Lectures on Finite Fields and Galois Rings PDF Download
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Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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.
Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
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.
Author: Zhe-xian Wan
Publisher: World Scientific Publishing Company
ISBN: 9813102268
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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.
Author: Zhexian Wan
Publisher:
ISBN: 9789812795076
Category :
Languages : en
Pages :
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Book Description
Author: Zhe-xian Wan
Publisher: World Scientific Publishing Company
ISBN: 9813108223
Category : Mathematics
Languages : en
Pages : 387
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Book Description
A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.
Author: Irving Kaplansky
Publisher: University of Chicago Press
ISBN: 0226424510
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Author: Maurice Kibler
Publisher: Elsevier
ISBN: 0081023510
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics.The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access.This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering).Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. - Contains numerous examples that accompany the text - Includes an important chapter on mutually unbiased bases - Helps physicists and theoretical chemists understand this area of mathematics
Author: Nathan Carter
Publisher: American Mathematical Soc.
ISBN: 1470464330
Category : Education
Languages : en
Pages : 313
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Book Description
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Author: Mingwu Zhang
Publisher: Springer Nature
ISBN: 3031455134
Category : Computers
Languages : en
Pages : 450
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Book Description
This volume LNCS 14217 constitutes the refereed proceedings of the 17th International Conference on Provable and Practical Security, ProvSec 2023, held in Wuhan, China, during October 2023. The 20 full papers presented together with 3 short papers were carefully reviewed and selected from 71 submissions. The conference focuses on Fundamentals & Cryptographic Primitives; Cryptanalysis; Signature; Encryption; Privacy Preservation; and Blockchain Security.
Author: Dennis Hofheinz
Publisher: Springer Nature
ISBN: 303036030X
Category : Computers
Languages : en
Pages : 611
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Book Description
The two-volume set LNCS 11891 and 11892 constitutes the proceedings of the 17th International Conference on Theory of Cryptography, TCC 2019, held in Nuremberg, Germany, in December 2019. The 43 full papers presented were carefully reviewed and selected from 147 submissions. The Theory of Cryptography Conference deals with the paradigms, approaches, and techniques used to conceptualize natural cryptographic problems and provide algorithmic solutions to them and much more.
Author: Mehdi Tibouchi
Publisher: Springer Nature
ISBN: 3030920755
Category : Computers
Languages : en
Pages : 739
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Book Description
The four-volume proceedings LNCS 13090, 13091, 13092, and 13093 constitutes the proceedings of the 27th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2021, which was held during December 6-10, 2021. The conference was planned to take place in Singapore, but changed to an online format due to the COVID-19 pandemic. The total of 95 full papers presented in these proceedings was carefully reviewed and selected from 341 submissions. The papers were organized in topical sections as follows: Part I: Best paper awards; public-key cryptanalysis; symmetric key cryptanalysis; quantum security; Part II: physical attacks, leakage and countermeasures; multiparty computation; enhanced public-key encryption and time-lock puzzles; real-world protocols; Part III: NIZK and SNARKs; theory; symmetric-key constructions; homomorphic encryption and encrypted search; Part IV: Lattice cryptanalysis; post-quantum cryptography; advanced encryption and signatures; zero-knowledge proofs, threshold and multi-signatures; authenticated key exchange.
