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Introduction to Cryptography with Coding Theory, 3rd edition

  • Wade Trappe
  • , Lawrence C. Washington

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Introduction to Cryptography with Coding Theory explores a broad spectrum of cryptography topics, covered from a mathematical point of view. In a lively and conversational tone, the authors mix applied and theoretical aspects to build the solid foundation in cryptography and security that is essential for your cryptography, network security or computer security course. Relevant examples and exercises enable you to apply course concepts. Practical applications provide hands-on experience with the large-numbered cryptography of today's security systems, along with a discussion of security protocols. Extensively revised and updated, the 3rd Edition reflects trends in the rapidly changing field of cryptography, such as cryptocurrency.

Published by Pearson (May 1st 2020) - Copyright © 2021

ISBN-13: 9780135260166

Subject: Advanced Math

Category: Cryptography

  1. Overview of Cryptography and Its Applications
    • 1.1 Secure Communications
    • 1.2 Cryptographic Applications
  2. Classical Cryptosystems
    • 2.1 Shift Ciphers
    • 2.2 Affine Ciphers
    • 2.3 The VigenÈre Cipher
    • 2.4 Substitution Ciphers
    • 2.5 Sherlock Holmes
    • 2.6 The Playfair and ADFGX Ciphers
    • 2.7 Enigma
    • 2.8 Exercises
    • 2.9 Computer Problems
  3. Basic Number Theory
    • 3.1 Basic Notions
    • 3.2 The Extended Euclidean Algorithm
    • 3.3 Congruences
    • 3.4 The Chinese Remainder Theorem
    • 3.5 Modular Exponentiation
    • 3.6 Fermat and Euler
    • 3.7 Primitive Roots
    • 3.8 Inverting Matrices Mod n
    • 3.9 Square Roots Mod n
    • 3.10 Legendre and Jacobi Symbols
    • 3.11 Finite Fields
    • 3.12 Continued Fractions
    • 3.13 Exercises
    • 3.14 Computer Problems
  4. The One-Time Pad
    • 4.1 Binary Numbers and ASCII
    • 4.2 One-Time Pads
    • 4.3 Multiple Use of a One-Time Pad
    • 4.4 Perfect Secrecy of the One-Time Pad
    • 4.5 Indistinguishability and Security
    • 4.6 Exercises
  5. Stream Ciphers
    • 5.1 Pseudo-Random Bit Generation
    • 5.2 LFSR Sequences
    • 5.3 RC4
    • 5.4 Exercises
    • 5.5 Computer Problems
  6. Block Ciphers
    • 6.1 Block Ciphers
    • 6.2 Hill Ciphers
    • 6.3 Modes of Operation
    • 6.4 Multiple Encryption
    • 6.5 Meet-in-the-Middle Attacks
    • 6.6 Exercises
    • 6.7 Computer Problems
  7. The Data Encryption Standard
    • 7.1 Introduction
    • 7.2 A Simplified DES-Type Algorithm
    • 7.3 Differential Cryptanalysis
    • 7.4 DES
    • 7.5 Breaking DES
    • 7.6 Password Security
    • 7.7 Exercises
    • 7.8 Computer Problems
  8. The Advanced Encryption Standard: Rijndael
    • 8.1 The Basic Algorithm
    • 8.2 The Layers
    • 8.3 Decryption
    • 8.4 Design Considerations
    • 8.5 Exercises
  9. The RSA Algorithm
    • 9.1 The RSA Algorithm
    • 9.2 Attacks on RSA
    • 9.3 Primality Testing
    • 9.4 Factoring
    • 9.5 The RSA Challenge
    • 9.6 An Application to Treaty Verification
    • 9.7 The Public Key Concept
    • 9.8 Exercises
    • 9.9 Computer Problems
  10. Discrete Logarithms
    • 10.1 Discrete Logarithms
    • 10.2 Computing Discrete Logs
    • 10.3 Bit Commitment
    • 10.4 Diffie-Hellman Key Exchange
    • 10.5 The ElGamal Public Key Cryptosystem
    • 10.6 Exercises
    • 10.7 Computer Problems
  11. Hash Functions
    • 11.1 Hash Functions
    • 11.2 Simple Hash Examples
    • 11.3 The Merkle-Damg ̊ard Construction
    • 11.4 SHA-2
    • 11.5 SHA-3/Keccak
    • 11.6 Exercises
  12. Hash Functions: Attacks and Applications
    • 12.1 Birthday Attacks
    • 12.2 Multicollisions
    • 12.3 The Random Oracle Model
    • 12.4 Using Hash Functions to Encrypt
    • 12.5 Message Authentication Codes
    • 12.6 Password Protocols
    • 12.7 Blockchains
    • 12.8 Exercises
    • 12.9 Computer Problems
  13. Digital Signatures
    • 13.1 RSA Signatures
    • 13.2 The ElGamal Signature Scheme
    • 13.3 Hashing and Signing
    • 13.4 Birthday Attacks on Signatures
    • 13.5 The Digital Signature Algorithm
    • 13.6 Exercises
    • 13.7 Computer Problems
  14. What Can Go Wrong
    • 14.1 An Enigma ‘Feature’
    • 14.2 Choosing Primes for RSA
    • 14.3 WEP
    • 14.4 Exercises
  15. Security Protocols
    • 15.1 Intruders-in-the-Middle and Impostors
    • 15.2 Key Distribution
    • 15.3 Kerberos
    • 15.4 Public Key Infrastructures (PKI)
    • 15.5 X.509 Certificates
    • 15.6 Pretty Good Privacy
    • 15.7 SSL and TLS
    • 15.8 Secure Electronic Transaction
    • 15.9 Exercises
  16. Digital Cash
    • 16.1 Setting the Stage for Digital Economies
    • 16.2 A Digital Cash System
    • 16.3 Bitcoin Overview
    • 16.4 Cryptocurrencies
    • 16.5 Exercises
  17. Secret Sharing Schemes
    • 17.1 Secret Splitting
    • 17.2 Threshold Schemes
    • 17.3 Exercises
    • 17.4 Computer Problems
  18. Games
    • 18.1 Flipping Coins over the Telephone
    • 18.2 Poker over the Telephone
    • 18.3 Exercises
  19. Zero-Knowledge Techniques
    • 19.1 The Basic Setup
    • 19.2 The Feige-Fiat-Shamir Identification Scheme
    • 19.3 Exercises
  20. Information Theory
    • 20.1 Probability Review
    • 20.2 Entropy
    • 20.3 Huffman Codes
    • 20.4 Perfect Secrecy
    • 20.5 The Entropy of English
    • 20.6 Exercises
  21. Elliptic Curves
    • 21.1 The Addition Law
    • 21.2 Elliptic Curves Mod p
    • 21.3 Factoring with Elliptic Curves
    • 21.4 Elliptic Curves in Characteristic 2
    • 21.5 Elliptic Curve Cryptosystems
    • 21.6 Exercises
    • 21.7 Computer Problems
  22. Pairing-Based Cryptography
    • 22.1 Bilinear Pairings
    • 22.2 The MOV Attack
    • 22.3 Tripartite Diffie-Hellman
    • 22.4 Identity-Based Encryption
    • 22.5 Signatures
    • 22.6 Keyword Search
    • 22.7 Exercises
  23. Lattice Methods
    • 23.1 Lattices
    • 23.2 Lattice Reduction
    • 23.3 An Attack on RSA
    • 23.4 NTRU
    • 23.5 Another Lattice-Based Cryptosystem
    • 23.6 Post-Quantum Cryptography?
    • 23.7 Exercises
  24. Error Correcting Codes
    • 24.1 Introduction
    • 24.2 Error Correcting Codes
    • 24.3 Bounds on General Codes
    • 24.4 Linear Codes
    • 24.5 Hamming Codes
    • 24.6 Golay Codes
    • 24.7 Cyclic Codes
    • 24.8 BCH Codes
    • 24.9 Reed-Solomon Codes
    • 24.10 The McEliece Cryptosystem
    • 24.11 Other Topics
    • 24.12 Exercises
    • 24.13 Computer Problems
  25. Quantum Techniques in Cryptography
    • 25.1 A Quantum Experiment
    • 25.2 Quantum Key Distribution
    • 25.3 Shor’s Algorithm
    • 25.4 Exercises
  1. Mathematica® Examples
    • A.1 Getting Started with Mathematica
    • A.2 Some Commands
    • A.3 Examples for Chapter 2
    • A.4 Examples for Chapter 3
    • A.5 Examples for Chapter 5
    • A.6 Examples for Chapter 6
    • A.7 Examples for Chapter 9
    • A.8 Examples for Chapter 10
    • A.9 Examples for Chapter 12
    • A.10 Examples for Chapter 17
    • A.11 Examples for Chapter 18
    • A.12 Examples for Chapter 21
  2. Maple® Examples
    • B.1 Getting Started with Maple
    • B.2 Some Commands
    • B.3 Examples for Chapter 2
    • B.4 Examples for Chapter 3
    • B.5 Examples for Chapter 5
    • B.6 Examples for Chapter 6
    • B.7 Examples for Chapter 9
    • B.8 Examples for Chapter 10
    • B.9 Examples for Chapter 12
    • B.10 Examples for Chapter 17
    • B.11 Examples for Chapter 18
    • B.12 Examples for Chapter 21
  3. MATLAB® Examples
    • C.1 Getting Started with MATLAB
    • C.2 Examples for Chapter 2
    • C.3 Examples for Chapter 3
    • C.4 Examples for Chapter 5
    • C.5 Examples for Chapter 6
    • C.6 Examples for Chapter 9
    • C.7 Examples for Chapter 10
    • C.8 Examples for Chapter 12
    • C.9 Examples for Chapter 17
    • C.10 Examples for Chapter 18
    • C.11 Examples for Chapter 21
  4. Sage Examples
    • D.1 Computations for Chapter 2
    • D.2 Computations for Chapter 3
    • D.3 Computations for Chapter 5
    • D.4 Computations for Chapter 6
    • D.5 Computations for Chapter 9
    • D.6 Computations for Chapter 10
    • D.7 Computations for Chapter 12
    • D.8 Computations for Chapter 17
    • D.9 Computations for Chapter 18
    • D.10 Computations for Chapter 21

E. Answers and Hints for Selected Odd-Numbered Exercises

F. Suggestions for Further Reading

Bibliography

Index