Joachim von zur Gathen has taught about fifty courses on various topics in cryptology. His lively and interactive style has encouraged several original contributions by students throughout the book. His research is in cryptology, computer algebra, finite fields, algorithmics, and complexity theory.The author has held professorships at the universities of Toronto, Paderborn, and Bonn, each for more than a decade. He is now retired (and active). Visiting professorships include Australia (Canberra, Sydney), Chile (Santiago, Concepción), Germany (Saarbrücken), South Africa (Johannesburg), Spain (Alcalà, Santander), Switzerland (ETH and Universität Zürich), Uruguay (Montevideo), and USA (Berkeley). He is founder and was editor-in-chief for 25 years of the journal computational complexity, and was on the editorial boards of the journals Codes and Cryptography, Finite Fields and Their Applications, Journal of Symbolic Computation, and SIAM Journal of Computing.He is listed in various editions of Who's Who in the World. His previous work includes the book "Modern Computer Algebra" that has been called "the bible of computer algebra" and has been cited in over 2000 articles.

• 1 Introduction.- 2 Basic cryptosystems.- A Classical cryptology.- 3 The RSA cryptosystem.- B Key addition and modular arithmetic.- 4 Group cryptography and discrete logarithms.- 5 Elliptic curves.- C Breaking the unbreakable.- 6 Differential and linear cryptanalysis.- 7 Hash functions.- D Codebooks.- 8 Signatures.- 9 Security and reductions.- E Steganography.- 10 Identification and authentication.- F Transposition ciphers.- 11 Random generation.- G Some cryptographers.- 12 Proof systems and zero knowledge.- H People using cryptography.- 13 Integral lattices.- I The Zimmermann telegram.- 14 Quantum computation.- J Enigma, Turing, and Colossus.- 15 The computer algebra toolbox.- List of notation and sources of quotations, images, and ornaments.- Bibliography.- Index.

“The book is an excellent and very comprehensive introduction to cryptography. Based on lectures the author has been giving on the art of cryptography, it is suitable as a basis for a two-semester graduate or advanced undergraduate course for students in mathematics, computer science, or engineering. Rigorous arguments and proofs are given for lemmas, theorems, etc, which also distinguishes the book from many other introductory books on cryptography. Every chapter closes with a collection of exercises … .” (Wilfried Meidl, zbMATH 1350.94006, 2017)“The book under review is a very nice and enjoyable introduction to cryptographic science (cryptology). … audience is advanced undergraduate or graduate students in mathematics, computer science or engineering (albeit with a theoretical slant), and there are plenty of examples, exercises and problems to be worked out. The style of the exposition is clear and the details provided are sufficient, without being overwhelming. … Furthermore, the contents are more than enough for a two-semester course.” (Luca Giuzzi, Mathematical Reviews, June, 2016)“The work is an important contribution to the literature in that it is more detailed, abundantly illustrated, and more clearly explained and thorough than many other accounts. The text describes some of the most important systems in detail … and provides detailed backgrounds for these topics as well. Each of these important areas is explained and demonstrated for those who lack knowledge in these aspects.” (G. Mick Smith, Computing Reviews, computingreviews.com, May, 2016)“The book is intended for advanced undergraduates or beginning graduate students … . dedicates significant space to discussing theoretical aspects of security, including rigorous descriptions of the difference between axiomatic and empirical security … . CryptoSchool is very ambitious in its attempts to provide a self-contained overview of the past, present, and future of cryptography and largely succeeds at its goals.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)