We consider security issues for consensus-based distributed estimation problem. In a sensor network, an attacker with limited power injects random false data into the communication links so as to degrade the network performance. First, an optimal estimator is designed by minimizing the mean-squared estimation error of each sensor under hostile attacks. Then, a sufficient condition is provided to guarantee the stability of the proposed estimator. Finally, a set of suboptimal attacking sequences is obtained for the attacker to maximize the network estimation error. Illustrative examples are provided to verify the effectiveness of the suboptimal attacking strategy.Kalman filter based on the Kalman filter updated step; Stankovi K c et al.[12] put a priori estimation in the Kalman filter predict step.In real applications, security issue has been a big obstacle to the applications of WSNs because of its vulnerabilities to various types of potential hostile attacks. In recent years, many researchers begin to study security issues in WSNs [13]. For example, Shi et al. [14] study sensor data scheduling problem and construct a scheduling scheme to minimize the estimation error and satisfy the energy constraint. Li et al. [15] consider a scenario where the wireless communication channel between a sensor node and a remote estimator may be jammed by an external attacker. Mo et al. [16] study the performance of control systems under a replay attack model.Currently, the existing works on the attacking strategy can be classified into two types: one is denial of service (DoS). For example, Zhang et al.[17] focus on the DoS attack and build an optimal attacking schedule to maximize the expected average estimation error of the target system. Ren et al. [18] develop an optimal DoS attack strategies over Bayesian quickest change detection to maximize the detection cost for the remote center. The other is false data injection attack. For example, Mo et al. [19] study the influence of false data injection attack on the state estimation of an objective system whose monitor failed to detect anomalies. Zou et al. [20] study the state estimation problem for complex networks subject to false data injection attack. Xie et al. [21] consider the false data injection attack in power market operations and study the economic impact of this attack. In addition, the security problem in multi-agent systems has also attracted increasing interests. In [22], a distributed adaptive controller was proposed for multi-agent systems with missing control input in some intervals and also delays in the transmission of control input to agents. The intervals could be provisional failures of communication links, packet loss or false data injection. To defend against two different typical attacks in multi-agent system, Feng et al.[23] studied a distributed secure consensus tracking problem with connected and disconnected directed switching topologies.Most of the aforementioned works are aiming primarily at the centralized state estimations. To the best of ...