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A Course in Mathematical Cryptography

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 a chapter on noncommutative algebraic cryptography.

Author Information

Gilbert Baumslag †; Benjamin Fine, Fairfield U., USA; Martin Kreuzer, U. Passau, Germany; Gerhard Rosenberger, U. Hamburg, Germany.


"The book under review concerns mathematical cryptography: it presents old and new concepts and methods, which clearly show how mathematics is crucial for modern purposes. [...] Surely this book will provide an important service for the community: it will be useful for graduate students who want to be introduced to the subject, for postgraduate students who want to be acquainted with the different aspects of cryptography, and for researchers who want to know recent results in the area."
Patrizia Longobardi in: Mathematical Reviews Clippings MR3558843 94A60 October 2017

„Es werden alle relevanten Themen für eine Lehrveranstaltung besprochen."
Prof. Dr. Jörg Hettel, Markus Höfler, Hochschule Kaiserslautern

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Audience: Students in Mathematics and Computers Lecturers; Academic Libraries.