The purpose of a secure e-learning system based on cloud computing is to allow instructors and students to access their accounts at any time and from anywhere. These types of systems work to ensure that their users (instructors and students) are truly enrolled in the school or institute to prevent unauthorized users from accessing the resources and components of the system. Furthermore, the traditional authentication techniques used in the majority of educational systems suffer from several issues, such as cyber security attacks and weak management of resources. So, some students could be eager to take advantage of such a system's flaw in an effort to cheat. User authentication and end-user monitoring are more difficult in this situation. Multifactor adaptive authentication techniques are used to implement a system with simultaneous authentication. The proposed scheme system offers an effective, affordable, and human intervention-adaptive authentication and monitoring solution for e-learning environments. Additionally, our work can resist cyber security and contains some good metrics like mutual authentication, user anomalies, and others. In this paper, the proposed scheme system uses a two-factor authentication system based on Asymmetric Scalar Product Preserving Encryption (APSE) and fingerprint biometrics for managing and generating a user's account in a secure way. Our work also achieves a good balance between performance and security complexity compared to the state-of-the-art. So, we achieve good results for 1.69 ms for computation and 1280 bits for communication.