Non-commutative Cryptography and Complexity of Group-theoretic Problems

Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov (Autoren)

Buch | Hardcover

413 Seiten

2011
American Mathematical Society (Verlag)
978-0-8218-5360-3 (ISBN)

Titel z.Zt. nicht lieferbar
Versandkostenfrei
Auch auf Rechnung

Artikel merken

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. In particular, a lot of emphasis in the book is put on studying search problems, as compared to decision problems traditionally studied in combinatorial group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. This book also describes new interesting developments in the algorithmic theory of solvable groups and another spectacular new development related to complexity of group-theoretic problems, which is based on the ideas of compressed words and straight-line programs coming from computer science.

Erscheint lt. Verlag	16.1.2012
Reihe/Serie	Mathematical Surveys and Monographs
Verlagsort	Providence
Sprache	englisch
Gewicht	862 g
Themenwelt	Informatik ► Netzwerke ► Sicherheit / Firewall
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	0-8218-5360-0 / 0821853600
ISBN-13	978-0-8218-5360-3 / 9780821853603
Zustand	Neuware