Linear Cryptanalysis
Linear Cryptanalysis
Vincent Rijmen , Katholieke Universiteit Leuven, Belgium
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GBPApplications of cryptography are plenty in everyday life. This guidebook is about the security analysis or 'cryptanalysis' of the basic building blocks on which these applications rely. Rather than covering a variety of techniques at an introductory level, this book provides a comprehensive and in-depth treatment of linear cryptanalysis. The subject is introduced from a mathematical point of view, providing an overview of the most influential papers on linear cryptanalysis and placing them in a consistent framework based on linear algebra. A large number of examples and exercises are included, drawing upon practice as well as theory. The book is accessible to students with no prior knowledge of cryptography. It covers linear cryptanalysis starting from the basics, including linear approximations and trails, correlation matrices, automatic search, key-recovery techniques, up to advanced topics, such as multiple and multidimensional linear cryptanalysis, zero-correlation approximations, and the geometric approach.
- Helps beginners grasp concepts by introducing the geometric approach to linear cryptanalysis from a relatively concrete point of view
- Treats the subject rigorously from the get-go to facilitate learning advanced topics down the line
- Solutions to selected exercises provided online
Reviews & endorsements
'Eleven chapters, written by two renowned international experts, brilliantly and smoothly present the fundamentals of linear cryptanalysis. This valuable book covers all the concepts and tools useful to students. Extremely well-written, it also provides the necessary material for researchers wishing to deepen their knowledge of linear attacks and their extensions, and spreads the state of the art with novel features. Indispensable for all students and researchers interested in the subject, it will undoubtedly become an essential reference work.' Claude Carlet, University of Paris 8 and University of Bergen
'Vincent Rijmen and Tim Beyne have significantly advanced the field of linear cryptanalysis through their collaborative research. Their work has introduced innovative methodologies and deepened our understanding of cryptographic security.' Lars R. Knudsen, University of South Denmark
'The writing is clear, and the historic notes and exercises are great. This is a very nice book on cryptanalysis, which should be of interest to both novice and experienced cryptographers.' Carlos Cid, Simula UiB and Okinawa Institute of Science and Technology
'The initiative and effort of Prof. Tim Beyne and Prof. Vincent Rijmen to write the textbook on linear cryptanalysis is highly appreciated. This is timely and important. Cryptanalysis is a very important aspect of cryptology, and it all started with the introduction of linear cryptanalysis by Matsui. It has gained importance over time. The authors have made a comprehensive presentation on this subject. The book may be used as a text as well as a reference for advanced research. 'The main tool is correlation between two binary strings and its statistical analysis. The authors have handled all the issues thoroughly in such a way that it will be useful to both the beginners as well as the experts. In addition to a statistical approach, the authors have provided a geometric approach. 'I wish the book gets popular with the global crypto community, especially students and young researchers.' Bimal Kumar Roy, Indian Statistical Institute
Product details
November 2025Hardback
9781009607865
209 pages
229 × 152 mm
Not yet published - available from November 2025
Table of Contents
- Preface
- 1. Introduction
- 2. Correlation matrices
- 3. Optimization of linear trails
- 4. Statistics of linear cryptanalysis
- 5. Key-recovery techniques
- 6. Multiple linear cryptanalysis
- 7. Optimal statistical testing
- 8. Zero-correlation approximations
- 9. Miscellaneous extensions
- 10. Functions on Abelian groups
- 11. Geometric approach
- A. Normal distribution
- B. Statistical formulary
- C. List of block ciphers
- References
- Index.
