Mathematical foundations of public key cryptography. (2015)

• Record Type: Book
• Further Information: Note: Xiaoyun Wang, Guangwu Xu, Mingqiang Wang, Xianmeng Meng.
• Authors: Wang, Xiaoyun, 1966-; Xu, Guangwu; Wang, Mingqiang; Meng, Xianmeng
• Contents: Divisibility of Integers; The Concept of Divisibility; The Greatest Common Divisor and The Least Common Multiple; The Euclidean Algorithm; Solving Linear Diophantine Equations; Prime Factorization of Integers; ; Congruences; Residue Classes and Systems of Residues; Euler’s Theorem; Wilson’s Theorem; ; Congruence Equations; Basic Concepts of Congruences of High Degrees; Linear Congruences; Systems of Linear Congruence Equations and the Chinese Remainder Theorem; General Congruence Equations; Quadratic Residues; The Legendre Symbol and the Jacobi Symbol; ; Exponents and Primitive Roots; Exponents and Their Properties; Primitive Roots and Their Properties; Indices, Construction of Reduced System of Residues; N th Power Residues; ; Some Elementary Results for Prime Distribution ; Introduction to the Basic Properties of Primes and The Main Results of Prime Number Distribution; Proof of the Euler Product Formula; Proof of a Weaker Version of the Prime Number Theorem; Equivalent Statements of the Prime Number Theorem; ; Simple Continued Fractions; Simple Continued Fractions and Their Basic Properties; Simple Continued Fraction Representations of Real Numbers; Application of Continued Fraction In Cryptography—Attack to RSA with Small Decryption Exponents; ; Basic Concepts; Maps; Algebraic Operations; Homomorphisms and Isomorphisms between Sets with Operations; Equivalence Relations and Partitions; ; Group Theory; Definitions; Cyclic Groups; Subgroups and Cosets; Fundamental Homomorphism Theorem; Concrete Examples of Finite Groups; ; Rings and Fields; Definition of a Ring; Integral Domains, Fields, and Division Rings; Subrings, Ideals, and Ring Homomorphisms; Chinese Remainder Theorem; Euclidean Rings; Finite Fields; Field of Fractions; ; Some Mathematical Problems in Public Key Cryptography ; Time Estimation and Complexity of Algorithms; Integer Factorization Problem; Primality Tests; The RSA Problem and the Strong RSA Problem; Quadratic Residues; The Discrete Logarithm Problem; ; Basics of Lattices; Basic Concepts; Shortest Vector Problem; Lattice Basis Reduction Algorithm; Applications of LLL Algorithm; ; References ; ; Further Reading ; ; Index
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 005.82; Public key cryptography -- Mathematics
• Languages: English
• ISBNs: 9781498702249
• Related ISBNs: 9781498702232
• Notes: Note: Description based on CIP data; item not viewed.
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