How to reduce the size expansion of an encrypted image, based on the Paillier's cryptosystem?

More and more data, especially multimedia data, such as images, is transmitted over networks and archived in clouds. This data needs to be compressed and secured. In this paper, we propose an adaptation of Paillier's cryptosystem applied to images in order to perform homomorphic encryption, and compress them without loss of information. This allows us to reduce the size expansion between clear and encrypted messages, which by default is greater than 2 bits. To achieve this, in our method we propose to analyze the random values of the parameter r of the cryptosystem, in order to find encrypted values whose LSB are equal to 0. Then we are able to exploit this by removing the LSB in order to compress the encrypted image, as pixel values can be encoded on a smaller number of bits. This method is fully reversible, as we just need to add the previously removed LSB during the decryption phase, thus recovering the original image without any loss to quality. Experimental results show that it is possible to apply our method with large pixel block sizes, and therefore with public and private keys of up to 2048 bits.