Application of Lowner-John Ellipsoid in the Steganography of Lattice Vectors and a Review of The Gentry's FHE
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paper_title: Information Hiding Techniques for Steganography and Digital Watermarking

paper_content:

From the Publisher: ::: Steganography, a means by which two or more parties may communicate using "invisible" or "subliminal" communication, and watermarking, a means of hiding copyright data in images, are becoming necessary components of commercial multimedia applications that are subject to illegal use. This new book is the first comprehensive survey of steganography and watermarking and their application to modern communications and multimedia. ::: ::: Handbook of Information Hiding: Steganography and Watermarking helps you understand steganography, the history of this previously neglected element of cryptography, the hurdles of international law on strong cryptographic techniques, a description of possible applications, and a survey of the methods you can use to hide information in modern media. Included in this discussion is an overview of "steganalysis," methods which can be used to break steganographic communication. ::: ::: This comprehensive resource also includes an introduction to and survey of watermarking methods, and discusses this method's similarities and differences to steganography. You gain a working knowledge of watermarking's pros and cons, and you learn the legal implications of watermarking and copyright issues on the Internet.
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paper_title: Steganography An Art of Hiding Data

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In today's world the art of sending & displaying the hidden information especially in public places, has received more attention and faced many challenges. Therefore, different methods have been proposed so far for hiding information in different cover media. In this paper a method for hiding of information on the billboard display is presented. It is well known that encryption provides secure channels for communicating entities. However, due to lack of covertness on these channels, an eavesdropper can identify encrypted streams through statistical tests and capture them for further cryptanalysis. In this paper we propose a new form of steganography, on-line hiding of information on the output screens of the instrument. This method can be used for announcing a secret message in public place. It can be extended to other means such as electronic advertising board around sports stadium, railway station or airport. This method of steganography is very similar to image steganography and video steganography. Private marking system using symmetric key steganography technique and LSB technique is used here for hiding the secret information.
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paper_title: Public-Key Steganography

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Informally, a public-key steganography protocol allows two parties, who have never met or exchanged a secret, to send hidden messages over a public channel so that an adversary cannot even detect that these hidden messages are being sent. Unlike previous settings in which provable security has been applied to steganography, public-key steganography is information-theoretically impossible. In this work we introduce computational security conditions for public-key steganography similar to those introduced by Hopper, Langford and von Ahn [7] for the private-key setting. We also give the first protocols for public-key steganography and steganographic key exchange that are provably secure under standard cryptographic assumptions. Additionally, in the random oracle model, we present a protocol that is secure against adversaries that have access to a decoding oracle (a steganographic analogue of Rackoff and Simon’s attacker-specific adaptive chosen-ciphertext adversaries from CRYPTO 91 [10]).
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paper_title: On Khachiyan’s Algorithm for the Computation of Minimum Volume Enclosing Ellipsoids

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Given A@?{a^1,...,a^m}@?R^d whose affine hull is R^d, we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum-volume enclosing ellipsoid of A. In the case of centrally symmetric sets, we first establish that Khachiyan's barycentric coordinate descent (BCD) method is exactly the polar of the deepest cut ellipsoid method using two-sided symmetric cuts. This observation gives further insight into the efficient implementation of the BCD method. We then propose a variant algorithm which computes an approximate rounding of the convex hull of A, and which can also be used to compute an approximation to the minimum-volume enclosing ellipsoid of A. Our algorithm is a modification of the algorithm of Kumar and Yildirim, which combines Khachiyan's BCD method with a simple initialization scheme to achieve a slightly improved polynomial complexity result, and which returns a small ''core set.'' We establish that our algorithm computes an approximate solution to the dual optimization formulation of the minimum-volume enclosing ellipsoid problem that satisfies a more complete set of approximate optimality conditions than either of the two previous algorithms. Furthermore, this added benefit is achieved without any increase in the improved asymptotic complexity bound of the algorithm of Kumar and Yildirim or any increase in the bound on the size of the computed core set. In addition, the ''dropping idea'' used in our algorithm has the potential of computing smaller core sets in practice. We also discuss several possible variants of this dropping technique.
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paper_title: Extracting Spread-Spectrum Hidden Data From Digital Media

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We consider the problem of extracting blindly data embedded over a wide band in a spectrum (transform) domain of a digital medium (image, audio, video). We develop a novel multicarrier/signature iterative generalized least-squares (M-IGLS) core procedure to seek unknown data hidden in hosts via multicarrier spread-spectrum embedding. Neither the original host nor the embedding carriers are assumed available. Experimental studies on images show that the developed algorithm can achieve recovery probability of error close to what may be attained with known embedding carriers and host autocorrelation matrix.
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paper_title: Spread spectrum image steganography

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We present a new method of digital steganography, entitled spread spectrum image steganography (SSIS). Steganography, which means "covered writing" in Greek, is the science of communicating in a hidden manner. Following a discussion of steganographic communication theory and review of existing techniques, the new method, SSIS, is introduced. This system hides and recovers a message of substantial length within digital imagery while maintaining the original image size and dynamic range. The hidden message can be recovered using appropriate keys without any knowledge of the original image. Image restoration, error-control coding, and techniques similar to spread spectrum are described, and the performance of the system is illustrated. A message embedded by this method can be in the form of text, imagery, or any other digital signal. Applications for such a data-hiding scheme include in-band captioning, covert communication, image tamperproofing, authentication, embedded control, and revision tracking.
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paper_title: Detection of LSB Steganography via Sample Pair Analysis

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This paper introduces a new, principled approach to detecting LSB steganography in digital signals such as images and audio. It is shown that the length of hidden message embedded in the least significant bits of signal samples can be estimated with relatively high precision. The new steganalytic approach is based on some statistical measures of sample pairs that are highly sensitive to LSB embedding operations. The resulting detection algorithm is simple and fast. To evaluate the robustness of the proposed steganalytic approach, bounds on estimation errors are developed. Furthermore, the vulnerability of the new approach to possible attacks is also assessed, and counter measures are suggested.
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Title: Application of Lowner-John Ellipsoid in the Steganography of Lattice Vectors and a Review of The Gentry's FHE

Section 1: Introduction
Description 1: Provide the background and motivation for using Lowner-John Ellipsoid in steganography, and describe the significance of Gentry's Fully Homomorphic Encryption (FHE).

Section 2: Description of the Gentry's scheme for fully homomorphic encryption
Description 2: Explain the fundamentals of Gentry's scheme for Fully Homomorphic Encryption (FHE), and introduce the methodology of bootstrapping for extending somewhat homomorphic encryption.

Section 3: Lattice data steganography
Description 3: Detail the proposed method of data steganography based on Edges Based data Embedding (EBE) method, including the theoretical foundation and the use of convex polyhedrons.

Section 4: Extraction Algorithm
Description 4: Describe the approximate extraction algorithm for the steganography plan when using convex polyhedrons, and explain the application of the Khachiyan-Todd ellipsoid finding algorithm.

Section 5: Note 2
Description 5: Compare the proposed method with other spatial steganography methods, such as spread spectrum steganography and LSB steganography, and discuss the relative security and complexity.

Section 6: Conclusion
Description 6: Summarize the findings of the paper, the importance of the Lowner-John's ellipsoid in steganography, and provide suggestions for future work.