Cloud computing provides powerful computing ability of mobile devices in the Internet of Things (IoT) networks. However, the large amounts of data interaction with cloud suffers bandwidth limit and energy efficiency for data processing and transmission, and the energy consumption of data processing is far less than data transmission. In this paper, offloading is considered in transmission to improve the battery lifetime by employing a spectral-energy efficient transmission scheme with efficient computing in IoT-Cloud. The offloaded resource can be saved to serve more services if the physical air interface is designed efficiently. In addition, many personal things are unloaded to the IoT-Cloud which creates a risk of privacy and security. The improved offloading efficiency of data transmission scheme secure truncating orthogonal frequency division multiplexing (STOFDM) is generated by deliberately truncating the orthogonal frequency division multiplexing signal in time domain. Particularly, the truncations are selected by a dynamic random private matrix based on the proposed offloading power amplifier theorem. The corresponding legitimate receiver is designed with private mapping using the efficient fast Fourier transformation (FFT) for offloading computation. Moreover, the closed-form expression for the FFT-based STOFDM system is analyzed and be verified by simulation results. In light of the analysis, the STOFDM performs intercarrier interference as an orthogonal sequence is partially transmitted, which degrades the reliability of transmission link. Further, two enhanced detectors with low computing-complexity is also given to improve the performance of Bob while restrict eavesdropper's reception and further provides offloading computation.