1、 1 外文资料 Digital image steganography using stochastic modulation Jessica Fridrichand Miroslav Goljan Department of Electrical and Computer Engineering, SUNY Binghamton, Binghamton, NY 13902-6000, USA ABSTRACT In this paper, we present a new steganographic paradigm for digital images in raster formats
2、. Message bits areembedded in the cover image by adding a weak noise signal with a specified but arbitrary probabilistic distribution.This embedding mechanism provides the user with the flexibility to mask the embedding distortion as noisegenerated by a particular image acquisition device. This type
3、 of embedding will lead to more secure schemesbecause now the attacker must distinguish statistical anomalies that might be created by the embedding process fromthose introduced during the image acquisition itself. Unlike previously proposed schemes, this new approach, thatwe call stochastic modulat
4、ion, achieves oblivious data transfer without using noise extraction algorithms or errorcorrection. This leads to higher capacity (up to 0.8 bits per pixel) and a convenient and simple implementation withlow embedding and extraction complexity. But most importantly, because the embedding noise can h
5、ave arbitraryproperties that approximate a given device noise, the new method offers better security than existing methods. At theend of this paper, we extend stochastic modulation to a content-dependent device noise and we also discuss possibleattacks on this scheme based on the most recent advance
6、s in steganalysis. Keywords: Steganography, steganalysis, stochastic modulation, device noise 1. INTRODUCTION The purpose of steganography is to hide the very presence of communication by embedding messages into innocuous-looking cover objects, such as digital images. To accommodate a secret message
7、, the original cover image is slightly modified by the embedding algorithm to obtain the stego image. The embedding process usually incorporates a secret stego-key that governs the embedding process and it is also needed for the extraction of the hidden message. In contrast to watermarking when the
8、embedded message has a close relationship 2 to the cover image supplying data,such as sender or receiver information, authentications codes, etc., in steganography, the cover image is a mere decoy and has no relationship to the hidden data. The most important requirement for a steganographic system
9、is undetectability: stego images should be statistically indistinguishable from cover images. In other words, there should be no artifacts in the stego image that could be detected by an attacker with probability better than random guessing, given the full knowledge of the embedding algorithm except
10、 for the stego-key (Kerckhoffs principle). The early steganographic schemes focused on introducing as little distortion in the cover image as possible utilizing the seemingly intuitive heuristics that the smaller the embedding distortion is, the more secure the steganographic scheme becomes. However
11、, recent advances in steganalysis clearly showed that this is not the case. The Least Significant Bit embedding (LSB) with sequential or random message spread has been successfully attacked even for very short messages2,3,11. In essence, the LSB embedding is so easily detectable because it introduce
12、s distortion that never naturally occurs to images and creates an imbalance between appropriately defined statistical quantities. A better approach is to replace the operation of flipping the LSBs by randomly adding 1 or 1 to pixels (+1 embedding) and extracting the message bits from LSBs as in the
13、classical LSB embedding. This is the embedding algorithm of Hide8 and it has also been accepted (in a slightly different version) for steganography in the JPEG format10. It turns out that this simple modification of the LSB embedding paradigm is, in fact, much more difficult to detect4,11. The +1 em
14、bedding is a special case of our stochastic modulation when the noise added to the cover image has the following probability distribution P: P( = 1) = p/2, P( = 1) = p/2, P( = 0) = 1p (assuming the message is a random bit-stream and 100p % of pixels were used for embedding). Notice that in +1 embedd
15、ing, the message bits are still encoded and extracted as LSBs of pixels. In this paper, we show how to extend this embedding archetype to a noise with an arbitrary probabilistic distribution P defined on an arbitrary set of integers. The algorithm that achieves this is called stochastic modulation.
16、The embedding party (Alice) can use stochastic modulation, for example, in the following way. Alice will carry out experiments on her source of cover images and estimate the properties of the noise present in them. If Alices acquisition device is a digital camera, the noise depends on the exposition
17、 time, the amount and type of 3 ambient light at the scene, usage of a flash, the specific CCD sensor and camera circuitry, interpolation algorithms in cameras hardware, etc. The sensor and hardware noise are known to be well modeled by an i.i.d. Gaussian noise5. Because there is in general a great
18、variation in the amount of noise in the images due to the multitude of contributing effects mentioned above, one could slightly increase the amount of noise without introducing any easily detectable statistical artifacts. This idea is at the base of our stochastic modulation presented in this paper.
19、 Determining the actual security of stochastic modulation, however, is not an easy task due to the fact that we are adding a quantized noise to an already quantized (and processed) signal rather than at the point of acquisition when the light hits the CCD sensor. This issue is also discussed in the
20、paper. Before we close this introduction, we note that, similar to stochastic modulation, DSSS (Direct Sequence Spread Spectrum) embedding, that is widely used for robust watermarking, also superimposes message-modulated noise on the image. However, DSSS cannot be simply turned into a high-capacity
21、non-robust embedding needed for steganography due to the correlation-based message extraction. The paper is organized as follows. In the next section, we give a brief overview of related methods proposed in the past. Then, in Section 3, we describe the main ideas behind stochastic modulation and in
22、Section 4 we discuss some important implementation issues that need to be considered to establish practical communication. In Section 5, we investigate the security of the proposed algorithm from the point of view of recent advances in steganalysis. Stochastic modulation is extended to a content-dep
23、endent noise in Section 6. Finally, in Section 7 we conclude the paper and outline possible future research directions. 2. RELATED METHODS In the past, several researchers attempted to design steganographic schemes that embed messages by addingGaussian noise to the image. Marvel et al.7 describe a h
24、igh-capacity method for embedding message bits inuncompressed raw image formats. A special non-linear transformation together with the message bits is used togenerate a Gaussian signal that is added to the cover image. The purpose of the transformation is to maximize theseparation between two samples of a random Gaussian variable that encode a 0 and a 1. The message detector firstapplies an adaptive Wiener filter to the image to estimate the noise component. The noise
