Matrix embedding is a general coding method that can be applied to most steganographic schemes to improve their embedding efficiency-the number of message bits embedded per one embedding change. Because smaller number of embedding changes is less likely to disrupt statistic properties of the cover object, schemes that employ matrix embedding generally have better steganographic security. This gain is more important for long messages than for shorter ones because longer messages are easier to detect. Previously introduced approaches to matrix embedding based on Hamming codes are, however, not efficient for long messages. In this paper, we present novel matrix embedding schemes that are effcient for embedding messages close to the embedding capacity. One is based on a family of codes constructed from simplex codes and the second one on random linear codes of small dimension. The embedding effciency of the proposed methods is evaluated with respect to theoretically achievable bounds.
Construction of steganographic schemes in which the sender and the receiver do not share the knowledge about the location of embedding changes requires wet paper codes. Steganography with non-shared selection channels empowers the sender as now he is able to embed secret data by utilizing arbitrary side information, including a high-resolution version of the cover object (perturbed quantization steganography), local properties of the cover (adaptive steganography), and even pure randomness, e.g., coin flipping, for public key steganography. In this paper, we propose a new approach to wet paper codes using random linear codes of small codimension that at the same time improves the embedding efficiency-the number of message bits embedded per embedding change. We describe a practical algorithm, test its performance experimentally, and compare the results to theoretically achievable bounds. We point out an interesting ripple phenomenon that should be taken into account by practitioners. The proposed coding method can be modularly combined with most steganographic schemes to allow them to use non-shared selection channels and, at the same time, improve their security by decreasing the number of embedding changes.
In this paper, we show that the communication channel known as writing in memory with defective cells is a relevant information-theoretical model for a specific case of passive warden steganography when the sender embeds a secret message into a subset C of the cover object X without sharing the selection channel C with the recipient. The set C could be arbitrary, determined by the sender from the cover object using a deterministic, pseudo-random, or a truly random process. We call this steganography “writing on wet paper” and realize it using low-density random linear codes with the encoding step based on the LT process. The importance of writing on wet paper for covert communication is discussed within the context of adaptive steganography and perturbed quantization steganography. Heuristic arguments supported by tests using blind steganalysis indicate that the wet paper steganography provides improved steganographic security for embedding in JPEG images and is less vulnerable to attacks when compared to existing methods with shared selection channels.
In this paper, we propose a new method for estimating the number of embedding changes for non-adaptive ±K embedding in images. The method uses a high-pass FIR filter and then recovers an approximate message length using a Maximum Likelihood Estimator on those stego image segments where the filtered samples can be modeled using a stationary Generalized Gaussian random process. It is shown that for images with a low noise level, such as decompressed JPEG images, this method can accurately estimate the number of embedding changes even for K=1 and for embedding rates as low as 0.2 bits per pixel. Although for raw, never compressed images the message length estimate is less accurate, when used as a scalar parameter for a classifier detecting the presence of ±K steganography, the proposed method gave us relatively reliable results for embedding rates as low as 0.5 bits per pixel.
In this paper, we propose a new method for estimation of the number of embedding changes for non-adaptive ±k embedding in images. By modeling the cover image and the stego noise as additive mixture of random processes, the stego message is estimated from the stego image using a denoising filter in the wavelet domain. The stego message estimate is further analyzed using ML/MAP estimators to identify the pixels that were modified during embedding. For non-adaptive ±k embedding, the density of embedding changes is estimated from selected segments of the stego image. It is shown that for images with a low level of noise (e.g., for decompressed JPEG images) this approach can detect and estimate the number of embedding changes even for small values of k, such as k=2, and in some cases even for k=1.
This paper is an extension of our work on stego key search for JPEG images published at EI SPIE in 2004. We provide a more general theoretical description of the methodology, apply our approach to the spatial domain, and add a method that determines the stego key from multiple images. We show that in the spatial domain the stego key search can be made significantly more efficient by working with the noise component of the image obtained using a denoising filter. The technique is tested on the LSB embedding paradigm and on a special case of embedding by noise adding (the ±1 embedding). The stego key search can be performed for a wide class of steganographic techniques even for sizes of secret message well below those detectable using known methods. The proposed strategy may prove useful to forensic analysts and law enforcement.
Steganalysis in the wide sense consists of first identifying suspicious objects and then further analysis during which
we try to identify the steganographic scheme used for embedding, recover the stego key, and finally extract the
hidden message. In this paper, we present a methodology for identifying the stego key in key-dependent
steganographic schemes. Previous approaches for stego key search were exhaustive searches looking for some
recognizable structure (e.g., header) in the extracted bit-stream. However, if the message is encrypted, the search
will become much more expensive because for each stego key, all possible encryption keys would have to be tested.
In this paper, we show that for a very wide range of steganographic schemes, the complexity of the stego key search
is determined only by the size of the stego key space and is independent of the encryption algorithm. The correct
stego key can be determined through an exhaustive stego key search by quantifying statistical properties of samples
along portions of the embedding path. The correct stego key is then identified by an outlier sample distribution.
Although the search methodology is applicable to virtually all steganographic schemes, in this paper we focus on
JPEG steganography. Search techniques for spatial steganographic techniques are treated in our upcoming paper.
In this paper, we describe a new higher-order steganalytic method called Pairs Analysis for detection of secret messages embedded in digital images. Although the approach is in principle applicable to many different steganographic methods as well as image formats, it is ideally suited to 8-bit images, such as GIF images, where message bits are embedded in LSBs of indices to an ordered palette. The EzStego algorithm with random message spread and optimized palette order is used as an embedding archetype on which we demonstrate Pairs Analysis and compare its performance with the chi-square attacks and our previously proposed RS steganalysis. Pairs Analysis enables more reliable and accurate message detection than previous methods. The method was tested on databases of GIF images of natural scenes, cartoons, and computer-generated images. The experiments indicate that the relative steganographic capacity of the EzStego algorithm with random message spread is less than 10% of the total image capacity (0.1 bits per pixel).
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