Algebraic Informatics

Author by : Traian Muntean
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 5th International Conference on Algebraic Informatics, CAI 2013, held in Porquerolles, France in September 2013. The 19 revised full papers presented together with 5 invited articles were carefully reviewed and selected from numerous submissions. The papers cover topics such as data models and coding theory; fundamental aspects of cryptography and security; algebraic and stochastic models of computing; logic and program modelling.


Algebraic Curves Over Finite Fields

Author by : Carlos Moreno
Languange : en
Publisher by : Cambridge University Press
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Description : Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.


Algebraic Complexity Theory

Author by : Peter Bürgisser
Languange : en
Publisher by : Springer Science & Business Media
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Description : The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.


Arithmetic Of Finite Fields

Author by : Çetin Kaya Koç
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.


Algebraic Geometry In Coding Theory And Cryptography

Author by : Harald Niederreiter
Languange : en
Publisher by : Princeton University Press
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Description : This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books


Arithmetic Of Finite Fields

Author by : Jean Claude Bajard
Languange : en
Publisher by : Springer Nature
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Description :


Arithmetic Geometry Cryptography And Coding Theory

Author by : Alp Bassa
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.


Sequences And Their Applications

Author by : T. Helleseth
Languange : en
Publisher by : Springer Science & Business Media
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Description : Pseudorandom sequences have widespread applications, for instance, in spread spectrum, code division multiple access, optical and ultrawide band communication systems, as well as in ranging systems global positioning systems, circuit testing and stream ciphers. Such sequences also have strong ties to error-correcting codes. This volume contains survey and research papers on sequences and their applications. It brings together leading experts from discrete mathematics, computer science and communications engineering, and helps to bridge advances in these different areas. Papers in this volume discuss the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation.


Algebraic Informatics

Author by : Miroslav Ćirić
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 8th International Conference on Algebraic Informatics, CAI 2019, held in Niš, Serbia, in June/July 2019. The 20 revised papers presented were carefully reviewed and selected from 35 submissions. The papers present research at the intersection of theoretical computer science, algebra, and related areas. They report original unpublished research and cover a broad range of topics from automata theory and logic, cryptography and coding theory, computer algebra, design theory, natural and quantum computation, and related areas.


Computational And Algorithmic Problems In Finite Fields

Author by : Igor Shparlinski
Languange : en
Publisher by : Springer Science & Business Media
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Description : This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.


Algebraic Curves And Finite Fields

Author by : Harald Niederreiter
Languange : en
Publisher by : Walter de Gruyter GmbH & Co KG
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Description : Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.


Theory And Applications Of Models Of Computation

Author by : Mitsunori Ogihara
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 8th International Conference on Theory and Applications of Models of Computation, TAMC 2011, held in Tokyo, Japan, in May 2011. The 51 revised full papers presented together with the abstracts of 2 invited talks were carefully reviewed and selected from 136 submissions. The papers address the three main themes of the conference which were computability, complexity, and algorithms and are organized in topical sections on general algorithms, approximation, graph algorithms, complexity, optimization, circuit complexity, data structures, logic and formal language theory, games and learning theory, and cryptography and communication complexity.


Finite Fields Theory And Computation

Author by : Igor Shparlinski
Languange : en
Publisher by : Springer Science & Business Media
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Description : This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.


Algebraic Geometric Codes

Author by : M. Tsfasman
Languange : en
Publisher by : Springer Science & Business Media
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Description : 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.


Stacs 2005

Author by : Volker Diekert
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005, held in Stuttgart, Germany in February 2005. The 54 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 217 submissions. A broad variety of topics from theoretical computer science are addressed, in particular complexity theory, algorithmics, computational discrete mathematics, automata theory, combinatorial optimization and approximation, networking and graph theory, computational geometry, grammar systems and formal languages, etc.


Coding Theory And Algebraic Geometry

Author by : Henning Stichtenoth
Languange : en
Publisher by : Springer
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Description : About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.


Progress In Cryptology Indocrypt 2003

Author by : Thomas Johansson
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 4th International Conference on Cryptology in India, INDOCRYPT 2003, held in New Delhi, India in December 2003. The 29 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 101 submissions. The papers are organized in topical sections on stream ciphers, block ciphers, Boolean functions, secret sharing, bilinear pairings, public key cryptography, signature schemes, protocols, elliptic curve cryptography and algebraic geometry, implementation and digital watermarking, and authentication.


Finite Fields And Applications

Author by : Dieter Jungnickel
Languange : en
Publisher by : Springer Science & Business Media
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Description : The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.


Number Theory

Author by : David V. Chudnovsky
Languange : en
Publisher by : Springer Science & Business Media
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Description : New York Number Theory Seminar started its regular meeting in January, 1982. The Seminar has been meeting on a regular basis weekly during the academic year since then. The meeting place of the seminar is in midtown Manhattan at the Graduate School and University Center of the City Uni versity of New York. This central location allows number-theorists in the New York metropolitan area and vistors an easy access. Four volumes of the Seminar proceedings, containing expanded texts of Seminar's lectures had been published in the Springer's Lecture Notes in Mathematics series as volumes 1052 (1984), 1135 (1985), 1240 (1987), and 1383 (1989). Seminar co chairmen are pleased that some of the contributions to the Seminar opened new avenues of research in Number Theory and related areas. On a histori cal note, one of such contributions proved to be a contribution by P. Landweber. In addition to classical and modern Number Theory, this Semi nar encourages Computational Number Theory. This book presents a selection of invited lectures presented at the New York Number Theory Seminar during 1989-1990. These papers cover wide areas of Number Theory, particularly modular functions, Aigebraic and Diophantine Geometry, and Computational Number Theory. The review of C-L. Chai presents a broad view of the moduli of Abelian varieties based on recent work of the author and many other prominent experts. This provides the reader interested in Diophantine Analysis with access to state of the art research. The paper of D. V. and G. V.


Elliptic Curves And Modular Forms In Algebraic Topology

Author by : Peter S. Landweber
Languange : en
Publisher by : Springer
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Description : A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology. The resulting papers range, fom these topics through to quantum field theory, with considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.


Topics In Geometry Coding Theory And Cryptography

Author by : Arnaldo Garcia
Languange : en
Publisher by : Springer Science & Business Media
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Description : The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.


Computer Science

Author by : Ricardo Baeza-Yates
Languange : en
Publisher by : Springer Science & Business Media
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Description : Introduction. Historical Overview. Databases: Office Information Systems Engineering (J. Palazzo, D. Alcoba) Artificial Intelligence, Logic, and Functional Programming: A HyperIcon Interface to a Blackboard System for Planning Research Projects (P. Charlton, C. Burdorf). Algorithms and Data Structures: Classification of Quadratic Algorithms for Multiplying Polynomials of Small Degree Over Finite Fields (A. Averbuch et al.). Object Oriented Systems: A Graphical Interactive Object Oriented Development System (M. Adar et al.). Distributed Systems: Preserving Distributed Data Coherence Us.


Algebraic Geometry Codes Advanced Chapters

Author by : Michael Tsfasman
Languange : en
Publisher by : American Mathematical Soc.
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Description : Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.


Progress In Cryptology Indocrypt 2018

Author by : Debrup Chakraborty
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 19th International Conference on Cryptology in India, INDOCRYPT 2018, held in New Delhi, India, in December 2018. The 20 revised full papers presented in this book were carefully reviewed and selected from 60 submissions. The focus of the conference includes works on outsourced computation and searchable encryption; symmetric key cryptography and format preserving encryption; fault attacks and Hash functions; post quantum cryptography; asymmetric key cryptography and cryptanalysis; symmetric key cryptanalysis; theory; and secure computations and protocols.


Theory Of Cryptography

Author by : Rafael Pass
Languange : en
Publisher by : Springer Nature
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Description : This three-volume set, LNCS 12550, 12551, and 12552, constitutes the refereed proceedings of the 18th International Conference on Theory of Cryptography, TCCC 2020, held in Durham, NC, USA, in November 2020. The total of 71 full papers presented in this three-volume set was carefully reviewed and selected from 167 submissions. Amongst others they cover the following topics: study of known paradigms, approaches, and techniques, directed towards their better understanding and utilization; discovery of new paradigms, approaches and techniques that overcome limitations of the existing ones, formulation and treatment of new cryptographic problems; study of notions of security and relations among them; modeling and analysis of cryptographic algorithms; and study of the complexity assumptions used in cryptography. Due to the Corona pandemic this event was held virtually.


Coding Theory And Cryptography

Author by : David Joyner
Languange : en
Publisher by : Springer Science & Business Media
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Description : These are the proceedings of the Conference on Coding Theory, Cryptography, and Number Theory held at the U. S. Naval Academy during October 25-26, 1998. This book concerns elementary and advanced aspects of coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. Some of these papers are expository, whereas others are the result of original research. The emphasis is on geometric Goppa codes (Shokrollahi, Shokranian-Joyner), but there is also a paper on codes arising from combinatorial constructions (Michael). There are both, historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the work done by the British and their allies during World War II to crack the German and Japanese ciphers (Hamer, Hilton, Tutte, Weierud, Urling). Some mathematical aspects of the Enigma rotor machine (Sherman) and more recent research on quantum cryptography (Lomonoco) are described. There are two papers concerned with the RSA cryptosystem and related number-theoretic issues (Wardlaw, Cosgrave).