Group-Based Cryptography

Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander

ISBN 10: 3764388269 / ISBN 13: 9783764388263

Editore: Birkhauser Verlag AG, 2008

Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. Series: Advanced Courses in Mathematics - CRM Barcelona. Num Pages: 198 pages, biography. BIC Classification: PB. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 172 x 17. Weight in Grams: 494. . 2008. Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9783764388263

Riassunto:

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a 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. 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. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.

Dalla quarta di copertina:

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a 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.

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.

Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.

Dati bibliografici

Titolo: Group-Based Cryptography
Casa editrice: Birkhauser Verlag AG
Data di pubblicazione: 2008
Legatura: Brossura
Condizione: New