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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. Other sections are suitable for advanced undergraduate or graduate courses. Many exercises are included. The emphasis is on providing a (reasonably) complete explanation of the background for some selected systems. < Joachim von zur Gathen has held professorships at the universities of Toronto, Paderborn, and Bonn, each for more than a decade. He is now retired (and active). His numerous visiting professorships were in Australia, Chile, Germany, South Africa, Spain, Switzerland, Uruguay, and USA. He is founder and was editor-in-chief for 25 years of the journal computational complexity, and was on the editorial boards of several other journals. He is listed in various editions of Who's Who in the World.

Numerical solutions of algebraic equations --- Information systems --- Computer. Automation --- cryptografie --- cryptologie

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Mathematical control systems --- Engineering sciences. Technology --- Numerical solutions of differential equations --- Numerical methods of optimisation --- Boundary element methods --- Engineering mathematics --- Equations intégrales de frontière, Méthodes des --- Mathématiques de l'ingénieur --- Periodicals --- Périodiques --- Équations intégrales de frontière, Méthodes des --- Mathématiques de l'ingénieur --- #TS:TCON --- Engineering --- General and Others --- Civil Engineering --- Engineering. --- General and Others.

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This graduate-level text provides an application oriented introduction to the numerical methods for elliptic and parabolic partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises. For students with mathematics major it is an excellent introduction to the theory and methods, guiding them in the selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it provides a general framework for the formulation and analysis of methods. This second edition sees additional chapters on mixed discretization and on generalizing and unifying known approaches; broader applications on systems of diffusion, convection and reaction; enhanced chapters on node-centered finite volume methods and methods of convection-dominated problems, specifically treating the now-popular cell-centered finite volume method; and the consideration of realistic formulations beyond the Poisson's equation for all models and methods.

Mathematical analysis --- Numerical analysis --- Mathematics --- Mathematical physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- analyse (wiskunde) --- toegepaste wiskunde --- theoretische fysica --- economie --- informatica --- wiskunde --- ingenieurswetenschappen --- fysica --- numerieke analyse --- Differential equations, Partial --- Equacions en derivades parcials --- Solucions numèriques --- Numerical solutions.