Ensuring the reliable and secure data transmission in cloud systems is very essential and demanding task in the recent decades. For that purpose, various security frameworks have been deployed in the existing works, which are mainly focusing the improving the privacy and confidentiality of cloud data against the unauthenticated users. Yet, it facing the major problems of inefficient accessing, increased time consumption, computational complexity, storage complexity, and memory utilization rate.Hence, this research work intends to develop an advanced and efficient cryptography model, named as, hash based quadraplet wavelet permuted cryptography (HQWPC) for the secured cloud data storage and retrieval operations. Here, the bilinear mapping and group hash function generation processes are performed to generate the keys used for cryptographic operations. Also, the zig-zag scanning, wavelet coefficients extraction, and permutation processes are accomplished for data encryption. Consequently, the inverse of these operations is performed while decrypting the data. In addition to that, an integrated signature control policy authentication mechanism is employed for validating the authenticity of the cloud data users. This kind of signature verification process could efficiently increase the security level of cloud data. For validating the performance of the proposed security framework, various evaluation metrics have been utilized during analysis. Then, the obtained results are compared with the recent state-of-the-art models for proving the efficiency of the proposed technique over the other techniques.