Key pre-distribution in wireless sensor networks using multivariate polynomials
Farshid Delgosha, Faramarz Fekri · 2005
Key agreement in sensor networks is a dif- ficult problem because of resource constraints of the sensors. The classical approaches used in general networks are impractical in sensor networks. Hence, several key pre-distribution schemes are proposed. In this paper, we propose a hypercube multivariate scheme (HMS) that is a threshold-based scheme. In the HMS, a hypercube in the multidimensional space is designed and a number of multivariate polynomials are assigned to every point on the hypercube. The points on the hypercube are uniquely assigned to the sensors. Using this technique, a direct key is established between any two sensors at Hamming distance of one from each other. Other sensors are also able to establish indirect keys. Our analysis shows an improvement in the security of HMS compared to other similar schemes. We also propose a location-aware scheme that takes advantage of the distribution information to boost the security. In the proposed scheme, the target field is divided into hexagonal cells because of their efficient coverage compared to square cells. The sensors are randomly distributed in every cell. An HMS scheme is employed to pre-distribute keys in every cell. For the communication between adjacent cells, we propose a grid- based scheme in which the sensors of every cell are divided into groups. Shares of bivariate polynomials are stored in the sensors of every group. As a result, every two sensor in two adjacent cells are able to establish a direct key. Our security analysis shows improvements over similar schemes.