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Public-key cryptography : theory and practice
- Format:
- Book
- Author/Creator:
- Das, Abhijit, Author.
- Language:
- English
- Subjects (All):
- Public key cryptography--Mathematics--Security measures.
- Public key cryptography.
- Telecommunication--Mathematics--Access control.
- Telecommunication.
- Computers.
- Physical Description:
- 1 online resource (xxii, 562 p.) : ill.
- Edition:
- 1st edition
- Place of Publication:
- [Place of publication not identified] Pearson Education 2009
- Language Note:
- English
- System Details:
- text file
- Summary:
- "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 page.
- Contents:
- 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
- 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
- Subrings, Ideals and Quotient Rings
- 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
- 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
- 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
- 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
- Basic Key-Exchange Protocols
- Authenticated Key-Exchange Protocols
- 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
- Passwords
- Challenge-Response Algorithms
- Zero-Knowledge Protocols
- Standards
- IEEE Standards
- The Data Types
- Conversion Among Data Types
- RSA Standards
- PKCS #1
- PKCS #3
- Cryptanalysis in Practice
- 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
- 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
- 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
- Provably Difficult Computational Problems Are not Suitable
- One-way Functions and the Complexity Class UP
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references (p. 531-546) and index.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 9786612652271
- 9788131742105
- 8131742105
- 9781282652279
- 1282652273
- OCLC:
- 816564851
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