Wireless sensor networks will be broadly deployed in the real world and widely utilized for various applications. A prerequisite for secure communication among the sensor nodes is that the nodes should share a session key to bootstrap their trust relationship. The open problems are how to verify the identity of communicating nodes and how to minimize any information about the keys disclosed to the other side during key agreement. At any rate, any one of the existing schemes cannot perfectly solve these problems due to some drawbacks. Accordingly, we propose a new pre-distribution scheme with the following merits. First, it supports authentication services. Second, each node can only find some indices of key spaces that are shared with the other side, without revealing unshared key information. Lastly, it substantially improves resilience of network against node capture. Performance and security analyses have proven that our scheme is suitable for sensor networks in terms of performance and security aspects.