Textbook in PDF format Applications 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. If you study this book with care, you can expect to obtain a solid understanding of the basic theory of linear cryptanalysis, and familiarity with its most important extensions (multiple and multidimensional linear cryptanalysis, zero-correlation linear cryptanalysis... ). If you also diligently complete the exercises, you will be able to apply this knowledge in practice. In due time, you will have no trouble understanding the current literature. Nevertheless, in a book of this length, it is impossible to provide a complete overview of all related work, or even to reference all of it. The focus is decidedly on core cryptanalytic results, with many important but tangential topics (such as connections with linear codes, Boolean functions... ) deferred to the exercises. Most of the examples and exercises are related to block ciphers, but we expect that you will be able to apply linear cryptanalysis to other cryptographic primitives, such as stream ciphers, when you encounter them. Preface Introduction Correlation matrices Optimization of linear trails Statistics of linear cryptanalysis Key-recovery techniques Multiple linear cryptanalysis Optimal statistical testing Zero-correlation approximations Miscellaneous extensions Functions on Abelian groups Geometric approach Appendix A Normal distribution A.1 Univariate normal distribution A.2 Multivariate normal distribution Appendix B Statistical formulary Appendix C List of block ciphers