On Compression of Encrypted Images
Coding schemes for secure and efficient communication over noiseless public channels traditionally compress and then encrypt the source data. In some cases reversing the ordering of compression and encryption would be useful, e.g., in enabling the efficient distribution of protected media content. Indeed, not only is it possible to reverse the order, but under some conditions neither security nor compression efficiency need be sacrificed. In earlier work on this problem we have assumed that the source data is either memoryless or has a 1-D Markov structure. Such models are poor matches for the 2-D structure of images. In this work, we use a 2-D source model, and develop a scheme to compress encrypted images based on LDPC codes. We present practical simulation results for compressing bi-level images. In tests, we are able to compress an encrypted 10, 000 bit bi-level image to 4, 299 bits and successfully recover the image exactly. In previous works, the best analogous 1-D model (operating on a raster scanned data sequence of the same source) could only compress the image to 7, 710 bits.