The current boom in the Inteet of Things (IoT) is changing daily life in many ways, from wearable devices to con-nected vehicles and smart cities. We used to regard fog computing as an extension of cloud computing, but it is now becoming an ideal solution to transmit and process large-scale geo-distributed big data. We propose a Byzantine fault-tolerant networking method and two resource allocation strategies for IoT fog computing. We aim to build a secure fog network, called "SIoTFog," to tolerate the Byzantine faults and improve the efficiency of transmitting and processing IoT big data. We consider two cases, with a single Byzantine fault and with multiple faults, to compare the performances when facing different degrees of risk. We choose latency, number of forwarding hops in the transmission, and device use rates as the metrics. The simulation results show that our methods help achieve an efficient and reliable fog network.