A wireless sensor network is the formation of a temporary network of sensor nodes equipped with limited resources working in an ad hoc environment. Routing protocol is one of the key challenges while designing a wireless sensor network, which requires optimum use of limited resources of a sensor node, such as power and so on. Similarly, data security and integrity is another open issue that has emerged as a flash point in research community in the last decade. This article proposes a secure model for routing data from source to destination named as secure and energy-efficient routing. The proposed secure and energy-efficient routing is inherited from authentication and voice encryption scheme developed for Global System for Mobile Communications. Necessary modifications have been carried out in order to fit the Global System for Mobile Communications technology in a wireless sensor network ad hoc environment. Due to its low complexity, the secure and energy-efficient routing consumes lesser battery power both during encryption/decryption and for routing purposes. It is due to the XoR operation used in the proposed scheme which is considered as the most inexpensive process with respect to time and space complexity. It is observed through simulations that secure and energy-efficient routing can work effectively even in critical power level in a sensor network. The article also presents a simulation-based comparative analysis of the proposed secure and energy-efficient routing with two notable existing secure routing protocols. We proved that the proposed secure and energy-efficient routing helps to achieve the desired performance under dynamically changing network conditions with various numbers of malicious nodes. Moreover, in Global System for Mobile Communications, generally three linear feedback shift registers are used to fragment the key in data encryption mechanism. In this article, a mathematical model is proposed to increase the number of possible combinations of shift register in order to make the data encryption mechanism more secure which has never been done before. Due to its liner complexity, lesser power consumption, and more dynamic route updating, the secure and energy-efficient routing can easily find its use in the emerging Internet-of-Things systems.