Sleep scheduling algorithms for duty-cycled sensor networks have received great attention, since sensors should dynamically be awake and asleep to save energy consumption. Among all current sleep scheduling algorithms, only the recently proposed energy consumed uniformly-connected k-neighborhood (EC-CKN) algorithm focuses on not only the coverage of the resultant network, but also the network lifetime after sleep scheduling. However, all sleep scheduling processes ignore the fact that potential insider attacks actually can seriously affect or destroy proper sleep scheduling operations and properties. In this paper, we discuss these vulnerabilities and propose corresponding countermeasures for EC-CKN, i.e., secure neighborhood authentication.