An Introduction to Mathematical Cryptography / Joseph H. Silverman (2008)  

Público ISBD Título : An Introduction to Mathematical Cryptography Tipo de documento: documento electrónico Autores: Joseph H. Silverman ; SpringerLink (Online service) ; Jill Pipher ; Jeffrey Hoffstein Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XVI, 524 p. 29 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-77994-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Data  structures  (Computer  science)  encryption  Coding  theory  Algebra  Ordered  algebraic  Information  Number  Theory  and  Structures,  Cryptology  Encryption  Communication,  Circuits  Order,  Lattices,  Algebraic  Structures Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241 An Introduction to Mathematical Cryptography [documento electrónico] / Joseph H. Silverman ; SpringerLink (Online service) ; Jill Pipher ; Jeffrey Hoffstein . - New York, NY : Springer New York, 2008 . - XVI, 524 p. 29 illus : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) . ISBN : 978-0-387-77994-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Data  structures  (Computer  science)  encryption  Coding  theory  Algebra  Ordered  algebraic  Information  Number  Theory  and  Structures,  Cryptology  Encryption  Communication,  Circuits  Order,  Lattices,  Algebraic  Structures Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241

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The Arithmetic of Dynamical Systems / Joseph H. Silverman (2007)  

Público ISBD Título : The Arithmetic of Dynamical Systems Tipo de documento: documento electrónico Autores: Joseph H. Silverman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 241 Número de páginas: XVI, 511 p. 11 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-69904-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Data  structures  (Computer  science)  Dynamics  Ergodic  theory  Dynamical  Systems  and  Theory  Structures Clasificación: 51 Matemáticas Resumen: This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures. Key features: - Provides an entry for graduate students into an active field of research - Provides a standard reference source for researchers - Includes numerous exercises and examples - Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index This graduate-level text assumes familiarity with basic algebraic number theory. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, and the theory of Diophantine approximation, are introduced and referenced as needed. Mathematicians and graduate students will find this text to be an excellent reference Nota de contenido: An Introduction to Classical Dynamics -- Dynamics over Local Fields: Good Reduction -- Dynamics over Global Fields -- Families of Dynamical Systems -- Dynamics over Local Fields: Bad Reduction -- Dynamics Associated to Algebraic Groups -- Dynamics in Dimension Greater Than One En línea: http://dx.doi.org/10.1007/978-0-387-69904-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34517 The Arithmetic of Dynamical Systems [documento electrónico] / Joseph H. Silverman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XVI, 511 p. 11 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 241) . ISBN : 978-0-387-69904-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Data  structures  (Computer  science)  Dynamics  Ergodic  theory  Dynamical  Systems  and  Theory  Structures Clasificación: 51 Matemáticas Resumen: This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures. Key features: - Provides an entry for graduate students into an active field of research - Provides a standard reference source for researchers - Includes numerous exercises and examples - Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index This graduate-level text assumes familiarity with basic algebraic number theory. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, and the theory of Diophantine approximation, are introduced and referenced as needed. Mathematicians and graduate students will find this text to be an excellent reference Nota de contenido: An Introduction to Classical Dynamics -- Dynamics over Local Fields: Good Reduction -- Dynamics over Global Fields -- Families of Dynamical Systems -- Dynamics over Local Fields: Bad Reduction -- Dynamics Associated to Algebraic Groups -- Dynamics in Dimension Greater Than One En línea: http://dx.doi.org/10.1007/978-0-387-69904-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34517

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The Arithmetic of Elliptic Curves / Joseph H. Silverman (2009)  

Público ISBD Título : The Arithmetic of Elliptic Curves Tipo de documento: documento electrónico Autores: Joseph H. Silverman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 106 Número de páginas: XX, 514 p. 14 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-09494-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Algebraic  geometry  Number  theory  Geometry  Theory Clasificación: 51 Matemáticas Resumen: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell–Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics Nota de contenido: Algebraic Varieties -- Algebraic Curves -- The Geometry of Elliptic Curves -- The Formal Group of an Elliptic Curve -- Elliptic Curves over Finite Fields -- Elliptic Curves over C -- Elliptic Curves over Local Fields -- Elliptic Curves over Global Fields -- Integral Points on Elliptic Curves -- Computing the Mordell#x2013;Weil Group -- Algorithmic Aspects of Elliptic Curves En línea: http://dx.doi.org/10.1007/978-0-387-09494-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33820 The Arithmetic of Elliptic Curves [documento electrónico] / Joseph H. Silverman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2009 . - XX, 514 p. 14 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 106) . ISBN : 978-0-387-09494-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Algebraic  geometry  Number  theory  Geometry  Theory Clasificación: 51 Matemáticas Resumen: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell–Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics Nota de contenido: Algebraic Varieties -- Algebraic Curves -- The Geometry of Elliptic Curves -- The Formal Group of an Elliptic Curve -- Elliptic Curves over Finite Fields -- Elliptic Curves over C -- Elliptic Curves over Local Fields -- Elliptic Curves over Global Fields -- Integral Points on Elliptic Curves -- Computing the Mordell#x2013;Weil Group -- Algorithmic Aspects of Elliptic Curves En línea: http://dx.doi.org/10.1007/978-0-387-09494-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33820

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