To achieve security in wireless sensor networks(WSN), it is important to be able to encrypt and authenticate messages sent among sensor nodes. Due to resource constraints, many key agreement schemes used in general networks such as Diffie-Hellman and public-key based schemes are not suitable for wireless sensor networks. The current pre-distribution of secret keys uses q-composite random key and it randomly allocates keys. But there exists high probability not to be public-key among sensor nodes and it is not efficient to find public-key because of the problem for time and energy consumption. To remove problems in pre-distribution of secret keys, we propose a new cryptographic key management protocol, which is based on the clustering scheme but does not depend on probabilistic key. The protocol can increase efficiency to manage keys because, before distributing keys in bootstrap, using public-key shared among nodes can remove processes to send or to receive key among sensors. Also, to find outcompromised nodes safely on network, it selves safety problem by applying a function of lightweight attack-detection mechanism.