Introduction to Cryptography with Coding Theory

Brief Table of Contents

• Overview of Cryptography and Its Applications
  • 1.1 Secure Communications
  • 1.2 Cryptographic Applications
• 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
• 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
• 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
• Stream Ciphers
  • 5.1 Pseudo-Random Bit Generation
  • 5.2 LFSR Sequences
  • 5.3 RC4
  • 5.4 Exercises
  • 5.5 Computer Problems
• 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
• 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
• The Advanced Encryption Standard: Rijndael
  • 8.1 The Basic Algorithm
  • 8.2 The Layers
  • 8.3 Decryption
  • 8.4 Design Considerations
  • 8.5 Exercises
• 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
• 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
• 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
• 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
• 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
• What Can Go Wrong
  • 14.1 An Enigma ''Feature''
  • 14.2 Choosing Primes for RSA
  • 14.3 WEP
  • 14.4 Exercises
• 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
• 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
• Secret Sharing Schemes
  • 17.1 Secret Splitting
  • 17.2 Threshold Schemes
  • 17.3 Exercises
  • 17.4 Computer Problems
• Games
  • 18.1 Flipping Coins over the Telephone
  • 18.2 Poker over the Telephone
  • 18.3 Exercises
• Zero-Knowledge Techniques
  • 19.1 The Basic Setup
  • 19.2 The Feige-Fiat-Shamir Identification Scheme
  • 19.3 Exercises
• 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
• 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
• 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
• 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
• 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
• Quantum Techniques in Cryptography
  • 25.1 A Quantum Experiment
  • 25.2 Quantum Key Distribution
  • 25.3 Shor''s Algorithm
  • 25.4 Exercises
• 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
• 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
• 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
• 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