CS 484 - Applied Cryptography System Security

Information and Network Security Concepts

• Cybersecurity, Information Security, and Network Security
• The OSI Security Architecture
• Security Attacks
• Security Services
• Security Mechanisms
•  Cryptography
• Network Security
• Trust and Trustworthiness
• Standards

Introduction to Number Theory

• Divisibility and The Division Algorithm
• The Euclidean Algorithm
• Modular Arithmetic
• Prime Numbers4
• Fermat’s and Euler’s Theorems
• Testing for Primality
• The Chinese Remainder Theorem
• Discrete Logarithms
• Appendix 2A: The Meaning of Mod

Classical Encryption Techniques

• Symmetric Cipher Model
• Substitution Techniques
• Transposition Techniques

Block Ciphers and the Data Encryption Standard

• Traditional Block Cipher Structure
• The Data Encryption Standard
• A DES Example
• The Strength of DES
• Block Cipher Design Principles

Finite Fields

• Groups
• Rings
• Fields
• Finite Fields of the Form GF(p)
• Polynomial Arithmetic
• Finite Fields of the Form GF (2n)

Advanced Encryption Standard

• Finite Field Arithmetic
• AES Structure
• AES Transformation Functions
• AES Key Expansion
• An AES Example
• AES Implementation
• Appendix 6A: Polynomials with Coefficients in GF(28)

Block Cipher Operation

• Multiple Encryption and Triple DES
• Electronic CodeBook
• Cipher Block Chaining Mode
• Cipher Feedback Mode
• Output Feedback Mode
• Counter Mode
• XTS-AES Mode for Block-Oriented Storage Devices
• Format-Preserving Encryption

Random Bit Generation and Stream Ciphers

• Principles of Pseudorandom Number Generation
• Pseudorandom Number Generators
• Pseudorandom Number Generation Using a Block Cipher
• Stream Ciphers
• RC4
• Stream Ciphers Using Feedback Shift Registers
• True Random Number Generators

Public-Key Cryptography and RSA

• Principles of Public-Key Cryptosystems
• The RSA Algorithm

Other Public-Key Cryptosystems

• Diffie–Hellman Key Exchange
• Elgamal Cryptographic System
• Elliptic Curve Arithmetic
• Elliptic Curve Cryptography

Cryptographic Hash Functions

• Applications of Cryptographic Hash Functions
• Two Simple Hash Functions
• Requirements and Security
• Secure Hash Algorithm (SHA)
• SHA-3

Message Authentication Codes

• Message Authentication Requirements
• Message Authentication Functions
• Requirements for Message Authentication Codes
• Security of MACs
• MACs Based on Hash Functions: HMAC
• MACs Based on Block Ciphers: DAA and CMAC
• Authenticated Encryption: CCM and GCM
• Key Wrapping
• Pseudorandom Number Generation Using Hash Functions and MACs

Appendix A: Basic Concepts from Linear Algebra

• A.1 Operations on Vectors and Matrices
• A.2 Linear Algebra Operations Over Zn

Appendix B: Measures of Secrecy and Security

• B.1 Conditional Probability
• B.2 Perfect Secrecy
• B.3 Information and Entropy
• B.4 Entropy and Secrecy
• B.5 Min-Entropy

Appendix C: Data Encryption Standard

Appendix D: Simplified AES

• D.1 Overview
• D.2 S-AES Encryption and Decryption
• D.3 Key Expansion
• D.4 The S-box
• D.5 S-AES Structure

Appendix E: Mathematical Basis of the Birthday Attack

• E.1 Related Problem
• E.2 The Birthday Paradox
• E.3 Useful Inequality
• E.4 The General Case of Duplications
• E.5 Overlap Between Two Sets