Efficient Homomorphic Encryption for Multi-key Compressed Sensing in Lightweight Cloud-based Image Processing

With the rapid development of cloud storage and privacy computing technologies, users with limited resources are increasingly relying on cloud servers for the storage and computation of their image data. This approach ensures data security and convenient access. However, current image data security sharing schemes that support privacy computing often face issues such as high bandwidth consumption and significant ciphertext expansion, limiting their applicability. To address these challenges, we propose an innovative multi-key compressed sensing lightweight encryption scheme (MCSLE), based on compressed sensing technology. This scheme is the first to design a multi-key conversion algorithm for compressed sensing. It allows each sampling end to independently compress the sampled images using different keys. The cloud platform then completes the key conversion and unification. It provides flexible compression sampling capabilities, a robust privacy protection mechanism, and comprehensive support for homomorphic computing. Furthermore, we have designed a specialized image reconstruction algorithm for this scheme. It has undergone in-depth testing in various practical application scenarios, including medical image analysis, fire monitoring, and handwritten text recognition. The experimental results demonstrate that, unlike existing schemes with several tens of times ciphertext expansion, MCSLE can support homomorphic computation at a compression rate of 0.5 while maintaining high-quality image reconstruction.