Recently, the Internet of Things (IoT) has emerged as a significant advancement for Internet and mobile networks with various public safety network applications. An important use of IoT-based solutions is its application in post-disaster management, where the traditional telecommunication systems may be either completely or partially damaged. Since enabling technologies have restricted authentication privileges for mobile users, in this paper, a strategy of mobile-sink is introduced for the extension of user authentication over cloud-based environments. A seamless secure authentication and key agreement (S-SAKA) approach using bilinear pairing and elliptic-curve cryptosystems is presented. It is shown that the proposed S-SAKA approach satisfies the security properties, and as well as being resilient to node-capture attacks, it also resists significant numbers of other well-known potential attacks related with data confidentiality, mutual authentication, session-key agreement, user anonymity, password guessing, and key impersonation. Moreover, the proposed approach can provide a seamless connectivity through authentication over wireless sensor networks to alleviate the computation and communication cost constraints in the system. In addition, using Burrows-Abadi-Needham logic, it is demonstrated that the proposed S-SAKA framework offers proper mutual authentication and session key agreement between the mobile-sink and the base station.