Cybersecurity contains sev= eral highly technical sub-disciplines that require significant analytic thinking, formalism and mathematical knowledge. Examples of sub-fields that have stro= ng mathematical prerequisites include applied and theoretical cryptography, network security, incentive design, mechanism design, formal security modelling and adversarial modell= ing. The goal of this course is to introduce students to the ideas and mathemati= cal concepts used in these sub-disciplines.
This course is for students to be introduced to the ba= sic mathematical tools used in cybersecurity. Students will learn introductory mathematical knowledge from a number of disparate fields through the applications of such knowledge to many classical and modern security mechanisms. This course paves the road for taking more advanced security-related courses such as Applied Cryptography and Network Security.=
Tentative Topics:
= 1. Overview
= 2. Concepts and history
= 3. Math Foundation: Well-ordering Axiom, Principle of Mathematical Induction and the Well-Ordering Axiom
= 4. Math Foundation: Permutations and Combinations
= 5. Monoalphabetic Substitution Ciphers
= 5.1. Math Foundation: Concepts of number theory
= 5.2. Simple Ciphers
= 5.2.1. The Cast of Characters
= 5.2.2. Additive Ciphers
= 5.2.3. Multiplicative Ciphers
= 5.2.4. Affine Ciphers
= 5.2.5. Keyword Ciphers
= 5.3. Cryptoanalysis of Monoalphabetic= Substitution Ciphers
= 6. Polyalphabetic Substitution Ciphers
= 6.1. Math Foundation: Probability Basics
= 6.1.1. Events
= 6.1.2. Independent Events
= 6.1.3. Probability concepts and basic theorems
= 6.1.4. Expectation and deviations
= 6.2. Math Foundation: Basic Information Theory
= 6.3. Simple Ciphers
= 6.3.1. Changing Letters to Numbers
= 6.3.2. The Vigenere Cipher
= 6.4. Crytoanalysis of Polyalphabetic<= /span> Substitution Ciphers
= 6.5. One-time Pad
= 7. Polygraphic Substitution Ciphers
= 7.1. Math Foundation: Elementary Matrix Theory
= 7.2. Hill's System
= 7.3. Cryptoanalysis of Hill's System
= 8. Basics of Modern Cryptography
= 8.1. Concept of Algorithm and Asymptotic notation
= 8.2. Mathematic concept of security
= 8.3. One-way hash function and birthday paradox
= 8.4. Trapdoor one-way functions
= 8.4.1. Math Foundation: Basic Group Theory
= 8.4.2. Math Foundation: Revisit Number Theory
= 8.4.3. The RSA problem
= 8.4.1. The Diffie-Hellman Problem
= 8.5. Applications
= 8.5.1. RSA cryptosystem
= 8.5.2. RSA signature algorithm
= 8.5.3. El Gamal cryptosystem
= 8.5.4. El Gamal signature algorithm
= 9. Protocols and other mathematic foundations
= 9.1. Authentication protocols
= 9.2. Math Foundation: Propositional Logic
= 9.3. Authentication logic
= 9.4. Fair Exchange protocols
= 9.5. Math Foundation: Game theory and Mechanism design
= 9.6. Game theoretic analysis of exchange protocols.
Text Book: