Baumslag G. & oth. A Course in Mathematical Cryptography

De Gruyte, 2015. — XiV, 376 р. — (De Gruyter Graduate). — ISBN 978-3-11-037276-2, 978-3-11-037277-9, 978-3-11-038616-5.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.
Focuses on the mathematics of cryptographic protocols.
Discusses relevant ideas from computer science and complexity theory
Includes chapter on noncommutative algebraic cryptography.Basic Ideas of Cryptography
Symmetric Key Cryptosystems
Cryptanalysis and Complexity
Cryptographic Protocols
Elementary Number Theoretic Techniques
Some Number Theoretic Algorithms
Public Key Cryptography
Elliptic Curve Cryptography
Basic Concepts from Group Theory
Non-Commutative Group Based Cryptography
Platform Groups and Braid Group Cryptography
Further Applications Using Group Theory
Commutative Gröbner Basis Methods
Non-Commutative Gröbner Basis Methods
Lattice-Based Cryptography