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Public-key Cryptography: Theory and Practice

Book Description

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.

Table of Contents

  1. Copyright
  2. Preface
  3. Notations
  4. Overview
    1. Introduction
    2. Common Cryptographic Primitives
    3. Public-key Cryptography
    4. Some Cryptographic Terms
    5. Chapter Summary
  5. Mathematical Concepts
    1. Introduction
    2. Sets, Relations and Functions
    3. Groups
    4. Rings
    5. Integers
    6. Polynomials
    7. Vector Spaces and Modules
    8. Fields
    9. Finite Fields
    10. Affine and Projective Curves
    11. Elliptic Curves
    12. Hyperelliptic Curves
    13. Number Fields
    14. p-adic Numbers
    15. Statistical Methods
    16. Chapter Summary
    17. Suggestions for Further Reading
  6. Algebraic and Number-theoretic Computations
    1. Introduction
    2. Complexity Issues
    3. Multiple-precision Integer Arithmetic
    4. Elementary Number-theoretic Computations
    5. Arithmetic in Finite Fields
    6. Arithmetic on Elliptic Curves
    7. Arithmetic on Hyperelliptic Curves
    8. Random Numbers
    9. Chapter Summary
    10. Suggestions for Further Reading
  7. The Intractable Mathematical Problems
    1. Introduction
    2. The Problems at a Glance
    3. The Integer Factorization Problem
    4. The Finite Field Discrete Logarithm Problem
    5. The Elliptic Curve Discrete Logarithm Problem (ECDLP)
    6. The Hyperelliptic Curve Discrete Logarithm Problem
    7. Solving Large Sparse Linear Systems over Finite Rings
    8. The Subset Sum Problem
    9. Chapter Summary
    10. Suggestions for Further Reading
  8. Cryptographic Algorithms
    1. Introduction
    2. Secure Transmission of Messages
    3. Key Exchange
    4. Digital Signatures
    5. Entity Authentication
    6. Chapter Summary
    7. Suggestions for Further Reading
  9. Standards
    1. Introduction
    2. IEEE Standards
    3. RSA Standards
    4. Chapter Summary
    5. Suggestions for Further Reading
  10. Cryptanalysis in Practice
    1. Introduction
    2. Side-Channel Attacks
    3. Backdoor Attacks
    4. Chapter Summary
    5. Suggestions for Further Reading
  11. Quantum Computation and Cryptography
    1. Introduction
    2. Quantum Computation
    3. Quantum Cryptography
    4. Quantum Cryptanalysis
    5. Chapter Summary
    6. Suggestions for Further Reading
  12. Appendices
    1. Symmetric Techniques
      1. Introduction
      2. Block Ciphers
      3. Stream Ciphers
      4. Hash Functions
    2. Key Exchange in Sensor Networks
      1. Introduction
      2. Security Issues in a Sensor Network
      3. The Basic Bootstrapping Framework
      4. The Basic Random Key Predistribution Scheme
      5. Random Pairwise Scheme
      6. Polynomial-pool-based Key Predistribution
      7. Matrix-based Key Predistribution
      8. Location-aware Key Predistribution
    3. Complexity Theory and Cryptography
      1. Introduction
      2. Provably Difficult Computational Problems Are not Suitable
      3. One-way Functions and the Complexity Class UP
    4. Hints to Selected Exercises
  13. References
  14. Index