Image Statistics Preserving Encrypt-then-Compress Scheme Dedicated for JPEG Compression Standard

Abstract

In this paper, the authors analyze in more details an image encryption scheme, proposed by the authors in their earlier work, which preserves input image statistics and can be used in connection with the JPEG compression standard. The image encryption process takes advantage of fast linear transforms parametrized with private keys and is carried out prior to the compression stage in a way that does not alter those statistical characteristics of the input image that are crucial from the point of view of the subsequent compression. This feature makes the encryption process transparent to the compression stage and enables the JPEG algorithm to maintain its full compression capabilities even though it operates on the encrypted image data. The main advantage of the considered approach is the fact that the JPEG algorithm can be used without any modifications as a part of the encrypt-then-compress image processing framework. The paper includes a detailed mathematical model of the examined scheme allowing for theoretical analysis of the impact of the image encryption step on the effectiveness of the compression process. The combinatorial and statistical analysis of the encryption process is also included and it allows to evaluate its cryptographic strength. In addition, the paper considers several practical use-case scenarios with different characteristics of the compression and encryption stages. The final part of the paper contains the additional results of the experimental studies regarding general effectiveness of the presented scheme. The results show that for a wide range of compression ratios the considered scheme performs comparably to the JPEG algorithm alone, that is, without the encryption stage, in terms of the quality measures of reconstructed images. Moreover, the results of statistical analysis as well as those obtained with generally approved quality measures of image cryptographic systems, prove high strength and efficiency of the scheme’s encryption stage.

Statistical Analysis of the Negative–Positive Transformation in Image Encryption

“…The first term is a constant sum, and the second one corresponds to Equation (7). The simplified result is in Equation (27).…”

“…The demonstration considers the two following NPT cases: X = 1 and X = 0. When X = 1, then px ′ (i) = 255 − k i , and the resulting variance s ′ 2 k is expressed in Equation (31), taking into account the mean from Equation (27).…”

“…In contrast, our work evaluates the NPT effects on the image histogram to analyze its statistical security. Other theoretical analyses in the EtC domain concentrate on preserving image properties for an effective compression process [27]. Differing from these theoretical analyses focused on preserving compatibility, ours is grounded in security considerations.…”

Entropy Measures for Data Analysis II: Theory, Algorithms and Applications

“…The main objective of [4] is to study a special image-encryption scheme introduced in a former paper by the authors. This scheme preserves the input image statistics described by the auto-correlation matrix and can be combined with the JPEG compression standard.…”