The security issue in the state estimation problem is investigated for a networked control system (NCS). The communication channels between the sensors and the remote estimator in the NCS are vulnerable to attacks from malicious adversaries. The false data injection attacks are considered. The aim of this paper to find the so-called insecurity conditions under which the estimation system is insecure in the sense that there exist malicious attacks that can bypass the anomaly detector but still lead to unbounded estimation errors. In particular, a new necessary and sufficient condition for the insecurity is derived in the case that all communication channels are compromised by the adversary. Moreover, a specific algorithm is proposed for generating attacks with which the estimation system is insecure. Furthermore, for the insecure system, a system protection scheme through which only a few (rather than all) communication channels require protection against false data injection attacks is proposed. A simulation example is utilized to demonstrate the effectiveness of the proposed conditions/algorithms in the secure estimation problem for a flight vehicle. (C) 2017 Elsevier Ltd. All rights reserved.