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Matrix embedding for large payloads

Matrix embedding for large payloads,10.1109/TIFS.2006.879281,IEEE Transactions on Information Forensics and Security,Jessica J. Fridrich,David Soukal

Matrix embedding for large payloads   (Citations: 79)
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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 embed- ding 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. We describe two approaches. The first one is based on simplex codes and codes constructed from them, while the second approach uses random linear codes of small dimension. In Section II, we introduce the terminology and basic concepts of linear codes necessary to explain the embedding methods. In Section III, we briefly describe the principles of matrix embedding and state known bounds on achievable embedding efficiency. Matrix embedding based on simplex codes and random linear codes with small dimension is explained in Section IV. In the same section, the performance is compared to theoretically achievable bounds. Pseudo-codes are used to describe the embedding and extraction algorithms to ease the implementation and make this text self-contained. The paper is concluded in Section V.
Journal: IEEE Transactions on Information Forensics and Security , vol. 1, no. 3, pp. 390-395, 2006
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    • ...Later on, different authors suggested other linear codes, such as Golay [30], BCH [31], random codes of small dimension [32], and nonlinear codes based on the idea of a blockwise direct sum [29]...

    Tomáš Filleret al. Minimizing Additive Distortion in Steganography Using Syndrome-Trellis...

    • ...Fridrich and Soukal [8] discussed the scenario when the relative payload (the ratio of the hidden message length to the number of positions used for embedding in the cover object) is relatively large...
    • ...Fridrich and Soukal [8] proposed two matrix embedding methods based on random linear codes and simplex codes...
    • ...The decoding algorithms for random linear codes and simplex codes in [8] have time complexity and , respectively, where is the code length and is the dimension of the code...
    • ...Fridrich and Soukal [8] simulated embedding for a 1280 1024 image using random codes with block length and , and 14. The experiment run by Fridrich and Soukal [8] was on a Linux system with Pentium IV...
    • ...Fridrich and Soukal [8] simulated embedding for a 1280 1024 image using random codes with block length and , and 14. The experiment run by Fridrich and Soukal [8] was on a Linux system with Pentium IV...
    • ...Fridrich and Soukal [8] also considered the relative payload where is the number of hidden message bits and is the number of positions (e.g., pixels for an image) used for embedding in the cover object...
    • ...method is slightly smaller (within 0.5 when ) than those of Fridrich and Soukal [8]...
    • ...Fig. 4 shows the relation between embedding efficiency and the relative payloads for MPC and the two methods of Fridrich and Soukal [8]...
    • ...Fixed the levelofthetree,givenalarger wecanhidemoremessagebitsandthe relativepayloadislarger.Likethepreviousworksproposedby Fridrich and Soukal [8], our method can be applied to the situation that the relative payload is large...

    Chung-Li Houet al. An Optimal Data Hiding Scheme With Tree-Based Parity Check

    • ...The authors of [11], 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...
    • ...Some of the algorithms mentioned in [3, 4, 6, 11, 15, 18, 21, 23, 24] may have embedding efficiencies that are higher than the algorithm that we propose in this paper, but the utilized capacity of the image should be considered too...

    Masood Omoomiet al. An efficient high payload ±1 data embedding scheme

    • ...In [1], Fridrich et al proposed two approaches for large payloads based on matrix embedding...
    • ...Compared with the methods in [1], the proposed coding method is quite simple...

    Hongmei Liuet al. Minority codes with improved embedding efficiency for large payloads

    • ...could be defined by the covering code [1], [3], and many binary stego-codes have been constructed using structured codes [3]‐[7] or random codes [8], [9]...
    • ...Binary stego-codes based on random linear codes [8] and low-density generator matrix (LDGM) codes [9] can approach the rate-distortion bound of LSB embedding for large embedding rates...
    • ...The efficiency of LSB embedding can be improved with a binary stego-code, and equivalence between stego-codes and covering codes have been shown in [1], [3], [6], and [8]...
    • ...Let be an binary code with an covering radius . We can use to embed bits of messages into the LSBs of gray-scale symbols with at most changes by syndrome coding [6], [8]...
    • ...Similar to (3), (4) can be rewritten as the upper bound of embedding efficiency with respect to a given embedding rate [8]...
    • ...It has beenshown [1], [8] that binary random linear codes can reach the upper bound of embedding efficiency (5) asymptotically with the code length . The drawback of random codes is high computational complexity for encoding...
    • ...However, Fridrich et al. presented an embedding scheme with random linear codes in [8]...
    • ...This implies that SCF can provide embedding efficiency close to the upper bound even for very small embedding rate . One merit of random codes in [8] and [9] is that they can provide a continuous family of stego-codes depending on the embedding rate . Thus, if we generate stego-codes using random codes for all large embedding rates, e.g., , and collect all their SCFs, then we can get a family of near optimal stego-codes for arbitrarily ...
    • ...Usually implementation of stego-codes based on constructed covering codes isverysimple.Forrandomcodes,fastalgorithmswereproposed in [8] and [9]...

    Weiming Zhanget al. Near-optimal codes for information embedding in gray-scale signals

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