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

Improved coefficient recovery and its application for rewritable data embedding

JPEG is the most commonly utilized image coding standard for storage and transmission purposes. It achieves a good rate–distortion trade-off, and it has been adopted by many, if not all, handheld devices. However, often information loss occurs due to transmission error or damage to the storage device. To address this problem, various coefficient recovery methods have been proposed in the past, including a divide-and-conquer approach to speed up the recovery process. However, the segmentation technique considered in the existing method operates with the assumption of a bi-modal distribution for the pixel values, but most images do not satisfy this condition. Therefore, in this work, an adaptive method was employed to perform more accurate segmentation, so that the real potential of the previous coefficient recovery methods can be unleashed. In addition, an improved rewritable adaptive data embedding method is also proposed that exploits the recoverability of coefficients. Discrete cosine transformation (DCT) patches and blocks for data hiding are judiciously selected based on the predetermined precision to control the embedding capacity and image distortion. Our results suggest that the adaptive coefficient recovery method is able to improve on the conventional method up to 27% in terms of CPU time, and it also achieved better image quality with most considered images. Furthermore, the proposed rewritable data embedding method is able to embed 20,146 bits into an image of dimensions 512×512

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 Letter, 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