Comprehensive Analysis of Compressible Perceptual Encryption Methods—Compression and Encryption Perspectives

Abstract

Perceptual encryption (PE) hides the identifiable information of an image in such a way that its intrinsic characteristics remain intact. This recognizable perceptual quality can be used to enable computation in the encryption domain. A class of PE algorithms based on block-level processing has recently gained popularity for their ability to generate JPEG-compressible cipher images. A tradeoff in these methods, however, is between the security efficiency and compression savings due to the chosen block size. Several methods (such as the processing of each color component independently, image representation, and sub-block-level processing) have been proposed to effectively manage this tradeoff. The current study adapts these assorted practices into a uniform framework to provide a fair comparison of their results. Specifically, their compression quality is investigated under various design parameters, such as the choice of colorspace, image representation, chroma subsampling, quantization tables, and block size. Our analyses have shown that at best the PE methods introduce a decrease of 6% and 3% in the JPEG compression performance with and without chroma subsampling, respectively. Additionally, their encryption quality is quantified in terms of several statistical analyses. The simulation results show that block-based PE methods exhibit several favorable properties for the encryption-then-compression schemes. Nonetheless, to avoid any pitfalls, their principal design should be carefully considered in the context of the applications for which we outlined possible future research directions.

Statistical Analysis of the Negative–Positive Transformation in Image Encryption

“…Furthermore, various adaptations and versions based on the NPT have been developed. These proposals often strike a balance between security levels and the efficiency of compression savings [15]. One example is the injected negative-positive transformation (NINPT) [16] designed for compressed sensing.…”

“…On the other hand, a final discrete random variable is proposed, denoted as F, representing the number of color pixels with a value equal to h after the NPT. It is defined in Equation ( 14) and can be replicated for each color c. F = S tot + T tot (14) With this in mind, the expected value of F is given in Equation (15).…”

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy

“…While our proposal increases the encrypted image size by 8% and increases the entropy, during the decryption stage, it is restored to its original dimensions without any loss of data. On the contrary, when employed in formats such as JPEG in lossy compression mode, suboptimal results are frequently observed, characterized by entropy values around 7.90 [27].…”