polynomials ({f_{K,i}(x)}) and a distinct public matrix (G_K) are generated. A node (i) stores a secret vector (s_i) that incorporates both its own level’s parameters and those of all ancestor levels. The pairwise key between nodes (i) and (j) is computed as
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