Group-based Cryptography

• Main Authors: Myasnikov, Alexei (Author), Ushakov, Alexander (Author), Shpilrain, Vladimir (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Advanced Courses in Mathematics - CRM Barcelona, Centre de Recerca Matemàtica
• Subjects: Mathematics.; Group theory.; Computer mathematics.; Combinatorics.; Group Theory and Generalizations.; Computational Mathematics and Numerical Analysis.

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...

Table of Contents:

• 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.