Materias:

“…Key Topics and Features: * Solid introduction to analytic number theory, including full proofs of Dirichlet’s Theorem and the Prime Number Theorem * Solid treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals * First treatment in book form of the AKS algorithm that shows that primality testing is of polynomial time * Many interesting side topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The book’s user-friendly style, historical context, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) make it ideal for self study as well as classroom use. …”

Tabla de Contenidos: “…Intro -- Table of Contents -- About the Authors -- About the Technical Reviewer -- Chapter 1: Getting Started in Cryptography and Cryptanalysis -- Cryptography and Cryptanalysis -- Book Structure -- Conclusion -- References -- Chapter 2: MATLAB Cryptography Functions -- Conclusion -- References -- Chapter 3: Conversions Used in MATLAB for Cryptography -- Conclusion -- References -- Chapter 4: Basic Arithmetic Foundations -- Euclid's Division Lemma -- Greatest Common Divisor (gcd) -- Euclid's Algorithm -- The Extended Euclidean Algorithm -- Practical Implementations -- The Extended Euclidean Algorithm -- Prime Factors in MATLAB -- Computing the Modular Inverse -- Conclusion -- References -- Chapter 5: Number Theory -- Primality and Factorization -- Prime Numbers -- The Prime Number Theorem -- Congruency -- Inverse -- Chinese Remainder Theorem -- Primality Tests -- The Wilson Primality Test -- The Little Fermat Primality Test -- The Miller-Rabin Primality Test -- Algebraic Structures -- Conclusion -- References -- Chapter 6: Classic Cryptography -- Symmetric Cryptography -- Classic Ciphers -- The Caesar Cipher -- Example -- Mathematical Background -- Cryptanalysis -- Implementing the Caesar Cipher -- The Vigenère Cipher -- Example -- Mathematical Background -- Implementing the Vigenère Cipher -- The Hill Cipher -- Example -- Cryptanalysis -- Implementing the Hill Cipher -- Conclusion -- References -- Chapter 7: Pseudo-Random Number Generators -- Simple PRNGs -- Linear Congruential Generators -- Ranrot Generators -- Blum-Blum-Shub Generator -- Linear Circuit PRNGs -- Other PRNGs -- Practical Implementations -- Conclusion -- References -- Chapter 8: Hash Functions -- Security of Hash Functions -- Cryptographic Hash Functions -- Birthday Attack -- MD4 Function -- MD4 Function Description -- Cryptanalysis of MD4 -- MD5 Function -- SHA1 Function…”

Tabla de Contenidos: “…8 Prime Numbers 8.1 Prime Number Generators; 8.2 The Prime Number Theorem; 8.3 Products of Geometric Series; 8.4 The Riemann Zeta Function; 8.5 Real Numbers; 9 Logic and Meta-Mathematics; 9.1 The Collection of All Sets; 9.2 Other Than True or False; 9.3 The Logic of A Theory of Everything; 9.3.1 Gödel's Incompleteness Theorem; 9.3.2 Logically Closed Sets; 9.3.3 Applications; Bibliography; Index…”

Tabla de Contenidos: “…Arithmetic -- 2.1 Place value and decimals: basic structure -- 2.2 Order and factors -- 2.3 Standard written algorithms -- 2.4 Divisibility tests -- 2.5 Sequences -- 2.6 Commutative, associative and distributive laws -- 2.7 Infinite decimal expansions -- 2.8 The binary numeral system -- 2.9 The Prime Number Theorem -- 2.10 Chapter 2: Comments and solutions -- III. …”