Distributed Group Key Generation for Ubiquitous Networks
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for generating a group key in ubiquitous computing environments require a server and sequential exponent computation, leading to inefficiencies in time and cost, especially when nodes frequently enter and exit the network.
Innovation Solution
A method using a hash function to efficiently generate a group key by sharing secret keys between adjacent nodes, obtaining function values, broadcasting a result value, and performing XOR operations to derive a group key without the need for a server or exponent computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a server is used for computing, storing, and transmitting a group key, then the group key can be generated and shared, but the system complexity and cost increase
Solution Approach 1:
The patent extracts the group key generation process from the centralized server architecture and distributes it to individual nodes. Each node independently computes its contribution to the group key using the formula K_i = g^(a_i * b) mod p, where a_i is the node's private key and b is the group public key. This eliminates the need for a dedicated key management server while maintaining reliable group key generation.
Solution Approach 2:
Nodes perform self-service by autonomously generating their own key contributions and combining them with received contributions from other nodes. Each node calculates its partial key locally and combines it with partial keys from neighboring nodes through modular exponentiation, eliminating dependency on external key management infrastructure.
2Reliability
If exponent computation is performed sequentially in all sensor nodes, then a group key can be generated, but the time and cost efficiency deteriorates
Solution Approach 1:
The patent segments the group key generation process into independent parallel computations at each node. Instead of sequential exponentiation across all nodes, each node simultaneously computes its own partial key K_i = g^(a_i * b) mod p and receives partial keys from adjacent nodes, enabling parallel processing and significantly improving generation efficiency.
Solution Approach 2:
The patent transforms the computational approach by moving from sequential single-node exponentiation to parallel multi-node exponentiation. By introducing the dimension of parallel computation across the network, the system achieves O(1) time complexity for key generation regardless of the number of nodes, as all nodes compute simultaneously rather than sequentially.
3Reliability
If conventional group key generation methods are used, then security can be maintained, but the adaptability to dynamic networks with frequent node entry and exit deteriorates
Solution Approach 1:
The patent implements a dynamic group key generation mechanism where nodes can freely join or leave the network. When a node joins, it generates a new partial key contribution and combines it with existing group key material. When a node leaves, its contribution is automatically removed from the group key through regeneration. This dynamic approach maintains security while adapting to frequent network changes without requiring reconfiguration.
Data Source
AI summary
A method is provided for generating a group key, including sharing a plurality of secret keys with a plurality of nodes adjacent to a first node of the plurality of nodes, obtaining a plurality of function values using the plurality of secret keys and a result value using the plurality of function values, broadcasting the result value, receiving a plurality of result values generated using a method by which the result value has been obtained, from nodes of the plurality of nodes except for a corresponding node, and obtaining a group key using a plurality of function values extracted from the plurality of function values and the plurality of result values.