In this book, the most important cryptographic algorithms, protocols and constructions of the last decades are explained and justified from a mathematical point of view. The topics discussed range from public-key cryptography and zero-knowledge protocols to cryptography in blockchains and the Tor network. The authors succeed in presenting these complex topics in a simple and clear manner. Hardly any prior knowledge is required, as all the necessary mathematical and cryptographic background is provided in the book. The book has a modular structure so that the individual chapters can be read independently of one another. Each topic is presented at different levels: First, the concept is described as a mental model, then it is studied from a mathematical point of view, and finally the strengths and weaknesses of the respective protocol are discussed. The book is suitable for undergraduate students (e.g.

, in mathematics, computer science, electrical engineering) as well as for Internet users, tech managers, software developers and data protection/data security officers. This book is a translation of the original German 9th edition Moderne Verfahren der Kryptographie by Albrecht Beutelspacher, Jörg Schwenk and Klaus-Dieter Wolfenstetter, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2022. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. The authors Prof. Dr. Albrecht Beutelspacher taught mathematics at the Justus Liebig University in Giessen from 1988 to 2018. He is the director of the Mathematikum in Giessen.

Prof. Dr. Jörg Schwenk holds the chair for network and data security at the Ruhr University Bochum. Dipl. Math. Klaus-Dieter Wolfenstetter worked at Deutsche Telekom Innovation Laboratories in Berlin until 2016.