Information hiding by coverings

Galand, Fabien; Kabatiansky, Grigory

doi:10.1109/itw.2003.1216717

Cited by 62 publications

(39 citation statements)

References 4 publications

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“…We now briefly review a few relevant known facts about embedding schemes and covering codes that appeared in [1], [5] and establish some more terminology. Let M be the set of all messages.…”

Section: Matrix Embedding In Steganographymentioning

confidence: 99%

“…The matrix embedding theorem is taken from [1], [5] and gives a recipe on how to use an [n, k] code to communicate n − k bits using at most R changes in n pixels.…”

Section: Matrix Embedding In Steganographymentioning

confidence: 99%

“…Matrix embedding was introduced by Crandall [3], analyzed by Bierbrauer [1], and independently discovered by van Dijk et al [8] and Galand et al [5]. It was made popular by Westfeld who incorporated a specific implementation of matrix embedding using binary Hamming codes in his F5 algorithm [9].…”

Section: Introductionmentioning

confidence: 99%

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Matrix embedding for large payloads

2006

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Abstract-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.

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Section: Matrix Embedding In Steganographymentioning

confidence: 99%

“…The matrix embedding theorem is taken from [1], [5] and gives a recipe on how to use an [n, k] code to communicate n − k bits using at most R changes in n pixels.…”

Section: Matrix Embedding In Steganographymentioning

confidence: 99%

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Matrix embedding for large payloads

2006

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“…Crandall for the first time presented a matrix coding technique with improved hiding efficiency [7]. The relation between Stegnographic codes (Stego-codes) and covering codes was studied in [8].…”

Section: Introductionmentioning

confidence: 99%

Implementation of Variable Tone Variable Bits Gray-Scale Image Stegnography Using Discrete Cosine Transform

Khan¹,

Khan²,

Iqbal³

et al. 2013

JSIP

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Secure exchange of information is the basic need of modern digital world of e-communication which is achieved either by encrypting information or by hiding information in other information called cover media. Concealing information requires a well designed technique of Stegnography. This work presents a technique, variable tone variable bits (VTVB) Stegnography, to hide information in a cover image. The VTVB Stegnography hides variable data in discrete cosine transform (DCT) coefficients of the cover image. VTVB Stegnography provides variable data hiding capacity and variable distortion. Additional large data hiding this technique provide extra security due to the large key size making VTVB Stegnography technique much more immune to steganalysis. The hiding makes the existence of information imperceptible for steganalysis and the key of keeping a secret makes the recovering of information difficult for an intruder. The key size is depending on cover image and numbers of bits of discrete cosine transform (DCT) coefficients used for information embedding. This is a very flexible technique and can be used for low payload applications, e.g. watermarking to high payload applications, e.g. network Stegnography.

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“…In this case, the distortion is often measured with the number of embedding changes. The average number of bits embedded per one embedding change is called embedding efficiency and it constitutes an important numerical characteristic of a steganographic scheme.By mapping the individual pixels of the cover to elements of a finite field, for example, by associating a bit (or q-ary symbol from finite field F q ) with each pixel value 1 , one can formulate the problem of maximizing embedding efficiency within the framework of coding theory [3], [8]. In particular, it is known that a q-ary linear code C with length n, dimension k, parity check matrix H, and covering radius R can be used to communicate n − k q-ary symbols (or (n − k) lg q bits) in a cover consisting of n elements by making at most R changes in the following manner.…”

mentioning

confidence: 99%

Asymptotic Behavior of the ZZW Embedding Construction

Fridrich

2009

IEEE Trans.Inform.Forensic Secur.

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Abstract-We analyze asymptotic behavior of the embedding construction for steganography proposed by Zhang, Zhang, and Wang (ZZW) at 10th Information Hiding by deriving a closedform expression for the limit between embedding efficiency of the ZZW construction and the theoretical upper bound as a function of relative payload. This result confirms the experimental observation made in the original publication. I. MOTIVATION AND BACKGROUNDSteganography deals with secret communication by hiding messages in innocuous-looking objects, such as digital images, by slightly modifying the colors of their pixels. The goal is to make the stego images, which carry secret messages, statistically indistinguishable from the original unmodified (cover) images [2]. Statistical detectability of most steganographic schemes increases with embedding distortion (see, e.g., [10]). This is why most stegosystems limit the amplitude of embedding changes to the smallest possible value. In this case, the distortion is often measured with the number of embedding changes. The average number of bits embedded per one embedding change is called embedding efficiency and it constitutes an important numerical characteristic of a steganographic scheme.By mapping the individual pixels of the cover to elements of a finite field, for example, by associating a bit (or q-ary symbol from finite field F q ) with each pixel value 1 , one can formulate the problem of maximizing embedding efficiency within the framework of coding theory [3], [8]. In particular, it is known that a q-ary linear code C with length n, dimension k, parity check matrix H, and covering radius R can be used to communicate n − k q-ary symbols (or (n − k) lg q bits) in a cover consisting of n elements by making at most R changes in the following manner. Let x ∈ F n q be the vector of symbols assigned to n elements of the cover. Then, n − k message symbols, F n−k q , can be embedded in x by modifying the symbols of pixels to y = x + e(m − Hx), where e(s) is a coset leader of the coset corresponding to syndrome s. The recipient can read the message from the stego object as its syndrome, m = Hy, because Hy = Hx + m − Hx. The

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Information hiding by coverings

Cited by 62 publications

References 4 publications

Matrix embedding for large payloads

Matrix embedding for large payloads

Implementation of Variable Tone Variable Bits Gray-Scale Image Stegnography Using Discrete Cosine Transform

Asymptotic Behavior of the ZZW Embedding Construction

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