Algebra for Applications
Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression
Seiten
2015
|
1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-21950-9 (ISBN)
Springer International Publishing (Verlag)
978-3-319-21950-9 (ISBN)
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This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory.This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.
ARKADII SLINKO is currently Professor of Mathematics at the University of Auckland. He has published extensively in a wide range of journals. His current research is in applied discrete mathematics with particular focus on the mathematics of social choice, mathematical politics, decision theory, game theory and secret sharing.
Integers.- Cryptology.- Groups.- Fields.- Polynomials.- Secret Sharing.- Error-Correcting Codes.- Compression.- Appendix A: GAP.- Appendix B: Miscellanies.- Solutions to Exercises.
| Erscheint lt. Verlag | 29.8.2015 |
|---|---|
| Reihe/Serie | Springer Undergraduate Mathematics Series |
| Zusatzinfo | XIV, 328 p. 5 illus., 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 531 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | BCH Codes • cryptography • Cryptology • Elgamal Cryptosystem • Elliptic Curves • Error-correcting codes • Euler Totient Function • Factorisation • Fingerprinting Codes • finite field • Fitingof's Compression Code • Fitingof’s Compression Code • integers • Lagrange Interpolation • linear codes • Linear Secret Sharing Scheme • Miller-Rabin Pseudoprimality Test • permutation groups • polynomial • Prefix Codes • Primality Testing • Primes • reed-solomon codes • RSA cryptosystem • secret sharing scheme • Shamir's Threshold Secret Sharing Scheme • Shamir’s Threshold Secret Sharing Scheme |
| ISBN-10 | 3-319-21950-2 / 3319219502 |
| ISBN-13 | 978-3-319-21950-9 / 9783319219509 |
| Zustand | Neuware |
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