Crypto-Compression of Color Images Based on Paillier's Cryptosystem

An increasing amount of multimedia data, including images, is being transmitted over networks and stored in the Cloud. This data requires both compression and security measures. In this paper, we present a new method based on 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 plain and encrypted messages, which by default is greater than 2 bits. Our method is based on an analysis of the random values of the parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex> of the cryptosystem, in order to find encrypted values whose least significant bits (LSB) are equal to 0. Then we exploit this by removing k LSB par block to compress the encrypted image. 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 our method can be applied to color images with large pixel block sizes.