CryptoSchool

This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography—--the art of making secure building blocks—--and cryptanalysis—--the art of breaking them. The text describes some of the most important systems in detail, including AES, RSA, group-based and lattice-based cryptography, signatures, hash functions, random generation, and more, providing detailed underpinnings for most of them. With regard to cryptanalysis, it presents a number of basic tools such as the differential and linear methods and lattice attacks. 

This text, based on lecture notes from the author’s many courses on the art of cryptography, consists of two interlinked parts. The first, modern part explains some of the basic systems used today and some attacks on them. However, a text on cryptology would not be complete without describing its rich and fascinating history. As such, the colorfully illustrated historical part interspersed throughout the text highlights selected inventions and episodes, providing a glimpse into the past of cryptology.

The first sections of this book can be used as a textbook for an introductory course to computer science or mathematics students. Other sections are suitable for advanced undergraduate or graduate courses. Many exercises are included. The emphasis is on providing reasonably complete explanation of the background for some selected systems.

“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)

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.