Quantized Gaussian JPEG Steganography and Pool Steganalysis

Abstract

Currently, algorithms for compressed image steganography mainly embed hidden message by minimizing the resulting distortion or statistical detectability. However, as a result of purely heuristic distortion definitions and numerically solvable equations in statistical models, there are no closed-form solutions for JPEG steganography. The absence of closed-form expression to model JPEG steganography is the main limitation on understanding single image and pool steganalysis behavior. In this study, building upon our previously proposed framework for spatial steganography, we develop a statistical framework for JPEG steganography in which the cover and the hidden message are modeled by multivariate Gaussian distribution. Based on this statistical model, we propose a novel quantized Gaussian JPEG steganography that is able to accomplish embedding using any costs defined in spatial or discrete cosine transform (DCT) domain as well as residual variances. We conduct our experiments using a popular database with different compression qualities to determine the effectiveness of the proposed model. The experimental results show that the proposed model improves the security of previous works and outperforms the state-of-the-art JPEG steganography algorithms. Furthermore, we extend the closed-form expression of single image steganalysis error to pool steganalysis for an omniscience optimal detector. We employ the derived expression to approximate the empirical results of pool steganalysis based on the empirical detection error of single image steganalysis. The practical advantage of the approximation is that even though it is derived based on the adopted statistical model, it is accurate regardless of payload, embedding domain, embedding method, and steganalysis feature as long as the pooling strategy is optimal. In addition to approximation of the error, we employ the proposed model to make predictions about the variance behavior of pool steganalysis error. We mathematically show that the variance increases as the pool size increases in small payloads. The same behavior is observed in experimental results which re-validates our analytical model. We conclude that although pooling improves detector’s performance, it makes the detector less stable in low payloads and high pool sizes.