Number Theory and Cryptography

          Module 1: Fundamentals of Number Theory

Section 1: Introduction to Numbers  
- Lesson 1: Understanding Natural Numbers  
  Module 1, Section 1, Lesson 1: Understanding Natural Numbers  
- Lesson 2: Exploring Integers  
  Module 1, Section 1, Lesson 2: Exploring Integers

Section 2: Number Classifications  
- Lesson 1: Even and Odd Numbers  
  Module 1, Section 2, Lesson 1: Even and Odd Numbers  
- Lesson 2: Prime and Composite Numbers  
  Module 1, Section 2, Lesson 2: Prime and Composite Numbers

Section 3: Number Concepts  
- Lesson 1: Rational Numbers Explained  
  Module 1, Section 3, Lesson 1: Rational Numbers Explained  
- Lesson 2: Irrational Numbers Overview  
  Module 1, Section 3, Lesson 2: Irrational Numbers Overview

Section 4: Basic Operations  
- Lesson 1: Addition and Subtraction Principles  
  Module 1, Section 4, Lesson 1: Addition and Subtraction Principles  
- Lesson 2: Multiplication and Division Fundamentals  
  Module 1, Section 4, Lesson 2: Multiplication and Division Fundamentals

Section 5: Introduction to Mathematical Proof  
- Lesson 1: Understanding Proofs  
  Module 1, Section 5, Lesson 1: Understanding Proofs  
- Lesson 2: Simple Proof Techniques  
  Module 1, Section 5, Lesson 2: Simple Proof Techniques


Module 2: Prime Numbers and Divisibility

Section 1: Foundations of Prime Numbers  
- Lesson 1: Defining Prime Numbers  
  Module 2, Section 1, Lesson 1: Defining Prime Numbers  
- Lesson 2: Identifying Composite Numbers  
  Module 2, Section 1, Lesson 2: Identifying Composite Numbers

Section 2: Divisibility Rules  
- Lesson 1: Divisibility Basics  
  Module 2, Section 2, Lesson 1: Divisibility Basics  
- Lesson 2: Applying Divisibility Rules  
  Module 2, Section 2, Lesson 2: Applying Divisibility Rules

Section 3: Prime Factorization  
- Lesson 1: Factor Trees  
  Module 2, Section 3, Lesson 1: Factor Trees  
- Lesson 2: Unique Factorization Principle  
  Module 2, Section 3, Lesson 2: Unique Factorization Principle

Section 4: Special Number Properties  
- Lesson 1: Perfect Numbers and Deficient Numbers  
  Module 2, Section 4, Lesson 1: Perfect Numbers and Deficient Numbers  
- Lesson 2: Abundant Numbers  
  Module 2, Section 4, Lesson 2: Abundant Numbers

Section 5: Introduction to GCD and LCM  
- Lesson 1: Finding Greatest Common Divisor  
  Module 2, Section 5, Lesson 1: Finding Greatest Common Divisor  
- Lesson 2: Calculating Least Common Multiple  
  Module 2, Section 5, Lesson 2: Calculating Least Common Multiple


Module 3: Modular Arithmetic Concepts

Section 1: Basic Concepts of Modular Arithmetic  
- Lesson 1: Understanding Modular Arithmetic  
  Module 3, Section 1, Lesson 1: Understanding Modular Arithmetic  
- Lesson 2: Remainders in Division  
  Module 3, Section 1, Lesson 2: Remainders in Division

Section 2: Congruence and Equivalence  
- Lesson 1: Definition of Congruence  
  Module 3, Section 2, Lesson 1: Definition of Congruence  
- Lesson 2: Solving Simple Congruences  
  Module 3, Section 2, Lesson 2: Solving Simple Congruences

Section 3: Properties of Modular Arithmetic  
- Lesson 1: Addition and Multiplication Rules  
  Module 3, Section 3, Lesson 1: Addition and Multiplication Rules  
- Lesson 2: Reduction Techniques  
  Module 3, Section 3, Lesson 2: Reduction Techniques

Section 4: Applications of Modular Arithmetic  
- Lesson 1: Clock Arithmetic  
  Module 3, Section 4, Lesson 1: Clock Arithmetic  
- Lesson 2: Patterns in Remainders  
  Module 3, Section 4, Lesson 2: Patterns in Remainders

Section 5: Problem-Solving with Modular Concepts  
- Lesson 1: Modular Equations  
  Module 3, Section 5, Lesson 1: Modular Equations  
- Lesson 2: Using Modular Techniques in Puzzles  
  Module 3, Section 5, Lesson 2: Using Modular Techniques in Puzzles


Module 4: Introduction to Cryptography

Section 1: Cryptography Fundamentals  
- Lesson 1: What is Cryptography?  
  Module 4, Section 1, Lesson 1: What is Cryptography?  
- Lesson 2: History of Cryptography  
  Module 4, Section 1, Lesson 2: History of Cryptography

Section 2: Basic Encryption Techniques  
- Lesson 1: Substitution Ciphers  
  Module 4, Section 2, Lesson 1: Substitution Ciphers  
- Lesson 2: Transposition Ciphers  
  Module 4, Section 2, Lesson 2: Transposition Ciphers

Section 3: Modern Cryptography Foundations  
- Lesson 1: Symmetric vs Public-Key  
  Module 4, Section 3, Lesson 1: Symmetric vs Public-Key  
- Lesson 2: Cryptographic Terminology  
  Module 4, Section 3, Lesson 2: Cryptographic Terminology

Section 4: Mathematical Foundations in Cryptography  
- Lesson 1: Role of Prime Numbers  
  Module 4, Section 4, Lesson 1: Role of Prime Numbers  
- Lesson 2: Importance of Modular Arithmetic in Cryptography  
  Module 4, Section 4, Lesson 2: Importance of Modular Arithmetic in Cryptography

Section 5: Basic Cryptographic Systems  
- Lesson 1: Introduction to RSA  
  Module 4, Section 5, Lesson 1: Introduction to RSA  
- Lesson 2: Simple Cryptographic Algorithms  
  Module 4, Section 5, Lesson 2: Simple Cryptographic Algorithms


Module 5: Cryptographic Applications

Section 1: Algorithms in Cryptography  
- Lesson 1: Overview of Cryptographic Algorithms  
  Module 5, Section 1, Lesson 1: Overview of Cryptographic Algorithms  
- Lesson 2: Algorithm Complexity Basics  
  Module 5, Section 1, Lesson 2: Algorithm Complexity Basics

Section 2: Secure Communication  
- Lesson 1: Encrypting Messages  
  Module 5, Section 2, Lesson 1: Encrypting Messages  
- Lesson 2: Decoding Techniques  
  Module 5, Section 2, Lesson 2: Decoding Techniques

Section 3: Digital Signatures and Authentication  
- Lesson 1: What are Digital Signatures?  
  Module 5, Section 3, Lesson 1: What are Digital Signatures?  
- Lesson 2: Basic Authentication Methods  
  Module 5, Section 3, Lesson 2: Basic Authentication Methods

Section 4: Practical Cryptography  
- Lesson 1: Implementing Simple Encryption  
  Module 5, Section 4, Lesson 1: Implementing Simple Encryption  
- Lesson 2: Hands-on Cryptographic Exercises  
  Module 5, Section 4, Lesson 2: Hands-on Cryptographic Exercises

Section 5: Ethical and Practical Considerations  
- Lesson 1: Importance of Ethical Cryptography  
  Module 5, Section 5, Lesson 1: Importance of Ethical Cryptography  
- Lesson 2: Reviewing Cryptographic Systems  
  Module 5, Section 5, Lesson 2: Reviewing Cryptographic Systems