Book description
Cryptography has become essential as bank transactions, credit card infor-mation, contracts, and sensitive medical information are sent through inse-cure channels. This book is concerned with the mathematical, especially algebraic, aspects of cryptography. It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in mathematics and computer science, but may also be of interest to researchers in the area.
Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such as
- Group-Based Cryptography
- Gröbner Basis Methods in Cryptography
- Lattice-Based Cryptography
Table of contents
- Cover
- Title
- Copyright Page
- Preface
- Table of content
- 1 Basic Ideas of Cryptography
- 2 Symmetric Key Cryptosystems
- 3 Cryptanalysis and Complexity
- 4 Cryptographic Protocols
- 5 Elementary Number Theoretic Techniques
- 6 Some Number Theoretic Algorithms
- 7 Public Key Cryptography
- 8 Elliptic Curve Cryptography
- 9 Basic Concepts from Group Theory
- 10 Group Based Cryptography
-
11 Braid Group Cryptography
- 11.1 Cryptographic Platforms and Platform Groups
- 11.2 The Ko-Lee and AAG Protocols
- 11.3 Some Other Group Based Cryptosystems
- 11.4 The Shamir Three-Pass
- 11.5 Hard Group Theoretic Properties
- 11.6 Braid Group Cryptography
- 11.7 The Braid Groups
- 11.8 Cryptanalysis of Braid Group Cryptosystems
- 11.9 Some Other Braid Group Based Protocols
- 11.10 Exercises
- 12 Further Applications
- 13 Commutative Grobner Basis Methods
- 14 Non-Commutative Grobner Basis Methods
- 15 Lattice-Based Cryptography
- Bibliography
- Index
Product information
- Title: A Course in Mathematical Cryptography
- Author(s):
- Release date: June 2015
- Publisher(s): De Gruyter
- ISBN: 9783110386165
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