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This text is intended for a one-semester course in cryptography at the advanced undergraduate/Master's degree level. It is suitable for students from various STEM backgrounds, including engineering, mathematics, and computer science, and may also be attractive for researchers and professionals who want to learn the basics of cryptography. Advanced knowledge of computer science or mathematics (other than elementary programming skills) is not assumed. The book includes more material than can be covered in a single semester. The Preface provides a suggested outline for a single semester course, though instructors are encouraged to select their own topics to reflect their specific requirements and interests. Each chapter contains a set of carefully written exercises which prompts review of the material in the chapter and expands on the concepts. Throughout the book, problems are stated mathematically, then algorithms are devised to solve the problems. Students are tasked to write computer programs (in C++ or GAP) to implement the algorithms. The use of programming skills to solve practical problems adds extra value to the use of this text. This book combines mathematical theory with practical applications to computer information systems. The fundamental concepts of classical and modern cryptography are discussed in relation to probability theory, complexity theory, modern algebra, and number theory. An overarching theme is cyber security: security of the cryptosystems and the key generation and distribution protocols, and methods of cryptanalysis (i.e., code breaking). It contains chapters on probability theory, information theory and entropy, complexity theory, and the algebraic and number theoretic foundations of cryptography. The book then reviews symmetric key cryptosystems, and discusses one-way trap door functions and public key cryptosystems including RSA and ElGamal. It contains a chapter on digital signature schemes, including material on message authentication and forgeries, and chapters on key generation and distribution. It contains a chapter on elliptic curve cryptography, including new material on the relationship between singular curves, algebraic groups and Hopf algebras.

Number theory --- Ergodic theory. Information theory --- Mathematical control systems --- coderen --- getallenleer --- informatietheorie --- Cryptography. --- Data encryption (Computer science) --- Xifratge (Informàtica) --- Criptografia

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Xifratge (Informàtica) --- Criptografia --- Escriptura --- Símbols --- Escriptura secreta --- Protecció de dades --- Seguretat informàtica --- Signatures electròniques --- Generadors de nombres aleatoris --- Nombres primers --- Criptografia (Informàtica) --- Criptografia (Matemàtica) --- Criptologia --- Encriptació (Informàtica) --- Encriptació de dades (Informàtica) --- Esteganografia --- Llenguatges xifrats --- Xifratge de dades (Informàtica) --- Cryptography. --- Data encryption (Computer science) --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers

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Public key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more.

Coding theory --- Cryptography --- Codage --- Cryptographie --- Mathematics --- Mathématiques --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Mathématiques --- Mathematics. --- Coding theory. --- Codificació, Teoria de la. --- Criptografia --- Matemàtica. --- Escriptura secreta --- Escriptura xifrada --- Esteganografia --- Escriptura --- Simbolisme --- Símbols --- Xifratge (Informàtica) --- Xifres i claus --- Teoria de la codificació --- Dades --- Electrònica digital --- Informació, Teoria de la --- Màquines, Teoria de --- Senyal, Teoria del (Telecomunicació) --- Programació (Ordinadors) --- Compressió (Informàtica) --- Compressió (Telecomunicació) --- Teoria de la informació --- Compressió de dades (Telecomunicació) --- Compressió de dades (Informàtica)

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Computational intelligence. --- Engineering --- Data processing. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Cibernètica --- Seguretat informàtica --- Protecció de dades --- Protecció de dades personals --- Protecció de la informació (Informàtica) --- Regulació de dades --- Processament de dades --- Xifratge (Informàtica) --- Delegats de protecció de dades --- Dret a l'oblit --- Identitat digital --- Informàtica (Seguretat) --- Mesures de seguretat (Informàtica) --- Seguretat (Informàtica) --- Seguretat dels sistemes informàtics --- Sistemes de seguretat --- Control d'accés als ordinadors --- Seguretat de les xarxes d'ordinadors --- Pirates informàtics --- Automàtica --- Cervells electrònics --- Comunicació --- Electrònica --- Anàlisi de sistemes --- Biònica --- Control automàtic --- Ordinadors --- Robòtica --- Sistemes autoorganitzatius --- Sistemes de control biològic --- Teoria de la informació --- Xarxes neuronals (Informàtica)

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This book presents the leading models of social network diffusion that are used to demonstrate the spread of disease, ideas, and behavior. It introduces diffusion models from the fields of computer science (independent cascade and linear threshold), sociology (tipping models), physics (voter models), biology (evolutionary models), and epidemiology (SIR/SIS and related models). A variety of properties and problems related to these models are discussed including identifying seeds sets to initiate diffusion, game theoretic problems, predicting diffusion events, and more. The book explores numerous connections between social network diffusion research and artificial intelligence through topics such as agent-based modeling, logic programming, game theory, learning, and data mining. The book also surveys key empirical results in social network diffusion, and reviews the classic and cutting-edge research with a focus on open problems.

Intel·ligència artificial --- Xifratge (Informàtica) --- Xarxes socials en línia --- Artificial intelligence. --- Data encryption (Computer science). --- Artificial Intelligence. --- Cryptology. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Comunitats virtuals --- Xarxes socials per Internet --- Xarxes socials virtuals --- Xarxes socials (Internet) --- Mitjans de comunicació social --- Pàgines web --- Xarxes socials --- Dades --- Encriptació (Informàtica) --- Encriptació de dades (Informàtica) --- Criptografia --- Protecció de dades --- Seguretat informàtica --- Biònica --- Ciència cognitiva --- Informàtica --- Màquines, Teoria de --- Ordinadors neuronals --- Simulació, Mètodes de --- Sistemes autoorganitzatius --- Vida artificial