In this paper we propose a symmetric cryptographic approach named Square Key Matrix Management Scheme (SKMaS) in which a sensor node named Key Distribution Server (KDS) is responsible for the security of key management. When the system starts up, the KDS sends its individual key and two sets of keys to sensor nodes. With the IDs, any two valid sensor nodes, e.g. i and j, can individually identify the corresponding communication keys (CKs) to derive a dynamic shared key (DSK) for encrypting/decrypting messages transmitted between them. When i leaves the underlying network, the CKs and the individually keys currently utilized by i can be reused by a newly joining sensor, e.g. h. However, when h joins the network, if no such previously-used IDs are available, h will be given a new ID, CKs and the individually key by the KDS. The KDS encrypts the CKs, with which an existing node q can communicate with h, with individual key so that only q rather than h can correctly decrypt the CKs. The lemmas and security analyses provided in this paper prove that the proposed system can protect at least three common attacks.