At present days, exponential growth in the transmission of multimedia data takes place due to a significant rise in network bandwidth and video image compression technologies. However, the transmission of videos over wireless channels often brings an unseen risk that sensitive video details might be corrupted and distributed in an illegal way. So, the security of video transmission has become a hot research topic. Several encryption models have been presented in the literature, yet, it is believed that the performance of encryption process can be further improved. In this perspective, an efficient novel video encryption technique is presented using an enhanced variant of Fully Homomorphic Encryption (FHE) model called as EFHE model. By the hybridization of Ducas and Micciancio (DM) with the FHE model presented by Gentry, Sahai, and Waters (GSW), matrix operations vector additions are properly employed in the proposed EFHE model. In addition, a new key generation scheme to increase the fastness of the encryption process. The EFHE model is designed and placed on a cloud environment which leads to reduced cloud user’s communication and computation complexity. It is ensured that the presented EFHE model is highly efficient and secure over the compared methods.