Public-key cryptography : theory and practice

Public-key cryptography : theory and practice

"This book covers mathematical tools for understanding public-key cryptography and cryptanalysis. Key topics in the book include common cryptographic primitives and symmetric techniques, quantum cryptography, complexity theory, and practical cryptanalytic techniques."--Resource description...

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Detalles Bibliográficos
Otros Autores: Das, Abhijit Author (author), Madhavan, C. E. Veni Contributor (contributor)
Formato: Libro electrónico
Idioma:Inglés
Publicado: [Place of publication not identified] Pearson Education 2009
Edición:1st edition
Materias:
Public key cryptography > Mathematics > Security measures
Telecommunication > Mathematics > Access control
Computers
Telecommunications
Electrical & Computer Engineering
Engineering & Applied Sciences
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628347606719
Tabla de Contenidos:
  • Cover
  • Public-key CryptographyTheory and Practice
  • Copyright
  • Contents
  • Preface
  • Notations
  • Overview
  • Introduction
  • Common Cryptographic Primitives
  • The Classical Problem: Secure Transmission of Messages
  • Key Exchange
  • Digital Signatures
  • Entity Authentication
  • Secret Sharing
  • Hashing
  • Certification
  • Public-key Cryptography
  • The Mathematical Problems
  • Realization of Key Pairs
  • Public-key Cryptanalysis
  • Some Cryptographic Terms
  • Models of Attacks
  • Models of Passive Attacks
  • Public Versus Private Algorithms
  • Mathematical Concepts
  • Introduction
  • Sets, Relations and Functions
  • Set Operations
  • Relations
  • Functions
  • The Axioms of Mathematics
  • Groups
  • Definition and Basic Properties
  • Subgroups, Cosets and Quotient Groups
  • Homomorphisms
  • Generators and Orders
  • Sylow's Theorem
  • Rings
  • Definition and Basic Properties
  • Subrings, Ideals and Quotient Rings
  • Homomorphisms
  • Factorization in Rings
  • Integers
  • Divisibility
  • Congruences
  • Quadratic Residues
  • Some Assorted Topics
  • Polynomials
  • Elementary Properties
  • Roots of Polynomials
  • Algebraic Elements and Extensions
  • Vector Spaces and Modules
  • Vector Spaces
  • Modules
  • Algebras
  • Fields
  • Splitting Fields and Algebraic Closure
  • Elements of Galois Theory
  • Finite Fields
  • Existence and Uniqueness of Finite Fields
  • Polynomials over Finite Fields
  • Representation of Finite Fields
  • Affine and Projective Curves
  • Plane Curves
  • Polynomial and Rational Functions on Plane Curves
  • Maps Between Plane Curves
  • Divisors on Plane Curves
  • Elliptic Curves
  • The Weierstrass Equation
  • The Elliptic Curve Group
  • Elliptic Curves over Finite Fields
  • Hyperelliptic Curves
  • The Defining Equations
  • Polynomial and Rational Functions
  • The Jacobian
  • Number Fields
  • Some Commutative Algebra.
  • Number Fields and Rings
  • Unique Factorization of Ideals
  • Norms of Ideals
  • Rational Primes in Number Rings
  • Units in a Number Ring
  • p-adic Numbers
  • The Arithmetic of p-adic Numbers
  • The p-adic Valuation
  • Hensel's Lemma
  • Statistical Methods
  • Random Variables and Their Probability Distributions
  • Operations on Random Variables
  • Expectation, Variance and Correlation
  • Some Famous Probability Distributions
  • Sample Mean, Variation and Correlation
  • Algebraic and Number-theoretic Computations
  • Introduction
  • Complexity Issues
  • Order Notations
  • Randomized Algorithms
  • Reduction Between Computational Problems
  • Multiple-precision Integer Arithmetic
  • Representation of Large Integers
  • Basic Arithmetic Operations
  • GCD
  • Modular Arithmetic
  • Elementary Number-theoretic Computations
  • Primality Testing
  • Generating Random Primes
  • Modular Square Roots
  • Arithmetic in Finite Fields
  • Arithmetic in the Ring F2[X]
  • Finite Fields of Characteristic 2
  • Selecting Suitable Finite Fields
  • Factoring Polynomials over Finite Fields
  • Arithmetic on Elliptic Curves
  • Point Arithmetic
  • Counting Points on Elliptic Curves
  • Choosing Good Elliptic Curves
  • Arithmetic on Hyperelliptic Curves
  • Arithmetic in the Jacobian
  • Counting Points in Jacobians of Hyperelliptic Curves
  • Random Numbers
  • Pseudorandom Bit Generators
  • Cryptographically Strong Pseudorandom Bit Generators
  • Seeding Pseudorandom Bit Generators
  • The Intractable Mathematical Problems
  • Introduction
  • The Problems at a Glance
  • The Integer Factorization Problem
  • Older Algorithms
  • The Quadratic Sieve Method
  • Factorization Using Elliptic Curves
  • The Number Field Sieve Method
  • The Finite Field Discrete Logarithm Problem
  • Square Root Methods
  • The Index Calculus Method
  • Algorithms for Prime Fields.
  • Algorithms for Fields of Characteristic 2
  • The Elliptic Curve Discrete Logarithm Problem (ECDLP)
  • The MOV Reduction
  • The SmartASS Method
  • The Xedni Calculus Method
  • The Hyperelliptic Curve Discrete Logarithm Problem
  • Choosing the Factor Base
  • Checking the Smoothness of a Divisor
  • The Algorithm
  • Solving Large Sparse Linear Systems over Finite Rings
  • Structured Gaussian Elimination
  • The Conjugate Gradient Method
  • The Lanczos Method
  • The Wiedemann Method
  • The Subset Sum Problem
  • The Low-Density Subset Sum Problem
  • The Lattice-Basis Reduction Algorithm
  • Cryptographic Algorithms
  • Introduction
  • Secure Transmission of Messages
  • The RSA Public-key Encryption Algorithm
  • The Rabin Public-key Encryption Algorithm
  • The Goldwasser-Micali Encryption Algorithm
  • The Blum-Goldwasser Encryption Algorithm
  • The ElGamal Public-key Encryption Algorithm
  • The Chor-Rivest Public-key Encryption Algorithm
  • The XTR Public-key Encryption Algorithm
  • The NTRU Public-key Encryption Algorithm
  • Key Exchange
  • Basic Key-Exchange Protocols
  • Authenticated Key-Exchange Protocols
  • Digital Signatures
  • The RSA Digital Signature Algorithm
  • The Rabin Digital Signature Algorithm
  • The ElGamal Digital Signature Algorithm
  • The Schnorr Digital Signature Algorithm
  • The Nyberg-Rueppel Digital Signature Algorithm
  • The Digital Signature Algorithm
  • The Elliptic Curve Digital Signature Algorithm
  • The XTR Signature Algorithm
  • The NTRUSign Algorithm
  • Blind Signature Schemes
  • Undeniable Signature Schemes
  • Signcryption
  • Entity Authentication
  • Passwords
  • Challenge-Response Algorithms
  • Zero-Knowledge Protocols
  • Standards
  • Introduction
  • IEEE Standards
  • The Data Types
  • Conversion Among Data Types
  • RSA Standards
  • PKCS #1
  • PKCS #3
  • Cryptanalysis in Practice
  • Introduction
  • Side-Channel Attacks.
  • Timing Attack
  • Power Analysis
  • Fault Analysis
  • Backdoor Attacks
  • Attacks on RSA
  • An Attack on ElGamal Signatures
  • An Attack on ElGamal Encryption
  • Countermeasures
  • Quantum Computation and Cryptography
  • Introduction
  • Quantum Computation
  • System
  • Entanglement
  • Evolution
  • Measurement
  • The Deutsch Algorithm
  • Quantum Cryptography
  • Quantum Cryptanalysis
  • Shor's Algorithm for Computing Period
  • Breaking RSA
  • Factoring Integers
  • Computing Discrete Logarithms
  • Symmetric Techniques
  • Introduction
  • Block Ciphers
  • A Case Study: DES
  • The Advanced Standard: AES
  • Multiple Encryption
  • Modes of Operation
  • Stream Ciphers
  • Linear Feedback Shift Registers
  • Stream Ciphers Based on LFSRs
  • Hash Functions
  • Merkle's Meta Method
  • The Secure Hash Algorithm
  • Key Exchange in Sensor Networks
  • Complexity Theory and Cryptography
  • Introduction
  • Provably Difficult Computational Problems Are not Suitable
  • One-way Functions and the Complexity Class UP
  • Introduction
  • Security Issues in a Sensor Network
  • The Basic Bootstrapping Framework
  • The Basic Random Key Predistribution Scheme
  • The q-composite Scheme
  • Multi-path Key Reinforcement
  • Random Pairwise Scheme
  • Multi-hop Range Extension
  • Polynomial-pool-based Key Predistribution
  • Pairwise Key Predistribution
  • Grid-based Key Predistribution
  • Matrix-based Key Predistribution
  • Location-aware Key Predistribution
  • Closest Pairwise Keys Scheme
  • Location-aware Polynomial-pool-based Scheme
  • Complexity Theoryand Cryptography
  • Hints to Selected Exercises
  • References
  • Index.

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