Cloud computing has gained attention in recent years, and it is now used to support many aspects of human life. The amount of data transmitted via the internet is getting bigger and bigger every day. The increasing volume of essential data focuses on securing the stored data in cloud service providers' remote servers. The primary security obstacle in cloud computing is that the users can not directly control the remotely-stored data. Confidentiality is the most crucial problem in the cloud computing environment. Security has the most pressing concern in the cloud computing environment, and encryption plays a vital role in securing data. The existing methods encrypt the stored data using standard encryption algorithms without achieving the desired confidentiality level. Both symmetric and asymmetric encryption algorithms have some drawbacks. This paper proposes two-hybrid algorithms to overcome these drawbacks and ensure data confidentiality. The first is a hybrid between the Blowfish (symmetric) and Fully Homomorphic Encryption (FHE) symmetric algorithm. However, the second hybrid is the FastRSA (asymmetric) and the FHE symmetric algorithm. By comparing our proposed algorithms with other cryptographic methods, they have less encryption time than AES and Blowfish algorithms. A comparison is performed based on encryption time, throughput, and power consumption parameters. Compared with other encryption algorithms, the proposed method proved superior in processing time efficiency.