Applications of Finite Fields:
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 in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryp...
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1993
|
| Schriftenreihe: | The Springer International Series in Engineering and Computer Science, Communications and Information Theory
199 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | 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 in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted 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. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references |
| Beschreibung: | 1 Online-Ressource (XIV, 218 p) |
| ISBN: | 9781475722260 |
| DOI: | 10.1007/978-1-4757-2226-0 |
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| author | Blake, Ian F. Gao, XuHong Mullin, Ronald C. Vanstone, Scott A. |
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| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
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| spelling | Blake, Ian F. Verfasser aut Applications of Finite Fields by Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian ; edited by Alfred J. Menezes Boston, MA Springer US 1993 1 Online-Ressource (XIV, 218 p) txt rdacontent c rdamedia cr rdacarrier The Springer International Series in Engineering and Computer Science, Communications and Information Theory 199 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 in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted 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. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references Engineering Electrical Engineering Discrete Mathematics in Computer Science Coding and Information Theory Coding theory Computer science / Mathematics Electrical engineering Galois-Feld (DE-588)4155896-0 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Galois-Feld (DE-588)4155896-0 s 2\p DE-604 Gao, XuHong aut Mullin, Ronald C. aut Vanstone, Scott A. aut Erscheint auch als Druck-Ausgabe 9781441951304 https://doi.org/10.1007/978-1-4757-2226-0 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blake, Ian F. Gao, XuHong Mullin, Ronald C. Vanstone, Scott A. Applications of Finite Fields Engineering Electrical Engineering Discrete Mathematics in Computer Science Coding and Information Theory Coding theory Computer science / Mathematics Electrical engineering Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4155896-0 (DE-588)4143413-4 |
| title | Applications of Finite Fields |
| title_auth | Applications of Finite Fields |
| title_exact_search | Applications of Finite Fields |
| title_full | Applications of Finite Fields by Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian ; edited by Alfred J. Menezes |
| title_fullStr | Applications of Finite Fields by Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian ; edited by Alfred J. Menezes |
| title_full_unstemmed | Applications of Finite Fields by Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian ; edited by Alfred J. Menezes |
| title_short | Applications of Finite Fields |
| title_sort | applications of finite fields |
| topic | Engineering Electrical Engineering Discrete Mathematics in Computer Science Coding and Information Theory Coding theory Computer science / Mathematics Electrical engineering Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Engineering Electrical Engineering Discrete Mathematics in Computer Science Coding and Information Theory Coding theory Computer science / Mathematics Electrical engineering Galois-Feld Aufsatzsammlung |
| url | https://doi.org/10.1007/978-1-4757-2226-0 |
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