David Soukal

Quantitative steganalysis of digital images: estimating the secret message length

Abstract.The objective of steganalysis is to detect messages hidden in cover objects, such as digital images. In practice, the steganalyst is frequently interested in more than whether or not a secret message is present. The ultimate goal is to extract and decipher the secret message. However, in the absence of the knowledge of the stego technique and the stego and cipher keys, this task may be extremely time consuming or completely infeasible. Therefore, any additional information, such as the message length or its approximate placement in image features, could prove very valuable to the analyst. In this paper, we present general principles for developing steganalytic methods that can accurately estimate the number of changes to the cover image imposed during embedding. Using those principles, we show how to estimate the secret message length for the most common embedding archetypes, including the F5 and OutGuess algorithms for JPEG, EzStego algorithm with random straddling for palette images, and the classical LSB embedding with random straddling for uncompressed image formats. The paper concludes with an outline of ideas for future research such as estimating the steganographic capacity of embedding algorithms.

Higher-order statistical steganalysis of palette images

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).

Perturbed quantization steganography

In this paper, we use the recently proposed wet paper codes and introduce a new approach to passive-warden steganography called perturbed quantization. In perturbed quantization, the sender hides data while processing the cover object with an information-reducing operation that involves quantization, such as lossy compression, downsampling, or A/D conversion. The unquantized values of the processed cover object are considered as side information to confine the embedding changes to those unquantized elements whose values are close to the middle of quantization intervals. This choice of the selection channel calls for wet paper codes as they enable communication with non-shared selection channel. Heuristic is presented that indicates that the proposed method provides better steganographic security than current JPEG steganographic methods. This claim is further supported by blind steganalysis of a specific case of perturbed quantization for recompressed JPEG images.

On steganographic embedding efficiency

In this paper, we study embedding efficiency, which is an important attribute of steganographic schemes directly influencing their security. It is defined as the expected number of embedded random message bits per one embedding change. Constraining ourselves to embedding realized using linear covering codes (so called matrix embedding), we show that the quantity that determines embedding efficiency is not the covering radius but the average distance to code. We demonstrate that for linear codes of fixed block length and dimension, the highest embedding efficiency (the smallest average distance to code) is not necessarily achieved using codes with the smallest covering radius. Nevertheless, we prove that with increasing code length and fixed rate (i.e., fixed relative message length), the relative average distance to code and the relative covering radius coincide. Finally, we describe several specific examples of q-ary linear codes with q matched to the embedding operation and experimentally demonstrate the improvement in steganographic security when incorporating the coding methods to digital image steganography.

Maximum likelihood estimation of length of secret message embedded using ±k steganography in spatial domain

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.

Searching for the stego-key

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.

Stochastic approach to secret message length estimation in ±k embedding steganography

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.

Efficient wet paper codes

Wet paper codes were proposed as a tool for constructing steganographic schemes with an arbitrary selection channel that is not shared between the sender and the recipient. In this paper, we describe new approaches to wet paper codes that enjoy low computational complexity and improved embedding efficiency (number of message bits per embedding change). Some applications of wet paper codes to steganography and data embedding in binary images are discussed.

Forensic steganalysis: determining the stego key in spatial domain steganography

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.

Matrix embedding for large payloads

Matrix embedding is a previously introduced coding method that is used in steganography to improve the embedding efficiency (increase the number of bits embedded per embedding change). Higher embedding efficiency translates into better steganographic security. This gain is more important for long messages than for shorter ones because longer messages are, in general, easier to detect. In this paper, we present two new approaches to matrix embedding for large payloads suitable for practical steganographic schemes-one based on a family of codes constructed from simplex codes and the second one based on random linear codes of small dimension. The embedding efficiency of the proposed methods is evaluated with respect to theoretically achievable bounds