Predistribution Scheme for Establishing Group Keys in Wireless Sensor Networks

Abstract

Special designs are needed for cryptographic schemes in wireless sensor networks (WSNs). This is because sensor nodes are limited in memory storage and computational power. In 1992, Blundo et al. proposed a noninteractive group key establishment scheme using a multivariate polynomial. Their scheme can establish a group key of $m$ sensors. Since each share is a polynomial involving $m-1$ variables and having degree $k$ , each sensor needs to store $(k+1)^{m-1}$ coefficients from GF $(p)$ , which is exponentially proportional to the size of group. This makes their scheme only practical when $m=2$ for peer-to-peer communication. So far, most existing predistribution schemes in WSNs establish pairwise keys for sensor nodes. In this paper, we propose a novel design to propose a predistribution scheme for establishing group keys in WSNs. Our design uses a special-type multivariate polynomial in $Z_{N} ,$ where $N$ is a RSA modulus. The advantage of using this type of multivariate polynomial can limit the storage space of each sensor to be $m(k+1)$ , which is linearly proportional to the size of group communication. In addition, we prove the security of the proposed scheme and show that the computational complexity of the proposed scheme is efficient.