Collected results on semigroups, graphs and codes

In this thesis we present a compendium of _ve works where discrete mathematics play a key role. The _rst three works describe di_erent developments and applications of the semigroup theory while the other two have more independent topics. First we present a result on semigroups and code e_ciency, where we introduce our results on the so-called Geil-Matsumoto bound and Lewittes' bound for algebraic geometry codes. Following that, we work on semigroup ideals and their relation with the Feng-Rao numbers; those numbers, in turn, are used to describe the Hamming weights which are used in a broad spectrum of applications, i.e. the wire-tap channel of type II or in the t-resilient functions used in cryptography. The third work presented describes the non-homogeneous patterns for semigroups, explains three di_erent scenarios where these patterns arise and gives some results on their admissibility. The last two works are not as related as the _rst three but still use discrete mathematics. One of them is a work on the applications of coding theory to _ngerprinting, where we give results on the traitor tracing problem and we bound the number of colluders in a colluder set trying to hack a _ngerprinting mark made with a Reed-Solomon code. And _nally in the last work we present our results on scientometrics and graphs, modeling the scienti_c community as a cocitation graph, where nodes represent authors and two nodes are connected if there is a paper citing both authors simultaneously. We use it to present three new indices to evaluate an author's impact in the community

A Concise Bounded Anonymous Broadcast Yielding Combinatorial Trace-and-Revoke Schemes

Broadcast Encryption is a fundamental primitive supporting sending a secure message to any chosen target set of $N$ users. While many efficient constructions are known, understanding the efficiency possible for an ``Anonymous Broadcast Encryption\u27\u27 (ANOBE), i.e., one which can hide the target set itself, is quite open. The best solutions by Barth, Boneh, and Waters (\u2706) and Libert, Paterson, and Quaglia (\u2712) are built on public key encryption (PKE) and their ciphertext sizes are, in fact, $N$ times that of the underlying PKE (rate=$N$). Kiayias and Samary (\u2712), in turn, showed a lower bound showing that such rate is the best possible if $N$ is an independent unbounded parameter. However, when considering certain user set size bounded by a system parameter (e.g., the security parameter), the problem remains interesting. We consider the problem of comparing ANOBE with PKE under the same assumption. We call such schemes Anonymous Broadcast Encryption for Bounded Universe -- AnoBEB. We first present an AnoBEB construction for up to $k$ users from LWE assumption, where $k$ is bounded by the scheme security parameter. The scheme does not grow with the parameter and beat the PKE method. Actually, our scheme is as efficient as the underlying LWE public-key encryption; namely, the rate is, in fact, $1$ and thus optimal. The scheme is achieved easily by an observation about an earlier scheme with a different purpose. More interestingly, we move on to employ the new AnoBEB in other multimedia broadcasting methods and, as a second contribution, we introduce a new approach to construct an efficient ``Trace and Revoke scheme\u27\u27 which combines the functionalites of revocation and of tracing people (called traitors) who in a broadcasting schemes share their keys with the adversary which, in turn, generates a pirate receiver. Note that, as was put forth by Kiayias and Yung (EUROCRYPT \u2702), combinatorial traitor tracing schemes can be constructed by combining a system for small universe, integrated via an outer traceability codes (collusion-secure code or identifying parent property (IPP) code). There were many efficient traitor tracing schemes from traceability codes, but no known scheme supports revocation as well. Our new approach integrates our AnoBEB system with a Robust IPP code, introduced by Barg and Kabatiansky (IEEE IT \u2713). This shows an interesting use for robust IPP in cryptography. The robust IPP codes were only implicitly shown by an existence proof. In order to make our technique concrete, we propose two explicit instantiations of robust IPP codes. Our final construction gives the most efficient trace and revoke scheme in the bounded collusion model

Data Hiding and Its Applications

Data hiding techniques have been widely used to provide copyright protection, data integrity, covert communication, non-repudiation, and authentication, among other applications. In the context of the increased dissemination and distribution of multimedia content over the internet, data hiding methods, such as digital watermarking and steganography, are becoming increasingly relevant in providing multimedia security. The goal of this book is to focus on the improvement of data hiding algorithms and their different applications (both traditional and emerging), bringing together researchers and practitioners from different research fields, including data hiding, signal processing, cryptography, and information theory, among others

John Bale and the National Identity and Church of Tudor England

Although some of John Bale's works seemed disconnected from contemporary events of his time (including his Biblical plays, bibliographic histories, and exegetical works), this dissertation contends that he took a highly active role in seeking to guide and influence England's national and political identity. Bale saw himself as a divinely called messenger to the monarch, to fellow preachers and writers, and to all Britons. King Johan, Bale's most famous play, demonstrated themes common in Bale's work, including the need for Biblical religion, the importance of British political and religious independence, and the leading role of the monarch in advancing these religious and political ideals. Bale depicted the ruler as having the ability to build on England's heritage of historical goodness and bring about its righteous potential. While loyal English clergy and citizens could help to build the Protestant land Bale envisioned, the Catholic Church and its adherents represented the greatest threat to this goal. Bale presented Catholics as treasonous heretics who had undercut England's sovereignty and perverted its proper religion for centuries. The Reformation and Henry VIII's break with Rome made it possible to escape this influence, but Queen Mary's reign--with its return to Catholic religion and reverence for the pope--showed how uncertain England's future could be. To combat these influences, Bale's works supported a national Protestant church, based in scriptural truth and headed by the monarch. Under Henry VIII and Edward VI, Bale sometimes saw his desired governmental and ecclesiastical unity realized, but its most lasting manifestation came during Elizabeth's reign. Bale died early in this period, but his influence continued as Archbishop Matthew Parker and Bishop John Jewel--who each had strong ties to Bale during his life--cooperated with Elizabeth in making Bale's vision a reality. Bale's true importance was thus more politically aligned and more lasting than is often acknowledged

The InfoSec Handbook

Computer scienc

The InfoSec Handbook

Computer scienc

British cinema of the 1950s

This book offers a startling re-evaluation of what has until now been seen as the most critically lacklustre period of the British cinema. Twenty writers contribute essays that rediscover and reassess the productions of the Festival of Britain decade, during which the vitality of wartime film-making flowed into new forms. Topics covered include genres such as the B-film, the war film, the woman's picture, the theatrical adaptation and comedy; also social issues such as censorship and the screen representation of childhood. The book includes fresh assessments of maverick directors such as Pat Jackson, Robert Hamer and Joseph Losey, and even of a maverick critic, Raymond Durgnat. There are also three personal views from people individually implicated in 1950s cinema: Corin Redgrave on Michael Redgrave, Isabel Quigly on film reviewing, and Bryony Dixon of the British Film Institute on film archiving and preservation. In its evocation and coverage of a fascinating time when the national cinema enjoyed an unprecedented popularity amongst home audiences, this volume offers the most exhilarating survey yet of 1950s British film. In its provocative challenge to conventional wisdom about this decade's movies, the book will prove indispensable to students of the cinema at all levels and a stimulating companion for the critic and the historian