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This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Computer science. --- Computer security. --- Data structures (Computer science). --- Number theory. --- Quantum field theory. --- String theory. --- Quantum physics. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Data Structures, Cryptology and Information Theory. --- Systems and Data Security. --- Appl.Mathematics/Computational Methods of Engineering. --- Number Theory. --- Quantum Field Theories, String Theory. --- Quantum Physics. --- Engineering --- Engineering analysis --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Models, String --- String theory --- Relativistic quantum field theory --- Number study --- Numbers, Theory of --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Informatics --- Computer privacy --- Computer system security --- Computer systems --- Computers --- Cyber security --- Cybersecurity --- Electronic digital computers --- Protection of computer systems --- Security of computer systems --- Mathematics --- Protection --- Security measures --- Mathematical analysis --- Physics --- Mechanics --- Thermodynamics --- Nuclear reactions --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Algebra --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Data protection --- Security systems --- Hacking --- Science --- Cryptography --- Mathematical models. --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data structures (Computer scienc. --- Quantum theory. --- Data Structures and Information Theory. --- Mathematical and Computational Engineering.

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Mathematical control systems --- Mathematics --- Applied physical engineering --- Engineering sciences. Technology --- Information systems --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- quantumcomputers --- economie --- informatica --- informatietechnologie --- wiskunde --- computerbeveiliging --- ingenieurswetenschappen --- informatietheorie

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This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis - Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.

Casimir effect --- Research --- Research, Industrial --- Technological innovations --- Breakthroughs, Technological --- Innovations, Industrial --- Innovations, Technological --- Technical innovations --- Technological breakthroughs --- Technological change --- Creative ability in technology --- Inventions --- Domestication of technology --- Innovation relay centers --- Technology transfer --- Contract research --- Industrial research --- Engineering experiment stations --- Science --- Science research --- Scientific research --- Information services --- Learning and scholarship --- Methodology --- Research teams --- Casimir force --- Casimir forces --- Effect, Casimir --- Force, Casimir --- Electric fields --- Vacuum polarization --- Zero-point field --- Mathematical models --- Fukuoka <2009> --- Casimir Operators. --- Mathematical Biology. --- Mathematics in Industry. --- Number Theory.