Arithmetic Of Finite Fields

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Arithmetic Of Finite Fields

Author : Çetin Kaya Koç
ISBN : 9783319162775
Genre : Computers
File Size : 75.53 MB
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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.
Category: Computers

Arithmetic Of Finite Fields

Author : Charles Small
ISBN : 0824785266
Genre : Mathematics
File Size : 75.26 MB
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Text for a one-semester course at the advanced undergraduate/beginning graduate level, or reference for algebraists and mathematicians interested in algebra, algebraic geometry, and number theory, examines counting or estimating numbers of solutions of equations in finite fields concentrating on top
Category: Mathematics

Arithmetic Of Finite Fields

Author : Claude Carlet
ISBN : 9783540730736
Genre : Computers
File Size : 58.90 MB
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This book constitutes the refereed proceedings of the First International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, held in Madrid, Spain in June 2007. It covers structures in finite fields, efficient implementation and architectures, efficient finite field arithmetic, classification and construction of mappings over finite fields, curve algebra, cryptography, codes, and discrete structures.
Category: Computers

Arithmetic Of Finite Fields

Author : M. Anwar Hasan
ISBN : 9783642137969
Genre : Computers
File Size : 36.71 MB
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The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the R&D community, with numerous individuals, as well as with prestigious organizations and societies, LNCS has grown into the most comprehensive computer science research forum available. The scope of LNCS, including its subseries LNAI and LNBI, spans the whole range of computer science and information technology including interdisciplinary topics in a variety of application fields. In parallel to the printed book, each new volume is published electronically in LNCS Online.
Category: Computers

Arithmetic Of Finite Fields

Author : Joachim von zur Gathen
ISBN : 9783540694984
Genre : Computers
File Size : 77.14 MB
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These are the proceedings of WAIFI 2008, the second workshop on the Ari- metic of Finite Fields, that was held in Siena, Italy, July 6-9, 2008. The ?rst workshop, WAIFI 2007, which was held in Madrid (Spain), was received quite enthusiasticallybymathematicians, computerscientists, engineersandphysicists who are performing research on ?nite ?eld arithmetic. We believe that there is a need for a workshop series bridging the gap between the mathematical theory of ?nite ?elds and their hardware/software implementations and technical - plications. We hope that the WAIFI workshopseries, which from now on will be held on even years, will help to ?ll this gap. Therewere 34 submissionsto WAIFI 2008, of which the ProgramCommittee selected 16 for presentation. Each submission was reviewed by at least three reviewers. Our thanks go to the Program Committee members for their many contributionsandhardwork.Wearealsogratefultotheexternalreviewerslisted below for their expertise and assistance in the deliberations. In addition to the contributions appearing in these proceedings, the workshop program included an invited lecture given by Amin Shokrollahi. Special compliments go out to Enrico Martinelli, General Co-chair, and to Roberto Giorgi and Sandro Bartolini, local organizers of WAIFI 2008, who broughtthe workshopto Siena, oneofthe mostbeautiful citiesofTuscany, Italy. WAIFI 2008 was organized by the Dipartimento di Ingegneria dell'Informazione of the University of Siena, Italy. The submission and selection of papers were done using the iChair software, developed at EPFL by Thomas Baign eres and Matthieu Finiasz. We also thank Deniz Karakoyunlu for his help in this matter.
Category: Computers

Arithmetic Of Finite Fields

Author : Lilya Budaghyan
ISBN : 9783030051532
Genre : Computers
File Size : 23.19 MB
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This book constitutes the thoroughly refereed post-workshop proceedings of the 7th International Workshop on the Arithmetic of Finite Field, WAIFI 2018, held in Bergen, Norway, in June 2018. The 14 revised full papers and six invited talks presented were carefully reviewed and selected from 26 submissions. The papers are organized in topical sections on invited talks; elliptic curves; hardware implementations; arithmetic and applications of finite fields and cryptography.
Category: Computers

Arithmetic Of Finite Fields

Author : Ferruh Özbudak
ISBN : 9783642316623
Genre : Computers
File Size : 58.46 MB
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This book constitutes the refereed proceedings of the 4th International Workshop on the Arithmetic of Finite Field, WAIFI 2012, held in Bochum, Germany, in July 2012. The 13 revised full papers and 4 invited talks presented were carefully reviewed and selected from 29 submissions. The papers are organized in topical sections on coding theory and code-based cryptography, Boolean functions, finite field arithmetic, equations and functions, and polynomial factorization and permutation polynomial.
Category: Computers

Hardware Implementation Of Finite Field Arithmetic

Author : Jean-Pierre Deschamps
ISBN : 9780071545822
Genre : Technology & Engineering
File Size : 82.71 MB
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Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of: Modulo m reduction Modulo m addition, subtraction, multiplication, and exponentiation Operations over GF(p) and GF(pm) Operations over the commutative ring Zp[x]/f(x) Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular
Category: Technology & Engineering

Finite Fields

Author : Rudolf Lidl
ISBN : 0521392314
Genre : Mathematics
File Size : 66.16 MB
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This book is devoted entirely to the theory of finite fields.
Category: Mathematics

Algebraic Curves Over Finite Fields

Author : Carlos Moreno
ISBN : 052145901X
Genre : Mathematics
File Size : 55.36 MB
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Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
Category: Mathematics

Field Arithmetic

Author : Michael D. Fried
ISBN : 9783540269496
Genre : Mathematics
File Size : 47.55 MB
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Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Category: Mathematics

Basic Structures Of Function Field Arithmetic

Author : David Goss
ISBN : 9783642614804
Genre : Mathematics
File Size : 44.61 MB
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From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
Category: Mathematics

Handbook Of Elliptic And Hyperelliptic Curve Cryptography

Author : Henri Cohen
ISBN : 1420034987
Genre : Mathematics
File Size : 41.80 MB
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The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.
Category: Mathematics

Computational Number Theory

Author : Abhijit Das
ISBN : 9781482205824
Genre : Computers
File Size : 75.54 MB
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Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract
Category: Computers

Applications Of Finite Fields

Author : Alfred J. Menezes
ISBN : 0792392825
Genre : Computers
File Size : 87.91 MB
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The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics, in recent years there has been a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. Applications of Finite Fields introduces some of these recent developments. This book focuses attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, Applications of Finite Fields does not attempt to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. This book is developed from a seminar held at the University of Waterloo. The purpose of the seminar was to bridge the knowledge of the participants whose expertise and interests ranged from the purely theoretical to the applied. As a result, this book will be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. Applications of Finite Fields is an excellent reference and may be used as a text for a course on the subject.
Category: Computers

Digital Signal Processing For Multimedia Systems

Author : Keshab K. Parhi
ISBN : 0824719247
Genre : Technology & Engineering
File Size : 45.48 MB
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Addresses a wide selection of multimedia applications, programmable and custom architectures for the implementations of multimedia systems, and arithmetic architectures and design methodologies. The book covers recent applications of digital signal processing algorithms in multimedia, presents high-speed and low-priority binary and finite field arithmetic architectures, details VHDL-based implementation approaches, and more.
Category: Technology & Engineering

Real 802 11 Security

Author : Jon Edney
ISBN : 0321136209
Genre : Computers
File Size : 62.73 MB
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This book describes new approaches to wireless security enabled by the recent development of new core technologies for Wi-Fi/802.11. It shows how the new approaches work and how they should be applied for maximum effect. For system administrators, product designers, or advanced home users.
Category: Computers

Information Networking

Author : China) International Conference on Advances in Structural Dynamics (2000 : Hong Kong
ISBN : 9783540408277
Genre : Computers
File Size : 50.32 MB
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This book constitutes the thoroughly refereed post-proceedings of the International Conference on Information Networking, ICOIN 2003, held at Cheju Island, Korea in February 2003. The 100 revised full papers presented were carefully selected during two rounds of reviewing and revision. The papers are organized in topical sections on high-speed network technologies, enhanced Internet protocols, QoS in the Internet, mobile Internet, network security, network management, and network performance.
Category: Computers