Algebra for Applications

Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression

Arkadii Slinko (Autor)

Buch | Softcover

XIV, 368 Seiten

2020 | 2nd ed. 2020
Springer International Publishing (Verlag)
978-3-030-44073-2 (ISBN)

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Modern societies are awash with data that needs to be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorised access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory and can only be properly understood with a good knowledge of these fields. This textbook provides the mathematical tools and applies them to study key aspects of data transmission such as encryption and compression.

Designed for an undergraduate lecture course, this textbook provides all of the background in arithmetic, polynomials, groups, fields, and elliptic curves that is required to understand real-life applications such as cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. It explains in detail how these applications really work. The book uses the free GAP computational package, allowing the reader to develop intuition about computationallyhard problems and giving insights into how computational complexity can be used to protect the integrity of data.

The first undergraduate textbook to cover such a wide range of applications, including some recent developments, this second edition has been thoroughly revised with the addition of new topics and exercises. Based on a one semester lecture course given to third year undergraduates, it is primarily intended for use as a textbook, while numerous worked examples and solved exercises also make it suitable for self-study.

Arkadii M. Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand. Before taking this position in 1993 he was a Senior Research Fellow of the interdisciplinary Institute of Systems Analysis of Russian Academy of Sciences in Moscow. He has published extensively in a wide range of journals in mathematics, computer science, economics, and politics. His current research focuses on the mathematics of social choice, game theory, and secret sharing.

1 Integers.- 2 Cryptology.- 3 Groups.- 4 Fields.- 5 Polynomials.- 6 Secret Sharing.- 7 Error-Correcting Codes.- 8 Compression.- Appendix A: GAP.- Appendix B: Miscellanea.- Solutions to Exercises.- Index.

Erscheinungsdatum	03.06.2020
Reihe/Serie	Springer Undergraduate Mathematics Series
Zusatzinfo	XIV, 368 p. 17 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	587 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
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	3-030-44073-7 / 3030440737
ISBN-13	978-3-030-44073-2 / 9783030440732
Zustand	Neuware