Sensor Data Cryptography in Wireless Sensor Networks

We consider decentralized estimation of a noise- corrupted deterministic signal in a bandwidth-constrained sensor network communicating through an insecure medium. Each sensor collects a noise-corrupted version, performs a local quantization, and transmits a 1-bit message to an ally fusion center through a wireless medium where the sensor outputs are vulnerable to unauthorized observation from enemy/third-party fusion centers. In this paper, we introduce an encrypted wireless sensor network (eWSN) concept where stochastic enciphers operating on binary sensor outputs are introduced to disguise the sensor outputs, creating an eWSN scheme. Noting that the plaintext (original) and ciphertext (disguised) messages are constrained to a single bit due to bandwidth constraints, we consider a binary channel-like scheme to probabilistically encipher (i.e., flip) the sensor outputs. We first consider a symmetric key encryption case where the “0” and “1” enciphering probabilities are equal. The key is represented by the bit enciphering probability. Specifically, we derive the optimal estimator of the deterministic signal approached from a maximum-likelihood perspective and the Cramer-Rao lower bound for the estimation problem utilizing the key. Furthermore, we analyze the effect of the considered cryptosystem on enemy fusion centers that are unaware of the fact that the WSN is encrypted (i.e., we derive the bias, variance, and mean square error (MSE) of the enemy fusion center). We then extend the cryptosystem to admit unequal enciphering schemes for “0” and “1”, and analyze the estimation problem from both the prospectives of ally (that has access to the enciphering keys) and (third-party) enemy fusion centers. The results show that when designed properly, a significant amount of bias and MSE can be introduced to an enemy fusion center with the cost to the ally fusion center being a marginal increase [factor of $(1-\Omega _{1}-\Omega _{0})^{-2}$, where $1-\Omega _{j}$, $j=0,1$ is the “$j$” enciphering probability] in the estimation variance (compared to the variance of a fusion center estimate operating in a vulnerable WSN).