Cloud Computing (CC) is a solution that efficiently maps cloud tasks to resources, ensuring highperformance utilization in computing. But, the challenge lies in managing attacks while managing a large data flow. For this reason, Lightweight deep learning model to secure authentication (LDLSA) was developed using Deep Convolutional Neural Network (DCNN) and Homomorphic Encryption (HE) is developed for deep face recognition authentication, enhancing privacy protection in CC. However, these models are computationally expensive, require extensive training data and lack information on cloud-stored authentication data for privacy preservation. In this paper, DL with Cloud Authentication (dCAuth) is proposed to resolve the above mentioned issues to provide efficient cloud authentication with lesser complexity. This method employs a spurring algorithm for dwindling DCNN with recall (dDCNNr) to handle the number of parameters in DCNN to handle a large number of parameters for cloud authentication. dDCNNr model reduces execution time and improves classification accuracy, but it necessitates faster training time. To solve this, Fully Connected (FC) layers of DCNN is replaced with Hopfield Neural Network (HNN). The model utilises a DCNN for feature extraction and HNN for pattern recognition highly focusing on authentication, both the process have similar training phase with known patterns by adjusted weights. The proposed authentication method stores encrypted Neural Network (NN) weights in the cloud, eliminating the need for a verification table. The weights for unknown input patterns are generated during pattern recall. The HNN weight matches input indicating a known or legal pattern, aiming to identify a known pattern that best fits the input with minimum processing resources. The proposed authentication model integrates DCNN and HNN to rapidly and precisely recall the legitimate user ID and face image (password) information. The model effectively manages the large training data and parameters, ensuring privacy for cloud-stored authentication data, simultaneously reducing the time duration of registration and password changes (old to new face image). Finally, an extensive simulation reveals that the proposed model achieves accuracy of 94.15%, 94.53% and 94.38% on Georgia Tech face (GTF), Labelled Faces in the Wild (LFW) and Biometric Signature (BS) database respectively.