This paper presents a key management scheme based on quadratic form polynomial for wireless sensor network (WSN) for the problems that some existing key pre-distribution schemes are limited in key sharing and network connectivity probability between neighbor nodes.It beyonds the current ideas for establishing shared key based on quadratic symmetric polynomial and presents the multiple asymmetric quadratic form polynomial

and analyzes the orthogonal diagonalization properties of quadratic form to generate the key information by the relationship between eigenvalues and eigenvectors of the quadratic form

the nodes could achieve identification and generate the unique session keys between the neighbor nodes through exchanging the key information.Compared to some existing key pre-distribution schemes

the analysis of performance show that this scheme could resist captive

have good scalability and connectivity

and have a lower storage cost

a lower communication overhead.