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 Grobner Basis Methods in Cryptography Lattice Based CryptographyFocuses on the mathematics of cryptographic protocols Discusses relevant ideas from computer science and complexity theory Includes a chapter on noncommutative algebraic cryptography