### Citations

166 | The hardness of approximate optima in lattices, codes, and systems of linear equations
- Arora, Babai, et al.
- 1997
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Citation Context ...m (NCP) for binary linear codes (see Section 2.4 in [11] by Roth). NCP is to find a codeword c such that wt(y − c) is minimum, given a k × n matrix A over GF (2) and a vector y ∈ GFn(2). Arora et al. =-=[1]-=- have proved that even approximating NCP within any constant factor is NP-hard. In general, NCP is extremely difficult. However under the tree-based structure, we can efficiently solve it. Hiding a me... |

113 |
Introduction to coding theory
- Roth
- 2006
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Citation Context ... such that wt(δ) is minimum. Finding δ with least weight is the well known coset leader problem [9]. It is equivalent to the nearest codeword problem (NCP) for binary linear codes (see Section 2.4 in =-=[11]-=- by Roth). NCP is to find a codeword c such that wt(y − c) is minimum, given a k × n matrix A over GF (2) and a vector y ∈ GFn(2). Arora et al. [1] have proved that even approximating NCP within any c... |

103 | F5-A steganographic algorithm: high capacity despite better steganalysis, in
- Westfeld
- 2001
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Citation Context ...ortion is hard in general. In some special cases, there exist constructive and fast methods. Fridrich et al. [7] utilized LT codes to improve the computational complexity of wet paper codes. Westfeld =-=[12]-=- derived a hash function to efficiently obtain the stego object. Li et al. [10] proposed a scheme called tree based parity check (TBPC) to reduce distortion on a cover object based on a tree structure... |

42 |
Matrix embedding for large payloads
- Fridrich, Soukal
- 2006
(Show Context)
Citation Context ..., which turns out to be very successful. Fridrich et al. [6] proposed a scheme, called the wet paper code, for the situation that some positions in the cover object are invariant. 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. Matrix embedding uses ... |

41 | Writing on wet paper
- Fridrich, Goljan, et al.
- 2005
(Show Context)
Citation Context ...scheme that uses the least number of changes over the tree-based parity check model. Crandall [4] first introduced the idea of matrix embedding, which turns out to be very successful. Fridrich et al. =-=[6]-=- proposed a scheme, called the wet paper code, for the situation that some positions in the cover object are invariant. Fridrich and Soukal [8] discussed the scenario when the relative payload (the ra... |

25 |
Some notes on steganography, Posted on steganography mailing list, http://os.inf.tu-dresden.de/ westfeld/crandall.pdf
- Crandall
- 1998
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Citation Context ...istortion is a crucial issue for steganographic methods. In this paper, we propose an efficient embedding scheme that uses the least number of changes over the tree-based parity check model. Crandall =-=[4]-=- first introduced the idea of matrix embedding, which turns out to be very successful. Fridrich et al. [6] proposed a scheme, called the wet paper code, for the situation that some positions in the co... |

17 |
Covering radius-Survey and recent results
- Cohen, Karpovsky, et al.
- 1985
(Show Context)
Citation Context ...odifications for embedding L bits. The covering radius of the codes used for matrix embedding determines the maximum modifications. For (2q − 1, q) simplex codes, the covering radius is 2q−1 − 1 (see =-=[3]-=- in Appendix B proposed by G. Cohen et al.). The lower embedding efficiency is (2q − 1− q)/(2q−1 − 1) = 2−Θ(logn/n). By Theorem III.2, MPC is equivalent to an (n, L, (L+ 1)/2) linear stego-code. The m... |

17 |
Efficient wet paper codes
- Fridrich, Goljan, et al.
(Show Context)
Citation Context ...s (abbreviated stego-codes). For matrix embedding, finding the stego object with least distortion is hard in general. In some special cases, there exist constructive and fast methods. Fridrich et al. =-=[7]-=- utilized LT codes to improve the computational complexity of wet paper codes. Westfeld [12] derived a hash function to efficiently obtain the stego object. Li et al. [10] proposed a scheme called tre... |

10 | Asymptotic behavior of the ZZW embedding construction
- Fridrich
- 2009
(Show Context)
Citation Context ...ecently, Zhang [14] et al. gave a construction (called the ZZW construction) to generate a family of codes with arbitrary small relative payloads from any code with a large relative payload. Fridrich =-=[5]-=- proved that the embedding efficiency of the family of codes generated by the ZZW construction Copyright (c) 2010 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained f... |

9 |
Maximizing steganographic embedding efficiency by combining Hamming codes and wet paper codes
- Zhang, Zhang, et al.
- 2008
(Show Context)
Citation Context ...ix embedding method, but is more efficient than those based on linear codes. Due to its simplicity, the TBPC method provides very efficient embedding and extraction algorithms. Recently, Zhang et al. =-=[14]-=- proposed a systematic method Copyright (c) 2010 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sen... |

4 | Linear codes for high payload steganography - Khatirinejad, Lisoněk - 2009 |

3 |
Covering codes,” North-Holland
- Cohen, Honkala, et al.
- 1997
(Show Context)
Citation Context ... embedding in the cover object) is relatively large. Matrix embedding uses (n, k) linear codes, which are also called syndrome coding (appears in [9] by Khatirinejad and Lisoněk) or coset encoding ( =-=[2]-=- introduced by G. Cohen et al.). It embeds and extracts a message by using the parity check matrix H of an (n, k) linear code. Zhang and Li [13] generalized the idea of matrix embedding and defined th... |

3 |
S.Y.: “Data hiding with tree based parity check
- Li, Au, et al.
(Show Context)
Citation Context ...fast methods. Fridrich et al. [7] utilized LT codes to improve the computational complexity of wet paper codes. Westfeld [12] derived a hash function to efficiently obtain the stego object. Li et al. =-=[10]-=- proposed a scheme called tree based parity check (TBPC) to reduce distortion on a cover object based on a tree structure. The TBPC method can be formulated as a matrix embedding method, but is more e... |

2 |
A coding problem in steganography,” Designs
- Zhang, Li
- 2008
(Show Context)
Citation Context ...in [9] by Khatirinejad and Lisoněk) or coset encoding ( [2] introduced by G. Cohen et al.). It embeds and extracts a message by using the parity check matrix H of an (n, k) linear code. Zhang and Li =-=[13]-=- generalized the idea of matrix embedding and defined the codes with the matrix H as steganographic codes (abbreviated stego-codes). For matrix embedding, finding the stego object with least distortio... |