The FFT has been a staple in the field of mathematics and computer science for almost 60 years. And yet, it still endures as an efficient algorithm in a multitude of fields. However, as significant technical advances has been made since its inception the demand on methods constantly get higher and higher, and the FFT is seldom enough to solve the problems of this day and age on its own. So how does the FFT perform on its own with today’s standards? This thesis aims to use the FFT to create two algorithms, an Image Denoising algorithm and a Digital Watermarking algorithm respectively, and analyse the efficacy of the algorithms with today’s standards. The results showed that the FFT on its own competently tackles problems well, however with increased demands on the algorithms, the limitations of the FFT became apparent. This underscores the prevalent trend of integrating the FFT with other specializedmethods, ensuring its continued relevance in an era of continuously advancing technologicaldemands.

In the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and q are primes we use Lehmann's primality test on the commitments. The chapter is based on the paper, "RSA signature schemes with subliminal-free public key" (Tatra Mountains Mathematical Publications 41 (2008)). In chapter 7 a one-time signature scheme using run-length encoding is presented, which in the random oracle model offers security against chosen-message attacks. For parameters of interest, the proposed scheme enables about 33% faster verification with a comparable signature size than a construction of Merkle and Winternitz. The public key size remains unchanged (1 hash value). The main cost for the faster verification is an increase in the time required for signing messages and for key generation. The chapter is based on the paper "A one-time signature using run-length encoding" (Information Processing Letters Vol. 108, Issue 4, (2008)). / by Viktoria Villanyi. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

by Hau-Leung Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 41-42). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Paper I --- p.5 / Chapter 1.2 --- Paper II --- p.6 / Chapter 2 --- The Inexact Newton-Like Method for Inverse Eigen- value Problem --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- The Newton-Like Method --- p.9 / Chapter 2.3 --- The Inexact Newton-Like Method --- p.11 / Chapter 2.4 --- Convergence Analysis --- p.14 / Chapter 2.5 --- Numerical Experiments --- p.22 / Chapter 3 --- A DCT Based Watermarking Scheme for Copyright Protection of Images --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Preliminary --- p.28 / Chapter 3.2.1 --- Gray-level image --- p.28 / Chapter 3.2.2 --- Color image --- p.29 / Chapter 3.2.3 --- The Discrete Cosine transform --- p.30 / Chapter 3.3 --- Watermarking Approaches --- p.31 / Chapter 3.3.1 --- Insertion procedures --- p.31 / Chapter 3.3.2 --- Retrieval procedures --- p.33 / Chapter 3.4 --- Experimental results --- p.34 / Chapter 3.5 --- Other Applications --- p.38 / Chapter 3.5.1 --- Data Hiding --- p.38 / Chapter 3.5.2 --- Authentication --- p.39 / Chapter 3.5.3 --- Fingerprinting --- p.39 / Chapter 3.5.4 --- Copy Control --- p.39 / Chapter 3.6 --- Conclusion --- p.40 / Bibliography --- p.41

With the rapid development of digital multimedia and internet techniques in the last few years, more and more digital images are being distributed to an ever-growing number of people for sharing, studying, or other purposes. Sharing images digitally is fast and cost-efficient thus highly desirable. However, most of those digital products are exposed without any protection. Thus, without authorization, such information can be easily transferred, copied, and tampered with by using digital multimedia editing software. Watermarking is a popular resolution to the strong need of copyright protection of digital multimedia. In the image forensics scenario, a digital watermark can be used as a tool to discriminate whether original content is tampered with or not. It is embedded on digital images as an invisible message and is used to demonstrate the proof by the owner. In this thesis, we propose a novel localized geometric-distortion resilient digital watermarking scheme to embed two invisible messages to images. Our proposed scheme utilizes two complementary watermarking techniques, namely, local circular region (LCR)-based techniques and block discrete cosine transform (DCT)-based techniques, to hide two pseudo-random binary sequences in two kinds of regions and extract these two sequences from their individual embedding regions. To this end, we use the histogram and mean statistically independent of the pixel position to embed one watermark in the LCRs, whose centers are the scale invariant feature transform (SIFT) feature points themselves that are robust against various affine transformations and common image processing attacks. This watermarking technique combines the advantages of SIFT feature point extraction, local histogram computing, and blind watermark embedding and extraction in the spatial domain to resist geometric distortions. We also use Watson’s DCT-based visual model to embed the other watermark in several rich textured 80×80 regions not covered by any embedding LCR. This watermarking technique combines the advantages of Harris feature point extraction, triangle tessellation and matching, the human visual system (HVS), the spread spectrum-based blind watermark embedding and extraction. The proposed technique then uses these combined features in a DCT domain to resist common image processing attacks and to reduce the watermark synchronization problem at the same time. These two techniques complement each other and therefore can resist geometric and common image processing attacks robustly. Our proposed watermarking approach is a robust watermarking technique that is capable of resisting geometric attacks, i.e., affine transformation (rotation, scaling, and translation) attacks and other common image processing (e.g., JPEG compression and filtering operations) attacks. It demonstrates more robustness and better performance as compared with some peer systems in the literature.

Safeguarding creative content in a digital form has become increasingly difficult. It is progressively easier to copy, modify and redistribute digital media, which causes great declines in business profits. For example, the International Federation of the Phonographic Industry estimates that in 2001 the worldwide sales of pirated music CDs were 475 million US dollars. While a large amount of time and money is committed to creating intellectual property, legal means have not proven to be sufficient for the protection of this property. Digital watermarking is a steganographic technique that has been proposed as a possible solution to this problem. A digital watermark hides embedded information about the origin, status, owner and/or destination of the data, often without the knowledge of the viewer or user. This dissertation examines a technique for digital watermarking which utilizes properties of the Discrete Wavelet Transform (DWT). Research has been done in this field, but which wavelet family is superior is not adequately addressed. This dissertation studies the influence of the wavelet family when using a blind, nonvisible watermark in digital media. The digital watermarking algorithm uses a database of multiple images with diverse properties. Various watermarks are embedded. Eight different families of wavelets with dissimilar properties are compared. How effective is each wavelet? To objectively measure the success of the algorithm, the influence of the mother wavelet, the imperceptibility of the embedded watermark and the readability of the extracted watermark, the Peak Signal-to-Noise Ratio and the Image Quality Index for each wavelet family and image are obtained. Two common categories of digital watermarking attacks are removing the watermark and rendering the watermark undetectable. To simulate and examine the effect of attacks on the images, noise is added to the image data. Also, to test the effect of reducing an image in size, each image containing the embedded watermark is compressed. The dissertation asks the questions: “Is the wavelet family chosen to implement the algorithm for a blind, nonvisible watermark in digital images of consequence? If so, which family is superior?” This dissertation conclusively shows that the Haar transform is the best for blind, non-visible digital watermarking.

Digital image watermarking has gained a great interest in the last decade among researchers. Having such a great community which provide a continuously growing list of proposed algorithms, it is rapidly finding solutions to its problems. However, still we are far away from being successful. Therefore, more and more people are entering the field to make the watermarking idea useful and reliable for digital world. Of these various watermarking algorithms, some outperform others in terms of basic watermarking requirements like robustness, invisibility, processing cost, etc. In this thesis, we study the performances of different watermarking algorithms in terms of robustness. Algorithms are chosen to be representatives of different categories such as spatial and transform domain. We evaluate the performance of a selected set of 9 different methods from the watermarking literature against again a selected set of attacks and distortions and try to figure out the properties of the methods that make them vulnerable or invulnerable against these attacks.

The objective of this thesis is to present a robust watermarking algorithm for H.264 and to address challenges in compressed-domain video watermarking. To embed a perceptually invisible watermark in highly compressed H.264 video, we use a human visual model. We extend Watson's human visual model developed for 8x8 DCT block to the 4x4 block used in H.264. In addition, we use P-frames to increase the watermark payload. The challenge in embedding the watermark in P-frames is that the video bit rate can increase significantly. By using the structure of the encoder, we significantly reduce the increase in video bit rate due to watermarking. Our method also exploits both temporal and texture masking. We build a theoretical framework for watermark detection using a likelihood ratio test. This framework is used to develop two different video watermark detection algorithms; one detects the watermark only from watermarked coefficients and one detects the watermark from all the ac coefficients in the video. These algorithms can be used in different video watermark detection applications where the detector knows and does not know the precise location of watermarked coefficients. Both watermark detection schemes obtain video watermark detection with controllable detection performance. Furthermore, control of the detector's performance lies completely with the detector and does not place any burden on the watermark embedding system. Therefore, if the video has been attacked, the detector can maintain the same detection performance by using more frames to obtain its detection response. This is not the case with images, since there is a limited number of coefficients that can be watermarked in each image before the watermark is visible.

In recent years, digital watermarking technique has become the most useful method for protecting the ownership of a user's digital content, and it can be used to verify ownership by embedding a user's digital watermark into that digital content. By showing the watermark, someone can prove legal ownership of the intelligent property on the digital content. Because of the maturity of e-commerce on the Internet, users can purchase digital content through buyer-seller watermarking protocols, and these protocols can help users to embed their watermarks into their digital content. After the transaction is terminated, users can also obtain their own digital content with the desired watermark embedded. However, when users attempt to exchange their digital content with each other over a network, it is important that a secure and efficient method be used. If users directly execute one of the above buyer-seller watermarking protocols, they will find that it cannot achieve significant transfers of digital content. On the other hand, they cannot be guaranteed that the transaction will be fair and efficient. Besides, when users are located on different networks, it is important to understand how they can obtain a protocol that is fair and efficient. To address these problems, we propose efficient and fair digital content exchange protocols for different networks such as Ethernets, P2P networks and cloud networks. Our proposed protocols can achieve identity authentication before performing the digital content exchange protocol, and can also maintain fair transactions between users. Finally, we also provide the formal security proofs for the proposed protocols and properties comparisons with other related schemes. Moreover, our protocols also offer solutions that are suitable for users who are located on different networks, and guarantee that digital content exchange transactions will be performed fairly and efficiently.

The major topic of this dissertation is how to improve the image quality and application of digital watermarking techniques. Most traditional digital watermarking techniques focus on the development and improvement of embedding algorithm. But fewer people really care about the degradation of the image quality of digital watermarking techniques. Meanwhile, the application of digital watermarking technique seems to be limited in the copyright protection. Therefore, the techniques used to improve the image quality and to expand the application of digital watermarking technique are proposed in this dissertation. The concept of the proposed technique used to improve the image quality of digital watermarking technique is different from the concept of traditional watermarking techniques which directly modify the features of image to embed digital watermark. Dissimilarly, the proposed technique uses the relation between the features to embed the digital watermark. In this way, the probability of modifying the feature can be efficiently reduced. Therefore, the image quality of watermarked image can be improved. Besides, the proposed technique works like a pre-process. The proposed technique can be easily applied to present traditional digital watermarking techniques without changing the original embedding and extracting process. The expansion of digital watermarking techniques application consists of two techniques. The first one uses the digital watermarking technique to provide the ¡§Image Refining¡¨ function for digital images. In the proposed technique, the RS (Reed-Solomon) codes of original image are used as a watermark and are embedded in the original image. The watermarking information can provide the error correction capability while the original image is distorted (refining function). If there is some alterations made to the watermarked image and they are within the error correction capability of the RS parities, the alterations will be corrected by the RS decoding to restore the original image. The second one applies the digital watermarking techniques on the Pay-TV system. Conventional key distribution methods used in Pay-TV system emphasize on the method¡¦s refinement in order to reduce the frequency of the keys distributed over network. The proposed method uses the digital watermarking technique to hide the cryptographic keys into routine encrypted video program without any increasing of video program size for the economy of network bandwidth and degradation in perceptual quality. The purpose of this thesis is to improve the practicability of digital watermarking techniques. The proposed techniques could supplement the incompleteness of the traditional digital watermarking techniques with additional functions and applications. In this way, traditional digital watermarking techniques can not only be used for copyright protection but also be the new choice of resolving problem in the future digital environment.

Thèse doctorat : Informatique : Villeurbanne, INSA : 2007. / Thèse rédigée en anglais. Titre provenant de l'écran-titre. Bibliogr. p. 139-147. Publications de l'auteur p. 133-134. Index auteurs.