Algebra for Applications
Springer International Publishing (Verlag)
978-3-031-82625-2 (ISBN)
This textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information.
The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study.
This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version.
Arkadii Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand.
Integers.- Cryptology.- Groups.- Fields.- Polynomials.- Secret Sharing.- Error-Correcting Codes.- Compression.- Appendix A: GAP.- Appendix B: Miscellanea.- Solutions to Exercises.- Index.
| Erscheinungsdatum | 22.05.2025 |
|---|---|
| Reihe/Serie | Springer Undergraduate Mathematics Series |
| Zusatzinfo | XVII, 395 p. 11 illus., 2 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Schlagworte | BCH code • diffie-hellman • digital signature • Elgamal Cryptosystem • Error-correcting codes • Euler Totient Function • Fingerprinting Codes • Fitingof Compression Code • Huffman compression code • ideal secret sharing scheme • Lagrange Interpolation • Linear Secret Sharing Scheme • Miller-Rabin Pseudoprimality Test • Prefix Codes • Primality Testing • Public Key Cryptography • reed-solomon codes • RSA cryptosystem • Secret key cryptography • Shamir's Secret Sharing Scheme • Shamir’s Secret Sharing Scheme |
| ISBN-10 | 3-031-82625-6 / 3031826256 |
| ISBN-13 | 978-3-031-82625-2 / 9783031826252 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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