Provably Secure Steganography: Achieving Zero K-L Divergence using Statistical Restoration (original) (raw)

Statistical restoration for robust and secure steganography

2005

We investigate data hiding techniques that attempt to defeat steganalysis by restoring the statistics of the composite image to resemble that of the cover. The approach is to reserve a number of host symbols for statistical restoration: host statistics perturbed by data embedding are restored by suitably modifying the symbols from the reserved set. While statistical restoration has broad applicability to a variety of hiding methods, we illustrate our ideas here for quantization index modulation (QIM) based hiding. We propose a method for significantly reducing the detectability of QIM, while preserving its robustness to attacks. We next use the framework of statistical restoration to develop a method to combat steganalysis techniques which detect block-DCT embedding by evaluating the increase in blockiness of the image due to hiding. Numerical results demonstrating the efficacy of these techniques are provided.

Determining Achievable Rates for Secure, Zero Divergence, Steganography

2006

In steganography (the hiding of data into innocuous covers for secret communication) it is difficult to estimate how much data can be hidden while still remaining undetectable. To measure the inherent detectability of steganography, Cachin [1] suggested thesecure measure, where is the Kullback Leibler (K-L) divergence between the cover distribution and the distribution after hiding. At zero divergence, an optimal statistical detector can do no better than guessing; the data is undetectable. The hider's key question then is, what hiding rate can be used while maintaining zero divergence? Though work has been done on the theoretical capacity of steganography, it is often difficult to use these results in practice. We therefore examine the limits of a practical scheme known to allow embedding with zero-divergence. This scheme is independent of the embedding algorithm and therefore can be generically applied to find an achievable secure hiding rate for arbitrary cover distributions.

New results on robustness of secure steganography

2006

abstract Steganographic embedding is generally guided by two performance constraints at the encoder. Firstly, as is typical in the field of watermarking, all the transmission codewords must conform to an average power constraint. Secondly, for the embedding to be statistically undetectable (secure), it is required that the density of the watermarked signal must be equal to the density of the host signal.

Turning Cost-Based Steganography into Model-Based

Proceedings of the 2020 ACM Workshop on Information Hiding and Multimedia Security, 2020

Most modern steganographic schemes embed secrets by minimizing the total expected cost of modifications. However, costs are usually computed using heuristics and cannot be directly linked to statistical detectability. Moreover, as previously shown by Ker at al., cost-based schemes fundamentally minimize the wrong quantity that makes them more vulnerable to knowledgeable adversary aware of the embedding change rates. In this paper, we research the possibility to convert cost-based schemes to model-based ones by postulating that there exists payload size for which the change rates derived from costs coincide with change rates derived from some (not necessarily known) model. This allows us to find the steganographic Fisher information for each pixel (DCT coefficient), and embed other payload sizes by minimizing deflection. This rather simple measure indeed brings sometimes quite significant improvements in security especially with respect to steganalysis aware of the selection channel. Steganographic algorithms in both spatial and JPEG domains are studied with feature-based classifiers as well as CNNs.

Content-Adaptive Steganography by Minimizing Statistical Detectability

—Most current steganographic schemes embed the secret payload by minimizing a heuristically defined distortion. Similarly, their security is evaluated empirically using classifiers equipped with rich image models. In this paper, we pursue an alternative approach based on a locally-estimated multivariate Gaussian cover image model that is sufficiently simple to derive a closed-form expression for the power of the most powerful detector of content-adaptive LSB matching but, at the same time, complex enough to capture the non-stationary character of natural images. We show that when the cover model estimator is properly chosen, state-of-the-art performance can be obtained. The closed-form expression for detectability within the chosen model is used to obtain new fundamental insight regarding the performance limits of empirical steganalysis detectors built as classifiers. In particular, we consider a novel detectability-limited sender and estimate the secure payload of individual images.

Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

IEEE Transactions on Information Theory, 2000

An analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper. Following embedding of the message into the covertext, the resulting stegotext is required to have exactly the same probability distribution as the covertext. Then no statistical test can reliably detect the presence of the hidden message. We refer to such steganographic schemes as perfectly secure. A few such schemes have been proposed in recent literature, but they have vanishing rate. We prove that communication performance can potentially be vastly improved; specifically, our basic setup assumes independently and identically distributed (i.i.d.) covertext, and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code. The permutation is a secret key shared between encoder and decoder. We derive (positive) capacity and random-coding exponents for perfectly-secure steganographic systems. The error exponents provide estimates of the code length required to achieve a target low error probability.

Information-Theoretic Bounds for Steganography in Multimedia

2022

Steganography in multimedia aims to embed secret data into an innocent looking multimedia cover object. This embedding introduces some distortion to the cover object and produces a corresponding stego object. The embedding distortion is measured by a cost function that determines the detection probability of the existence of the embedded secret data. A cost function related to the maximum embedding rate is typically employed to evaluate a steganographic system. In addition, the distribution of multimedia sources follows the Gibbs distribution which is a complex statistical model that restricts analysis. Thus, previous multimedia steganographic approaches either assume a relaxed distribution or presume a proposition on the maximum embedding rate and then try to prove it is correct. Conversely, this paper introduces an analytic approach to determining the maximum embedding rate in multimedia cover objects through a constrained optimization problem concerning the relationship between the maximum embedding rate and the probability of detection by any steganographic detector. The KL-divergence between the distributions for the cover and stego objects is used as the cost function as it upper bounds the performance of the optimal steganographic detector. An equivalence between the Gibbs and correlated-multivariate-quantized-Gaussian distributions is established to solve this optimization problem. The solution provides an analytic form for the maximum embedding rate in terms of the WrightOmega function. Moreover, it is proven that the maximum embedding rate is in agreement with the commonly used Square Root Law (SRL) for steganography, but the solution presented here is more accurate. Finally, the theoretical results obtained are verified experimentally.

Information-Theoretic Limits for Steganography in Multimedia

Steganography in multimedia aims to embed secret data into an innocent multimedia cover object. The embedding introduces some distortion to the cover object and produces a corresponding stego-object. The embedding distortion is measured by a cost function that determines the probability of detection of the existence of secret embedded data. An accurate definition of the cost function and its relation to the maximum embedding rate is the keystone for the proper evaluation of a steganographic system. Additionally, the statistical distribution of multimedia sources follows the Gibbs distribution which is a complex statistical model that prohibits a thorough mathematical analysis.Previous multimedia steganographic approaches either assume a relaxed statistical distribution of multimedia sources or presume a proposition on the maximum embedding rate then try to prove the correctness of the proposition. Alternatively, this paper introduces an analytical procedure for calculating the maxim...

Message Guided Adaptive Random Steganography using Countingout Embedding

International Journal of Computer Applications, 2011

Digital data protection turns out to be the most essential constituent in the cyber world where digital crime is mounting to its worst. To establish secured data communication a technique called Steganography, one of the fruitful attempts for data hiding, has evolved. The rationale of this scheme is to blot out the message in to an innocuous cover media. For good stego system imperceptibility, randomization and capacity are the important considerations. In this paper we propose a novel keyless random algorithm in image steganography which induces an enhanced security by incorporating "counting-out" embedding. It uses message bits embedded in the current pixel which acts as a key for the next pixel to which data is to be embedded. This method provides adaptive randomization without affecting the imperceptibility and capacity.

Secure Steganography for Digital Images

International Journal of Advanced Computer Science and Applications, 2016

The degree of imperceptibility of hidden image in the 'Digital Image Steganography' is mostly defined in relation to the limitation of Human Visual System (HVS), its chances of detection using statistical methods and its capacity to hide maximum information inside its body. Whereas, a tradeoff does exist between data hiding capacity of the cover image and robustness of underlying information hiding scheme. This paper is an exertion to underline the technique to embed information inside the cover at Stego key dependent locations, which are hard to detect, to achieve optimal security. Hence, it is secure under worst case scenario where Wendy is in possession of the original image (cover) agreed upon by Alice and Bob for their secret communication. Reliability of our proposed solution can be appreciated by observing the differences between cover, preprocessed cover and Stego object. Proposed scheme is equally good for color as well as gray scaled images. Another interesting aspect of this research is that it implicitly presents fusion of cover and information to be hidden in it while taking care of passive attacks on it.