Implementation of Elliptic Curves in the Polynomial Blom Key Pre-Distribution Scheme for Wireless Sensor Networks and Distributed Ledger Technology

Abstract

One of the challenges in securing wireless sensor networks (WSNs) is the key distribution; that is, a single shared key must first be known to a pair of communicating nodes before they can proceed with the secure encryption and decryption of the data. In 1984, Blom proposed a scheme called the symmetric key generation system as one method to solve this problem. Blom’s scheme has proven to be λ-secure, which means that a coalition of λ+1 nodes can break the scheme. In 2021, a novel and intriguing scheme based on Blom’s scheme was proposed. In this scheme, elliptic curves over a finite field are implemented in Blom’s scheme for the case when λ=1. However, the security of this scheme was not discussed. In this paper, we point out a mistake in the algorithm of this novel scheme and propose a way to fix it. The new fixed scheme is shown to be applicable for arbitrary λ. The security of the proposed scheme is also discussed. It is proven that the proposed scheme is also λ-secure with a certain condition. In addition, we also discuss the application of this proposed scheme in distributed ledger technology (DLT).