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This book covers public-key cryptography, describing in depth all major public-key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It explains the underlying mathematics needed to build these schemes, and examines the most common techniques used in attacking them. Illustrated with many examples, the book provides a solid foundation for professionals in government, cloud service providers, and large enterprises using public-key systems to secure their data. It is also useful for those taking the CISSP exam (Certified Information Systems Secur

Public key cryptography. --- Cryptography --- Mathematics. --- Public key cryptography --- Cryptography -- Mathematics

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This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

Computer science --- Cryptography --- Cryptographie --- Mathematics. --- Mathématiques --- Mathematics --- Coding theory. --- Cryptography --Mathematics. --- Coding theory --- Education --- Social Sciences --- Physical Sciences & Mathematics --- Algebra --- Book Studies & Arts --- Signs and symbols. --- Mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Representation, Symbolic --- Semeiotics --- Signs --- Symbolic representation --- Symbols --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Data structures (Computer science). --- Data encryption (Computer science). --- Algebra. --- Ordered algebraic structures. --- Information theory. --- Number theory. --- Number Theory. --- Coding and Information Theory. --- Data Structures, Cryptology and Information Theory. --- Data Encryption. --- Information and Communication, Circuits. --- Order, Lattices, Ordered Algebraic Structures. --- Abbreviations --- Omens --- Semiotics --- Sign language --- Symbolism --- Visual communication --- Signs and symbols --- Writing --- Ciphers --- Data encryption (Computer science) --- Data structures (Computer scienc. --- Data Structures and Information Theory. --- Cryptology. --- Data structures (Computer science) --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Mathematical analysis --- Math --- Science --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Number study --- Numbers, Theory of --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Communication theory --- Communication --- Cybernetics --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Cryptography - Mathematics

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The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

Cryptography -- Mathematics. --- Euclidean algorithm. --- Integer programming. --- Lattice theory. --- Cryptography --- Lattice theory --- Integer programming --- Euclidean algorithm --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Algorithms. --- Mathematics. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Algorism --- Computer science. --- Data structures (Computer science). --- Data encryption (Computer science). --- Computer science --- Computer Science. --- Data Structures. --- Data Encryption. --- Mathematics of Computing. --- Data Structures, Cryptology and Information Theory. --- Algorithm Analysis and Problem Complexity. --- Algebra --- Arithmetic --- Foundations --- Algorithms --- Number theory --- Programming (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data structures (Computer scienc. --- Computer software. --- Cryptology. --- Data Structures and Information Theory. --- Informatics --- Science --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Artificial intelligence --- Cryptography. --- Information theory. --- Data Science. --- Data processing. --- Communication theory --- Communication --- Cybernetics --- Computer mathematics