Rational Points On Curves Over Finite Fields

Author by : Harald Niederreiter
Languange : en
Publisher by : Cambridge University Press
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Description : Discussion of theory and applications of algebraic curves over finite fields with many rational points.


Algebraic Geometry Modeling In Information Theory

Author by : Edgar Martinez-Moro
Languange : en
Publisher by : World Scientific
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Total Read : 70
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Description : Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.


Algebraic Geometric Codes

Author by : Michael A. Tsfasman
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book focuses on the theory of algebraic geometry codes, a subject that has emerged at the meeting point of several fields of mathematics. Unlike other texts, it consistently seeks interpretations that connect coding theory to algebraic geometry and number theory. This approach makes the book useful for both coding experts and experts in algebraic geometry.


Locally Decodable Codes And Private Information Retrieval Schemes

Author by : Sergey Yekhanin
Languange : en
Publisher by : Springer Science & Business Media
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Description : Locally decodable codes (LDCs) are codes that simultaneously provide efficient random access retrieval and high noise resilience by allowing reliable reconstruction of an arbitrary bit of a message by looking at only a small number of randomly chosen codeword bits. Local decodability comes with a certain loss in terms of efficiency – specifically, locally decodable codes require longer codeword lengths than their classical counterparts. Private information retrieval (PIR) schemes are cryptographic protocols designed to safeguard the privacy of database users. They allow clients to retrieve records from public databases while completely hiding the identity of the retrieved records from database owners. In this book the author provides a fresh algebraic look at the theory of locally decodable codes and private information retrieval schemes, obtaining new families of each which have much better parameters than those of previously known constructions, and he also proves limitations of two server PIRs in a restricted setting that covers all currently known schemes. The author's related thesis won the ACM Dissertation Award in 2007, and this book includes some expanded sections and proofs, and notes on recent developments.


Algorithmic Number Theory

Author by : CRYPTO
Languange : en
Publisher by : Springer Science & Business Media
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Description : This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.


Secure Multiparty Computation And Secret Sharing

Author by : Ronald Cramer
Languange : en
Publisher by : Cambridge University Press
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Description : In a data-driven society, individuals and companies encounter numerous situations where private information is an important resource. How can parties handle confidential data if they do not trust everyone involved? This text is the first to present a comprehensive treatment of unconditionally secure techniques for multiparty computation (MPC) and secret sharing. In a secure MPC, each party possesses some private data, while secret sharing provides a way for one party to spread information on a secret such that all parties together hold full information, yet no single party has all the information. The authors present basic feasibility results from the last 30 years, generalizations to arbitrary access structures using linear secret sharing, some recent techniques for efficiency improvements, and a general treatment of the theory of secret sharing, focusing on asymptotic results with interesting applications related to MPC.


Mathematical Reviews

Author by : Anonim
Languange : en
Publisher by : Unknown
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Description :


Codes Cryptology And Curves With Computer Algebra

Author by : Ruud Pellikaan
Languange : en
Publisher by : Cambridge University Press
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Total Read : 93
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Description : Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.


Algebraic Curves Over A Finite Field

Author by : J. W. P. Hirschfeld
Languange : en
Publisher by : Princeton University Press
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Description : This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.


Auxiliary Polynomials In Number Theory

Author by : David Masser
Languange : en
Publisher by : Cambridge University Press
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Description : This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from number theory to algebraic geometry.


Algorithmic Number Theory

Author by : Florian Hess
Languange : en
Publisher by : Springer Science & Business Media
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Description : The ?rst Algorithmic Number Theory Symposium (ANTS) conference was hosted by Cornell University, Ithaca, New York, USA in 1994. The goal of the conference was to bring together number theorists from around the world, and to advance theoretical and practical research in the ?eld. ANTS I was soon followed by c- ferences in Bordeaux, France in 1996, Portland, Oregon, USA in 1998, Leiden, in the Netherlands in 2000, Sydney, Australia in 2002, and Burlington, Vermont, USA in 2004. Technische Universit ̈ at Berlin in Germany hosted ANTS VII during July, 23-28 2006. Five invited speakers attended ANTS VII. Thirty seven contributed papers were presented and a poster session was held. The invited speakers were Nigel Boston of the University of Wisconsin at Madison, John Cremona of the Univ- sity of Nottingham, Bas Edixhoven of Universteit Leiden, Jur ̈ gen Kluner ̈ s of U- versitat ̈ Kassel, and Don Zagier from the Max-Planck-Institut fur ̈ Mathematik, Bonn. Each submitted paper was reviewed by at least two experts external to the Program Committee which decided about acceptance or rejection on the basis of their recommendations. The Selfridge prize in computational number theory was awarded to the authors of the best contributed paper presented at the conference.


Some Problems Of Unlikely Intersections In Arithmetic And Geometry

Author by : Umberto Zannier
Languange : en
Publisher by : Princeton University Press
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Description : This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila).


Algorithmic Number Theory

Author by : Duncan Buell
Languange : en
Publisher by : Springer
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Description : The sixth Algorithmic Number Theory Symposium was held at the University of Vermont, in Burlington, from 13–18 June 2004. The organization was a joint e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- buted talks were presented, and a poster session was held. This volume contains the written versions of the contributed talks and three of the four invited talks. (Not included is the talk by Dan Bernstein.) ANTS in Burlington is the sixth in a series that began with ANTS I in 1994 at Cornell University, Ithaca, New York, USA and continued at Universit ́eB- deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998), the University of Leiden, Leiden, The Netherlands (2000), and the University of Sydney, Sydney, Australia (2002). The proceedings have been published as volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag’s Lecture Notes in Computer Science series. The organizers of the 2004 ANTS conference express their special gratitude and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes advice.


Algorithmic Number Theory

Author by : Wieb Bosma
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.


Algorithmic Number Theory

Author by : Wieb Bosma
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 80
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Description : This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.


Random Graphs

Author by : Béla Bollobás
Languange : en
Publisher by : Cambridge University Press
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Description : This is a revised and updated version of the classic first edition.


Information Security Practice And Experience

Author by : Joseph K. Liu
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 93
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Description : This book constitutes the proceedings of the 13th International Conference on Information Security and Practice and Experience, ISPEC 2017, held in Melbourne, Australia, in December 2017. The 34 full and 14 short papers presented together with 9 papers from the SocialSec Track in this volume were carefully reviewed and selected from 105 submissions. The papers cover topics such as blockchain, asymmetric encryption, symmetric encryption, lattice-based cryptography, searchable encryption, signature, authentication, cloud security, network security, cyber-physical security, social network and QR code security, software security and trusted computing, and SocialSec track.


Fault Analysis In Cryptography

Author by : Marc Joye
Languange : en
Publisher by : Springer Science & Business Media
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Description : In the 1970s researchers noticed that radioactive particles produced by elements naturally present in packaging material could cause bits to flip in sensitive areas of electronic chips. Research into the effect of cosmic rays on semiconductors, an area of particular interest in the aerospace industry, led to methods of hardening electronic devices designed for harsh environments. Ultimately various mechanisms for fault creation and propagation were discovered, and in particular it was noted that many cryptographic algorithms succumb to so-called fault attacks. Preventing fault attacks without sacrificing performance is nontrivial and this is the subject of this book. Part I deals with side-channel analysis and its relevance to fault attacks. The chapters in Part II cover fault analysis in secret key cryptography, with chapters on block ciphers, fault analysis of DES and AES, countermeasures for symmetric-key ciphers, and countermeasures against attacks on AES. Part III deals with fault analysis in public key cryptography, with chapters dedicated to classical RSA and RSA-CRT implementations, elliptic curve cryptosystems and countermeasures using fault detection, devices resilient to fault injection attacks, lattice-based fault attacks on signatures, and fault attacks on pairing-based cryptography. Part IV examines fault attacks on stream ciphers and how faults interact with countermeasures used to prevent power analysis attacks. Finally, Part V contains chapters that explain how fault attacks are implemented, with chapters on fault injection technologies for microprocessors, and fault injection and key retrieval experiments on a widely used evaluation board. This is the first book on this topic and will be of interest to researchers and practitioners engaged with cryptographic engineering.


Rational Points On Algebraic Varieties

Author by : Emmanuel Peyre
Languange : en
Publisher by : Birkhäuser
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Description : This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.


Applied Cryptography And Network Security

Author by : Jianying Zhou
Languange : en
Publisher by : Springer
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Description : The 1st International Conference on “Applied Cryptography and Network Se- rity” (ACNS 2003) was sponsored and organized by ICISA (International C- munications and Information Security Association), in cooperation with MiAn Pte. Ltd. and the Kunming government. It was held in Kunming, China in - tober 2003. The conference proceedings was published as Volume 2846 of the Lecture Notes in Computer Science (LNCS) series of Springer-Verlag. The conference received 191 submissions, from 24 countries and regions; 32 of these papers were accepted, representing 15 countries and regions (acceptance rate of 16.75%). In this volume you will ?nd the revised versions of the - cepted papers that were presented at the conference. In addition to the main track of presentations of accepted papers, an additional track was held in the conference where presentations of an industrial and technical nature were given. These presentations were also carefully selected from a large set of presentation proposals. This new international conference series is the result of the vision of Dr. Yongfei Han. The conference concentrates on current developments that advance the - eas of applied cryptography and its application to systems and network security. The goal is to represent both academic research works and developments in - dustrial and technical frontiers. We thank Dr. Han for initiating this conference and for serving as its General Chair.


Towards A Quarter Century Of Public Key Cryptography

Author by : Neal Koblitz
Languange : en
Publisher by : Springer Science & Business Media
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Description : Towards a Quarter-Century of Public Key Cryptography brings together in one place important contributions and up-to-date research results in this fast moving area. Towards a Quarter-Century of Public Key Cryptography serves as an excellent reference, providing insight into some of the most challenging research issues in the field.


Cryptographic Hardware And Embedded Systems Ches 2001

Author by : Cetin K. Koc
Languange : en
Publisher by : Springer
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Description : These are the proceedings of CHES 2001, the third Workshop on Cryptographic Hardware and Embedded Systems. The ?rst two CHES Workshops were held in Massachusetts, and this was the ?rst Workshop to be held in Europe. There was a large number of submissions this year, and in response the technical program was extended to 2 1/2 days. As is evident by the papers in these proceedings, many excellent submissions were made. Selecting the papers for this year’s CHES was not an easy task, and weregretthatwehadtorejectseveralveryinterstingpapersduetotheac l kof time. There were 66 submitted contributions this year, of which 31, or 47%, were selected for presentation. If we look at the number of submitted papers at CHES ’99 (42 papers) and CHES 2001 (51 papers), we observe a steady increase. We interpret this as a continuing need for a workshop series which combines theory and practice for integrating strong security features into modern communications and computer applications. In addition to the submitted contributions, Ross Anderson from Cambridge University, UK, and Adi Shamir from The Weizmann Institute, Israel, gave invited talks. As in previous years, the focus of the workshop is on all aspects of cryp- graphichardwareandembeddedsystemdesign.Ofspecialinterestwerecont- butions that describe new methods for e?cient hardware implementations and high-speed software for embedded systems, e.g., smart cards, microprocessors, DSPs, etc. CHES also continues to be an important forum for new theoretical andpractical?ndingsintheimportantandgrowing?eldofside-channelattacks.


Guide To Elliptic Curve Cryptography

Author by : Darrel Hankerson
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 60
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Description : After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic * Distills complex mathematics and algorithms for easy understanding * Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.


Galois Representations In Arithmetic Algebraic Geometry

Author by : A. J. Scholl
Languange : en
Publisher by : Cambridge University Press
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Description : Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.


Rational Points Rational Curves And Entire Holomorphic Curves On Projective Varieties

Author by : Carlo Gasbarri
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation. This book is co-published with the Centre de Recherches Mathématiques.


Public Key Cryptography

Author by : Abhijit Das
Languange : en
Publisher by : Pearson Education India
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Description : Public-key Cryptography provides a comprehensive coverage of the mathematical tools required for understanding the techniques of public-key cryptography and cryptanalysis. Key topics covered in the book include common cryptographic primitives and symmetric techniques, quantum cryptography, complexity theory, and practical cryptanalytic techniques such as side-channel attacks and backdoor attacks.Organized into eight chapters and supplemented with four appendices, this book is designed to be a self-sufficient resource for all students, teachers and researchers interested in the field of cryptography.