While cloud-based medical imaging archives offer scalability, remote access, and easy sharing of diagnostic information, the security of these types of sensitive images is difficult for resource-constrained medical devices. This paper introduces a secure and efficient medical image archiving system, called Resource-Constrained Encryption Framework (RCEF), which provides image security and efficiency. This framework covers resource assessment, adaptive encryption configuration, light image encryption, secure key management, integrity check, authenticated transmission, cloud storage and authorized reconstruction. The configuration of the encryption is based on the characteristics of the devices, such as processing power, memory, energy and bandwidth. The framework is tested by means of computed tomography (CT), magnetic resonance imaging (MRI), X-ray and ultrasound pictures and contrasted with traditional encryption methods. The experimental results show the time of encryption and decryption reduced, CPU usage reduced, memory consumed reduced, energy consumption reduced, and higher throughput. The results of security analysis show high entropy of cipher text, low degree of correlation between cipher text pixels, strong differential properties and key sensitivity. The Lossless authorized reconstruction preserves the diagnostically important information, which is appropriate for IoMT device, edge healthcare platform and secure cloud medical archive.