Wet Paper Codes With Improved Embedding Efficiency

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.In some applications, steganographic communication may be disrupted by an active warden, modelled here by a compound discrete memoryless channel. The transmitter and warden are subject to distortion constraints. We address the potential loss in communication performance due to the perfect-security requirement. This loss is the same as the loss obtained under a weaker order-1 steganographic requirement that would just require matching of first-order marginals of the covertext and stegotext distributions. Furthermore, no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric; steganographic capacity is then achieved by randomized linear codes. Our framework may also be useful for developing computationally secure steganographic systems that have near-optimal communication performance.

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“…The paper concludes with a February 16, 2007. Revised September 30,2007 DRAFT discussion in Section X.…”

Section: Introductionmentioning

confidence: 92%

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

Wang

Moulin²

2008

IEEE Trans. Inform. Theory

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“…For smaller n t , the number of changes is larger. Figure 4 shows the experimental results obtained for n = n t p = 10 6 and n = 4 · 10 6 elements, ρ = 0.1, and ∆ p = 20 lg p for p ≥ 1, along with the WPCs obtained from [6]. WPCs in Figure 4 were obtained from C t = C MAX and C t = C LDGM and can be realized in practice because the overhead of 20 bits (18 bits to communicate the parameters of W l plus two bits overhead) can be realized by WPCs described in Section 4.…”

Section: Practical Wpcs Obtained From Wet Zzwmentioning

confidence: 99%

“…It is also known [6] that the embedding efficiency of any steganographic scheme that embeds m bits using on average R a embedding changes must satisfy e m/R a ≤ α/H −1 (α), where α m/k is the relative message length (w.r.t. dry elements), H −1 (x) is the inverse of the binary entropy function H(x) = −x lg x − (x−1) lg(x−1) on x ∈ [0, 0.5], and lg is logarithm at the base The work on this paper was supported by Air Force Office of Scientific Research under the research grant number FA9550-08-1-0084.…”

Section: Introductionmentioning

confidence: 99%

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Wet ZZW construction for steganography

Filler

Fridrich

2009

2009 First IEEE International Workshop on Information Forensics and Security (WIFS)

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Wet paper codes are an essential tool for communication with non-shared selection channels. Inspired by the recent ZZW construction for matrix embedding [11], we propose a novel wet paper coding scheme with high embedding efficiency. The performance is analyzed under the assumption that wet cover elements form an i.i.d. Bernoulli sequence. Attention is paid to implementation details to minimize capacity loss in practice.

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“…Special codes, called wet paper codes, were proposed for embedding with wet pixels [4,11] (pixels prohibited to be modified for which I i = {x i }). The recently proposed Syndrome-Trellis Codes (STCs) [7,8] unify the approach, achieve near-optimal performance for various distortion costs ̺ i , and perform well even with a large number of wet pixels.…”

Section: Introductionmentioning

confidence: 99%

Minimizing additive distortion functions with non-binary embedding operation in steganography

Filler

Fridrich

2010

2010 IEEE International Workshop on Information Forensics and Security

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Most practical steganographic algorithms for empirical covers embed messages by minimizing a sum of per-pixel distortions. Current near-optimal codes for this minimization problem [7] are limited to a binary embedding operation. In this paper, we extend this work to embedding operations of larger cardinality. The need for embedding changes of larger amplitude and the merit of this construction are confirmed experimentally by implementing an adaptive embedding algorithm for digital images and comparing its security to other schemes.

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Wet Paper Codes With Improved Embedding Efficiency

Cited by 121 publications

References 13 publications

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

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

Wet ZZW construction for steganography

Minimizing additive distortion functions with non-binary embedding operation in steganography

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