Cloud computing has gained rapid growth in the development of different fields of science and engineering. However, due to the distributed nature of cloud computing, session key generation and establishment is the pressing issue. Session key management plays the utmost important role in the secure exchange of sensitive login credentials and transaction information. Moreover, conventional session key management mechanisms are inadequate and cannot be directly adopted in cloud-based environments. Hence, session key management is very much solely needed solution for reliable cloud-based service provisioning. In mutual authentication, bi-linear key pairing cryptosystem plays a critical role to generate and establish a session key. The existing mutual authentication schemes fail to support true mutual authentication in cloud-based environments as they are vulnerable to secret key leakage, perfect forward secrecy, and untraceability. To mitigate the effect of these attacks, this research develops an efficient multi-linear key pairing cryptosystem. In this cryptosystem, challenge-response messages are used for generating and establishing a one-time shared session key. Furthermore, the performance analysis of the proposed cryptosystem depicts a significant reduction of computation cost, authentication accuracy rates, and resistance to the aforementioned attacks.