Alexei Myasnikov & Vladimir Shpilrain 
Group-based Cryptography 

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.

Table of Content

Background on Groups, Complexity, and Cryptography.- Background on Public Key Cryptography.- Background on Combinatorial Group Theory.- Background on Computational Complexity.- Non-commutative Cryptography.- Canonical Non-commutative Cryptography.- Platform Groups.- Using Decision Problems in Public Key Cryptography.- Generic Complexity and Cryptanalysis.- Distributional Problems and the Average-Case Complexity.- Generic Case Complexity.- Generic Complexity of NP-complete Problems.- Asymptotically Dominant Properties and Cryptanalysis.- Asymptotically Dominant Properties.- Length-Based and Quotient Attacks.