Since current key management schemes are mainly designed for static and planar networks, they are not very suitable for the layer-cluster wireless sensor networks (WSNs), a WSN layer-cluster key management scheme based on quadratic polynomial and Lagrange interpolation polynomial is proposed, in which the main idea of this scheme along the research line of broadcast identity authentication, session key, group key, network key and personal key. Specifically, authentication key can be established on the basis of Fourier series for identity authentication; session key is established by a multiple asymmetric quadratic polynomial, in which session key information is encrypted by the authentication key to ensure the security of intermediate interactive information; based on the former two keys, group key is established on the basis of Lagrange interpolation polynomial, in which the nodes of the cluster are not directly involved; the generation and management of network key is similar to the group key, in which the establishment idea is to regard the BS and all cluster heads as a group; the generation and management of personal key is also similar to the group key, the difference is that the personal key can be obtained by cluster nodes through getting the Lagrange interpolation polynomial coefficients based on their own random key information. It is analyzed that the proposed layer-cluster key management scheme can guarantee the identity of network nodes firstly through forward authentication and reverse authentication, and session key, group key and network key will guarantee the independence of the keys' management and avoids the problem of single point failure compared with LEAP protocol, and personal key will guarantee the privacy of network.
Keywords: Lagrange interpolation polynomial; key management; layer-cluster key; quadratic polynomial; wireless sensor network.