Fast recovery of unknown coefficients in DCT-transformed images

The advancement of cryptography and cryptanalysis has driven numerous innovations over years. Among them is the treatment of cryptanalysis on selectively encrypted content as a recovery problem. Recent research has shown that linear programming is a powerful tool to recover unknown coefficients in DCT-transformed images. While the time complexity is polynomial, it is still too high for large images so faster methods are still desired. In this paper, we propose a fast hierarchical DCT coefficients recovery method by combining image segmentation and linear programming. In theory the proposed method can reduce the overall time complexity by a linear factor which is the number of image segments used. Our experimental results showed that, for 100 test images of different sizes and using a naive image segmentation method based on Otsu's thresholding algorithm, the proposed method is faster for more than 92% cases and the maximum improvement observed is more than 19 times faster. While being mostly faster, results also showed that the proposed method can roughly maintain the visual quality of recovered images in both objective and subjective terms.