One of the important steps in steganography is to figure out how to embed a certain amount of message into cover medium (usually image). Different images may have different capacity and on top of that compression must...
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ISBN:
(纸本)9781538655252
One of the important steps in steganography is to figure out how to embed a certain amount of message into cover medium (usually image). Different images may have different capacity and on top of that compression must also be considered. Embedding capacity is highly influenced by image complexity which reflects on quantized DCT histogram. for a lay person, the crucial factor is to know what kind of image is better suited for the amount of message to be hidden. Hence, the research aims at finding a relationship between image genre and steganographic capacity. The result shows that more objects in the image means more message to be hidden.
The famous f5 algorithmfor computing Grobner basis was presented by faugere in 2002. The original version off5 is given in programming codes, so it is a bit difficult to understand. In this paper, the f5 algorithm i...
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The famous f5 algorithmfor computing Grobner basis was presented by faugere in 2002. The original version off5 is given in programming codes, so it is a bit difficult to understand. In this paper, the f5 algorithm is simplified as f5B in a Buchberger＇s style such that it is easy to understand and implement. In order to describe f5B, we introduce f5-reduction, which keeps the signature of labeled polynomials unchanged after reduction. The equivalence between f5 and f5B is also shown. At last, some versions of the f5 algorithm are illustrated.
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Grobner bases taking into account the valuation of K. Because of the use of the valuation, this theory is promising...
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ISBN:
(纸本)9781450334358
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Grobner bases taking into account the valuation of K. Because of the use of the valuation, this theory is promising for stable computations over polynomial rings over a p-adic fields. We design a strategy to compute such tropical Grobner bases by adapting the Matrix-f5 algorithm. Two variants of the Matrix-f5 algorithm, depending on how the Macaulay matrices are built, are available to tropical computation with respective modifications. The former is more numerically stable while the latter is faster. Our study is performed both over any exact field with valuation and some inexact fields like Q(p) or f-q [t]. In the latter case, we track the loss in precision, and show that the numerical stability can compare very favorably to the case of classical Grobner bases when the valuation is non-trivial. Numerical examples are provided.
This paper presents a new framework for computing Grobner bases for ideals and syzygy modules. It is proposed to work in a module that accommodates any given ideal and the corresponding syzygy module (for the given ge...
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This paper presents a new framework for computing Grobner bases for ideals and syzygy modules. It is proposed to work in a module that accommodates any given ideal and the corresponding syzygy module (for the given generators of the ideal). A strong Grobner basis for this module contains Grobner bases for both the ideal and the syzygy module. The main result is a simple characterization of strong Grobner bases. This characterization can detect useless S-polynomials without reductions, thus yields an efficient algorithm. It also explains all the rewritten rules used in f5 and the recent papers in the literature. Rigorous proofs are given for the correctness and finite termination of the algorithm. for any term order for an ideal, one may vary signature orders (i.e. the term orders for the syzygy module). It is shown by computer experiments on benchmark examples that signature orders based on weighted terms are much better than other signature orders. This is useful for practical computation. Also, since computing Gobner bases for syzygies is a main computational task for free resolutions in commutative algebra, the algorithm of this paper should be useful for computing free resolutions in practice.
This paper introduces a new steganographic technique for secret data communication based on Public Key Digital Image steganography by combining public key cryptography with Digital Image Steganography. The proposed sc...
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ISBN:
(纸本)9781479940400
This paper introduces a new steganographic technique for secret data communication based on Public Key Digital Image steganography by combining public key cryptography with Digital Image Steganography. The proposed scheme employs RSA algorithm with 1024 bits key size for secret data encryption before inserting it into cover image and f5 steganographic technique to hide the encrypted message inside the cover image imperceptibly. The f5 algorithm embeds the message into randomly chosen Discrete Courier Transform (DCT) coefficients. By employing matrix embedding which minimizes the changes to be made to the length of certain message, it provides high Steganographic capacity, faster speed and can prevent visual and statistical attacks. The encryption key used in message encryption is big enough to thwart known cryptanalytic attacks. Experiments suggest that the stego image and cover images are perceptually similar. further, the stego images are robust against image processing distortions.
GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than f5. In this paper, the authors generalize GVW algorithm and presen...
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GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than f5. In this paper, the authors generalize GVW algorithm and present an algorithm to compute a Grobner bases for ideal when the coefficient ring is a principal ideal domain. K
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