Objective: Preserving the confidentiality of sensitive information is becoming more and more difficult and challenging, considering current scenarios, as a huge amount of multimedia data are stored and communicated over the internet among users and cloud computing environment. The existing cryptography security model for storing images on a cloud platform cannot resist various kinds of modern attacks, such as statistical, differential, brute force, cropping attack, etc., therefore, an improved bit scrambling technique using chaotic maps that can resist various kinds of security attacks is needed. The FEDM cipher image provides less correlation among neighboring pixels and images can be decrypted even under the presence of noise. This study proposed a FEDM model to achieve better UACI, NPCR, histogram, runtime, and processing time performance than the existing image security methods. Methods: Preserving the confidentiality of sensitive information is becoming more and more difficult and challenging considering current scenarios as a huge amount of multimedia data are stored and communicated over the internet among users and cloud computing environment. The existing cryptography security model for storing images on a cloud platform cannot resist various kinds of modern attacks such as statistical, differential, brute force, cropping attack, etc. Results: The overall results show that the proposed FEDM model attains much superior performance considering histogram, UACI, NPCR, and runtime. The FEDM model can resist against SA. The FEDM model attains better performance because IBS is used in each step of CS. Thus, a correlation between adjacent pixels is less and aids superior security performance. Further, the FEDM model attains better UACI and NPCR performance when compared with the exiting image encryption model. Conclusion: The FEDM security method can resist DA, noise, cropping attack, and linear attacks more efficiently due to a larger keyspace. Further, the FEDM takes less time for provisioning security. Along with this, FEDM works smoothly under a cloud computing environment. No prior work has considered runtime performance evaluation under the cloud computing environment. FEDM model will significantly aid in reducing the overall operational cost of a cloud computing environment with a reduction in processing time as cloud charge is based on hours of usage.