Abstract The Internet of Things (IoT) is composed of different networked objects (i.e., smart devices) which are interconnected to gather, process, refine, and exchange meaningful data over the Internet. These objects are assigned to their respective IP addresses, and they are able to send and receive data over a network without any human assistance. IoT offers different types of applications, such as, but not limited to, smart traffic monitoring, smart home, smart health care and smart cities, to name a few. In a Cyber-Physical System (CPS), computing elements coordinate and communicate with sensor devices, which monitor cyber and physical indicators, and actuators, and also modify the cyber and physical environment where they run. The synergy of computational as well as physical components, specifically the use of CPSs, led to the advancement of IoT implementations. In a cloud-driven IoT-based big data environment, a cloud-based platform is used to store the data generated by IoT devices (normally by sensor devices) which further can be considered as a big data warehouse. This environment is highly scalable and provides important real-time event processing (for example, in critical scenarios like surveillance and monitoring of an industrial plant). In IoT-based critical applications, the real-time data access is obligatory as and when it is required. Such access is possible if we permit only authorized external users to access the real-time data directly from the IoT sensors. Sometimes authorized user may also request for big data query processing and big data analytics over the data stored in cloud servers to figure out hidden patterns of some phenomena (i.e., chances of fire in an industrial plant in future). Therefore, we need secure authentication schemes for cloud-driven IoT-based big data environment in which a legitimate user and an IoT sensor can mutually authenticate each other and establish a common session key for secure communication. In this context, this paper first discusses the network and threat models of the authentication schemes for cloud-driven IoT-based big data environment. Some security requirements, issues and challenges of this environment are then discussed. A taxonomy of various existing authentication schemes applicable for cloud-driven IoT-based big data environment is also discussed, which covers a comparative study of these schemes. We identify and briefly discuss some future research challenges in designing the authentication schemes and other security protocols for cloud-driven IoT-based big data environment that need to be addressed in the future.