Download or read book Equations Over Finite Fields written by W. M. Schmidt and published by . This book was released on 2014-09-01 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Download or read book Fault Tolerant Architectures for Cryptography and Hardware Security written by SIKHAR PATRANABIS and published by Springer. This book was released on 2018-03-29 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses motivating examples and real-life attack scenarios to introduce readers to the general concept of fault attacks in cryptography. It offers insights into how the fault tolerance theories developed in the book can actually be implemented, with a particular focus on a wide spectrum of fault models and practical fault injection techniques, ranging from simple, low-cost techniques to high-end equipment-based methods. It then individually examines fault attack vulnerabilities in symmetric, asymmetric and authenticated encryption systems. This is followed by extensive coverage of countermeasure techniques and fault tolerant architectures that attempt to thwart such vulnerabilities. Lastly, it presents a case study of a comprehensive FPGA-based fault tolerant architecture for AES-128, which brings together of a number of the fault tolerance techniques presented. It concludes with a discussion on how fault tolerance can be combined with side channel security to achieve protection against implementation-based attacks. The text is supported by illustrative diagrams, algorithms, tables and diagrams presenting real-world experimental results.
Download or read book Algebraic Cryptanalysis written by Gregory Bard and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.
Download or read book Lacunary Polynomials Over Finite Fields written by L. Rédei and published by Elsevier. This book was released on 2014-05-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations. The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions. The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields.
Download or read book Finite Fields Theory and Computation written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Fields Theory and Applications written by Gary McGuire and published by American Mathematical Soc.. This book was released on 2010 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contributed papers. Finite fields continue to grow in mathematical importance due to applications in many diverse areas. This volume contains a variety of results advancing the theory of finite fields and connections with, as well as impact on, various directions in number theory, algebra, and algebraic geometry. Areas of application include algebraic coding theory, cryptology, and combinatorial design theory.
Download or read book Advances in Cryptology EUROCRYPT 96 written by Ueli Maurer and published by Springer. This book was released on 2003-05-15 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The EUROCRYPT ’96 conference was sponsored by the International Asso- ation for Cryptologic Research (IACR)l, in cooperation with the University of Saragossa. It took place at the Palacio de Congresos in Saragossa, Spain, during May 12-16, 1996. This was the fifteenth annual EUROCRYPT conference (this name has been used since the third conference held in 1984), each of which has been held in a different city in Europe. For the second time, proceedings were available at the conference. JosC Pastor Franco, the General Chair, was resp- sible for local organization and registration. His contribution to the snccess of the conference is gratefully acknowledged. The Program Committee considered 126 submitted papers and selected 34 for presentation. Each paper was sent to all members of the Program Committee and was assigned to at least three of them for careful evaluation. There were also two invited talks. James L. Massey, this year’s IACR Distinguished Ltcturer, gave a lecture entitled “The difficulty with difficulty”. Massey is the third to receive this honor, the first two being Gustavus Simmons and Adi Shamir. Shafi Goldwasser gave an invited talk entitled “Multi party secure protocols: past and present”. These proceedings contain revised versions of the 34 contributed talks. While the papers were carefully selected, they have not been refereed like submissions to a refereed journal. The authors bear full responsibility for the contents of their papers. Some authors may write final versions of their papers for publication in a refereed journal.
Download or read book Computational Algebra Course And Exercises With Solutions written by Ihsen Yengui and published by World Scientific. This book was released on 2021-05-17 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.
Download or read book Lectures on Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-05-31 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Download or read book Computational and Algorithmic Problems in Finite Fields written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-06-20 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Download or read book Gr bner Bases Coding and Cryptography written by Massimiliano Sala and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.
Download or read book Finite Fields Theory Applications and Algorithms written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
Download or read book Algebraic Informatics written by Franz Winkler and published by Springer Science & Business Media. This book was released on 2011-06-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Algebraic Informatics, CAI 2011, held in Linz, Austria, in June 2011. The 12 revised full papers presented together with 4 invited articles were carefully reviewed and selected from numerous submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, and algebraic aspects of cryptography.
Download or read book Algorithms and Theory of Computation Handbook written by Mikhail J. Atallah and published by CRC Press. This book was released on 1998-11-23 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
