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