Hybrid encryption techniques are gaining popularity in the cloud platform due to their ability to address security concerns and data storage challenges. In order to ensure confidentiality at every stage of processing, this article presents an innovative strategy that merges fully homomorphic encryption (FHE) and secure hash algorithm 3 (SHA-3), offering robust protection against cyber threats. FHE and SHA-3 offer a solution to this problem. We conducted experiments using different datasets to test the performance and security strength of this hybrid approach. Our method takes into account factors such as computational overheads, complexity requirements, key management challenges, and limited support from vendors/providers offering specialized hardware/software capable of supporting complex mathematical functions required by each technique separately before combined into a hybrid form suitable enough scaled-out horizontally across different nodes within clouds themselves today globally among end-users relying upon them heavily day-to-day tasks involving mission-critical workloads running inside virtualized machines hosted on public/private clouds ecosystems worldwide. The results show that implementing FHE together with SHA-3 can significantly improve an organization's overall cyber security posture when operating critical infrastructure components residing within cloud environments. According to the results, it performs better than other methods that are currently in used complexity of encryption and decoding, including homomorphic encryption and RSA, AES & DSA, and AES & RSA. The hybrid algorithm we are proposed using fully homomorphic & SHA3 with 2048 bits 0.789 seconds of encryption time and decryption time with 0.001 seconds and execution time with 4.25 seconds. Therefore, we conclude that our proposed hybrid encryption technique is the best approach to address cyber security risks associated with storing sensitive data in cloud computing environments.