© 2005

Complexity Theory and Cryptology

An Introduction to Cryptocomplexity


  • First book focusing on the interrelation of Cryptology and Complexity Theory


About this book


Modern cryptology employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research in complexity theory often is motivated by questions and problems arising in cryptology. This book takes account of this trend, and therefore its subject is what may be dubbed "cryptocomplexity,'' some sort of symbiosis of these two areas.

This textbook is suitable for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation. Starting from scratch, it is an accessible introduction to cryptocomplexity and works its way to the frontiers of current research. It provides the necessary mathematical background, has numerous figures, exercises, and examples, and presents some central, up-to-date research topics and challenges. Due to its comprehensive bibliography and subject index, it is also a valuable source for researchers, teachers, and practitioners working in these fields.


Complexity classes Complexity classes and hierarchies Computational complexity Cryptography Interactive proof systems Interactive proof systems and zero-knowledge One-way functions Public-key cryptography Zero-knowledge proofs algorithms complexity complexity theory foundations of comp

Authors and affiliations

  1. 1.Institut für InformatikUniversität DüsseldorfDüsseldorfGermany

Bibliographic information

Industry Sectors
IT & Software
Consumer Packaged Goods
Finance, Business & Banking


From the reviews:

"The book … provides introduction to both cryptology and complexity theory with special emphasis on their mutual pervasion. … All chapters have a set of exercises and problems as well as a summary describing the historical development of the notions and results presented and providing bibliographic remarks and references for further study. A comprehensive bibliography makes the book a valuable source for the researchers, teachers, and even practitioners working in complexity theory and cryptology. A useful book." (Jozef Vyskoc, Zentralblatt MATH, Vol. 1082, 2006)

"This book of 478 pages is an introduction to complexity theory and cryptology. It is very well suited for the reader who wants to learn these two closely related areas in theoretical computer science. … The nice aspect of this book is that it treats the two topics in an integrated approach. … The book could be used as a textbook for undergraduate and graduate students in computer sciences, mathematics, and engineering. Each chapter ends with pages of summary and bibliographic remarks." (Yongge Wang, Mathematical Reviews, Issue 2006 c)

"The book is intended as a textbook for advanced undergraduate and graduate students and is based on author’s long experience of teaching a series of interrelated courses on cryptocomplexity. … the book contains a very well organized index. … The book is well written and interesting. … I like the book and I think it is a good textbook for graduate students and for advanced undergraduate students. … a solid textbook for advanced students and a very good, comprehensive, reference for researchers." (Piotr Faliszewski, SIGACT News, Vol. 38 (2), 2007)