Reducing the ciphertext expansion in image homomorphic encryption via linear interpolation technique

Homomorphic encryption becomes one of the key components in many emerging applications, e.g., cloud computing, to achieve privacy-preserving data processing. However, one of the major drawbacks that precludes the widespread adoption of homomorphic encryption is the huge expansion of the ciphertext. This problem becomes even more severe when multimedia data (images/videos) are handled, as these files are essentially of large sizes. This work addresses this challenging issue and proposes a strategy of reducing the ciphertext expansion in image homomorphic encryption. To this end, a randomly selected subset of the pixels are encrypted using homomorphic cryptosystem to form one part of the ciphertext. The remaining pixels are encrypted by relating them with this random subset through a linear interpolation technique. The whole homomorphically encrypted image can be obtained, upon receiving all the ciphertexts, by exploiting the homomorphic property and the linearity. It is demonstrated that the proposed scheme is secure, and is capable of achieving significant reduction of the ciphertext expansion, while perfectly preserving the homomorphic property.