The data storage and data processing has been changes in cloud computing, it provides on-demand and scalable resources access. It also raises many security issues, especially with the advance development in the domain of quantum computing. Conventional encryption technologies such as RSA and DES are highly effective against traditional attacks but are becoming progressively exposed to quantum attacks because of the unmatched computational capabilities of quantum machines. To address these challenges, this study explores the defense techniques that must be Robustness against Advanced Cyber Threats through. Here, a low complexity-based technique named as Elliptic Galois Cryptography is developed for data processing and data storage in the Quantum Computing Environment (LEGC-SCDS-QCE). First, the data collection step involves data collection on cloud workload data from Kaggle. The collected data is then pre-processed by the Adaptive Tracking Dual Nested Kalman Filter (ATDNKF) to normalize the data and manage missing values. The data is then pre-processed, after which it is encrypted with Martino Homomorphic Encryption (MHE) to guarantee safe cloud storage and prevent attacks from quantum computing. Lastly, the Quantum Key Distribution (QKD) E91 protocol is used for securing distribute cryptographic keys to be used for encryption. Performance of current suggested LEGC-SCDS-QCE method against current methods such as Real-Time Cryptography Using Quantum Computing Integrated Patterns across Domains (RT-QUIP-CAD), Blockchain and Quantum Cryptography Based Novel Framework for Securing IoT Devices (BQCNF-SIoT) and Enhanced Steganographic Security through Quantum Key Distribution and Classical Cryptography Integration in Multi-layered Systems (ESS-QKD-MLS).