Download or read book Counting Polynomial Matrices over Finite Fields written by Julia Lieb and published by BoD – Books on Demand. This book was released on 2017-09-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.
Download or read book A Note on Polynomial Matrix Functions Over a Finite Field written by J. V. Brawley and published by . This book was released on 1977 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F = GF(q) denote the finite field of order q, and let F(n) denote the ring of n x n matrices over F. This paper obtains a unique representation for and determines the number of right (left) polynomial functions A:F(n) yields F(n).
Download or read book Topics in Galois Fields written by Dirk Hachenberger and published by Springer Nature. This book was released on 2020-09-29 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.
Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
Download or read book Counting Zeros of Polynomials Over Finite Fields written by Daniel Edwin Erickson and published by . This book was released on 1974 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Fields and their Applications written by James A. Davis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Fast Software Encryption written by Gregor Leander and published by Springer. This book was released on 2015-08-11 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 22nd International Workshop on Fast Software Encryption, held in Istanbul, Turkey, March 8-11, 2015. The 28 revised full papers presented were carefully reviewed and selected from 71 initial submissions. The papers are organized in topical sections on block cipher cryptanalysis; understanding attacks; implementation issues; more block cipher cryptanalysis; cryptanalysis of authenticated encryption schemes; proofs; design; lightweight; cryptanalysis of hash functions and stream ciphers; and mass surveillance.
Download or read book Scalar Polynomial Functions on the Nxn Matrices Over a Finite Field written by Joel Vincent Brawley and published by . This book was released on 1973 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of the theory of finite fields in areas of discrete linear modeling such as coding theory, finite linear sequential machines, algebraic cryptography and the construction of block designs is well-known. Many times one has the task of constructing (based on a finite field) a function having certain prescribed properties. Of such a nature is the material contained in the report. In particular, the authors determined among other things, necessary and sufficient conditions on a polynomial f(x) with coefficients in a finite field F in order that it defines via substitution a one-one onto function (a permutation) from F(nxn), the nxn matrices over F, to F(nxn).
Download or read book Progress in Cryptology AFRICACRYPT 2016 written by David Pointcheval and published by Springer. This book was released on 2016-04-07 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the 8th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2016, held in Fes, Morooco, in April 2016. The 18 papers presented in this book were carefully reviewed and selected from 65 submissions. The aim of Africacrypt 2016 is to provide an international forum for practitioners and researchers from industry, academia and government from all over the world for a wide ranging discussion of all forms of cryptography. Topics of interest are such as lattices; elliptic curves; secret-key cryptanalysis; efficient implementations; secure protocols; and public-key cryptography.
Download or read book Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.
Download or read book The Number of Polynomial Functions Which Permute the Matrices Over a Finite Field written by Joel V Brawley (Jr) and published by . This book was released on 1974 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F denote a finite field and let f sub (n x n) denote the n x n matrices over F.A function f:F sub (n x n) maps to F sub (n x n) is called a (scalar) polynomial function on F sub (n x n) if and only if there exists a polynomial f(x) an element of F(in brackets:(x)) which represents f under substitution. A formula is obtained for the number of polynomial function on F sub (n x n) which are permutations of F sub (n x n). In the process a procedure is outlined for obtaining a unique polynomial representations of each permutation polynomial function on F sub (n x n).
Download or read book Finite Fields and Applications written by Gary L. Mullen and published by Springer Science & Business Media. This book was released on 2004-03-19 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.
Download or read book Advances in Cryptology CRYPTO 2016 written by Matthew Robshaw and published by Springer. This book was released on 2016-07-25 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume-set, LNCS 9814, LNCS 9815, and LNCS 9816, constitutes the refereed proceedings of the 36th Annual International Cryptology Conference, CRYPTO 2016, held in Santa Barbara, CA, USA, in August 2016. The 70 revised full papers presented were carefully reviewed and selected from 274 submissions. The papers are organized in the following topical sections: provable security for symmetric cryptography; asymmetric cryptography and cryptanalysis; cryptography in theory and practice; compromised systems; symmetric cryptanalysis; algorithmic number theory; symmetric primitives; asymmetric cryptography; symmetric cryptography; cryptanalytic tools; hardware-oriented cryptography; secure computation and protocols; obfuscation; quantum techniques; spooky encryption; IBE, ABE, and functional encryption; automated tools and synthesis; zero knowledge; theory.
Download or read book Advances in Cryptology EUROCRYPT 2019 written by Yuval Ishai and published by Springer. This book was released on 2019-05-14 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume-set LNCS 11476, 11477, and 11478 constitute the thoroughly refereed proceedings of the 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2019,held in Darmstadt, Germany, in May 2019. The 76 full papers presented were carefully reviewed and selected from 327 submissions. The papers are organized into the following topical sections: ABE and CCA security; succinct arguments and secure messaging; obfuscation; block ciphers; differential privacy; bounds for symmetric cryptography; non-malleability; blockchain and consensus; homomorphic primitives; standards; searchable encryption and ORAM; proofs of work and space; secure computation; quantum, secure computation and NIZK, lattice-based cryptography; foundations; efficient secure computation; signatures; information-theoretic cryptography; and cryptanalysis.
Download or read book Advances in Information and Computer Security written by Atsuo Inomata and published by Springer. This book was released on 2018-08-08 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Workshop on Security, IWSEC 2018, held in Sendai, Japan, in September 2018. The 18 regular papers and 2 short papers presented in this volume were carefully reviewed and selected from 64 submissions. They were organized in topical sections named: Cryptanalysis, Implementation Security, Public-Key Primitives, Security in Practice, Secret Sharing, Symmetric-Key Primitives, and Provable Security.
Download or read book Lacunary Polynomials Over Finite Fields written by László Rédei and published by . This book was released on 1973 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
