A wireless sensor network consists of spatially distributed devices using sensors to monitor physical and environmental conditions. Key infection is a key distribution protocol for wireless sensor networks with a partially present adversary; a sensor node wishing to communicate secretly with other nodes simply sends a symmetric encryption key in the clear. The partially present adversary can eavesdrop on only a small fraction of the keys. Secrecy amplification is a post-deployment strategy to improve the security of key infection by combining multiple keys propagated along different paths. The previous mathematical analysis of secrecy amplification assumes that sensor nodes always transmit packets at the maximum strength. We provide a mathematical analysis of secrecy amplification where nodes adjust their transmission power adaptively (a.k.a. whispering mode).

Key infection is a lightweight key-distribution protocol for partially compromised wireless sensor networks, where sensor nodes send cryptographic keys in the clear. As the adversary is assumed to be present partially at the deployment stage, some keys are eavesdropped but others remain secret. To enhance the security of key infection, secrecy amplification combines keys propagated along different paths. Two neighbor nodes W1 and W2 can use another node W3 to update their key. If W3 is outside of the eavesdropping region of the adversary, the updated key is guaranteed to be secure. To date, the effectiveness of secrecy amplification has been demonstrated only by simulation. In this article, we present the first mathematical analysis of secrecy amplification. Our result shows that the effectiveness of secrecy amplification increases as the distance between the two neighbor nodes decreases.