Cryptography Course

Chapter 1: Foundations of Cryptography

Understanding the fundamental concepts, terminology, and historical context of cryptographic systems.

1.1 What is Cryptography?

Cryptography is the practice and study of techniques for secure communication in the presence of third parties called adversaries. It encompasses the entire process of creating and analyzing protocols that prevent adversaries from reading private messages.

Core Principles:

Confidentiality: Ensuring information is accessible only to authorized parties
Integrity: Maintaining the accuracy and completeness of data
Authentication: Verifying the identity of communicating parties
Non-repudiation: Preventing denial of actions or communications

"Back in my day, we kept secrets by whispering behind the barn! None of this mathematical nonsense!" - Eustace on traditional secrecy

Essential Terminology:

Plaintext: The original readable message or data
Ciphertext: The encrypted, unreadable version of the plaintext
Encryption: The process of converting plaintext into ciphertext
Decryption: The process of converting ciphertext back into plaintext
Key: Secret information used to control the encryption/decryption process
Algorithm (Cipher): The mathematical procedure used for encryption/decryption
Cryptanalysis: The study of analyzing and breaking cryptographic systems

1.2 Historical Perspective

Cryptography has been used throughout history to protect sensitive information. Understanding its evolution helps us appreciate modern techniques.

Ancient Cryptography (Before 1000 CE):

Scytale (7th century BCE): Spartan military used leather strips wrapped around rods
Caesar Cipher (50 BCE): Julius Caesar's substitution cipher with fixed shift
Polybius Square (150 BCE): Greek system encoding letters as coordinate pairs

Medieval Period (1000-1500 CE):

Frequency Analysis: Al-Kindi's breakthrough in breaking substitution ciphers
Polyalphabetic Ciphers: Johannes Trithemius and the Vigenère cipher
Steganography: Hidden writing techniques alongside cryptography

// Example: Caesar Cipher Implementation
function caesarCipher(text, shift) {
    return text.split('').map(char => {
        if (char.match(/[a-zA-Z]/)) {
            const code = char.charCodeAt(0);
            const base = code >= 65 && code <= 90 ? 65 : 97;
            return String.fromCharCode(((code - base + shift) % 26) + base);
        }
        return char;
    }).join('');
}

// Usage example
const plaintext = "ATTACK AT DAWN";
const encrypted = caesarCipher(plaintext, 3);
console.log("Encrypted:", encrypted); // "DWWDFN DW GDZQ"
                

1.3 Mathematical Foundations

Modern cryptography relies heavily on mathematical concepts. Understanding these foundations is crucial for implementing secure systems.

Number Theory Basics:

Prime Numbers: Numbers divisible only by 1 and themselves
Greatest Common Divisor (GCD): Largest number dividing two integers
Modular Arithmetic: Arithmetic operations with remainder division
Euler's Totient Function: Count of integers coprime to n

GCD(a,b) using Euclidean Algorithm:
gcd(a,b) = gcd(b, a mod b) until b = 0

Interactive Demo: Modular Arithmetic

Calculate (a + b) mod n:

Result will appear here...

Chapter 2: Classical Cryptography

Exploring traditional cipher systems, their implementations, and cryptanalytic techniques.

2.1 Substitution Ciphers

Substitution ciphers replace each element of plaintext with another element according to a fixed system.

Simple Substitution Cipher:

Each letter is consistently replaced with another letter throughout the message.

// Simple Substitution Cipher
const alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const key = "QWERTYUIOPASDFGHJKLZXCVBNM";

function simpleSubstitution(text, encrypt = true) {
    const from = encrypt ? alphabet : key;
    const to = encrypt ? key : alphabet;
    
    return text.split('').map(char => {
        const index = from.indexOf(char.toUpperCase());
        return index !== -1 ? to[index] : char;
    }).join('');
}
                

Security Analysis:

Simple substitution ciphers are vulnerable to frequency analysis. In English, 'E' appears about 12.7% of the time, 'T' about 9.1%, etc.

2.2 Transposition Ciphers

Transposition ciphers rearrange the order of characters in the plaintext according to a systematic method.

Try Rail Fence Cipher:

Encrypted text will appear here...

2.3 The Vigenère Cipher

A polyalphabetic substitution cipher that uses a keyword to determine shifting for each character.

Encryption: C[i] = (P[i] + K[i mod keylen]) mod 26
Decryption: P[i] = (C[i] - K[i mod keylen]) mod 26

"Why can't we just use the same letter for everything? This changing business is too complicated!" - Eustace on polyalphabetic ciphers

2.4 Frequency Analysis

The most powerful tool for breaking classical ciphers, based on the fact that letters appear with different frequencies in natural language.

Frequency Analysis Tool:

Frequency analysis will appear here...

Chapter 3: Modern Cryptography

Exploring contemporary cryptographic systems, including symmetric and asymmetric encryption.

3.1 Symmetric Key Cryptography

Symmetric encryption uses the same key for both encryption and decryption. Both parties must share the secret key securely.

Advanced Encryption Standard (AES):

Block size: 128 bits
Key sizes: 128, 192, or 256 bits
Rounds: 10, 12, or 14 (depending on key size)
Based on the Rijndael cipher

3.2 Public Key Cryptography

Asymmetric cryptography uses different keys for encryption and decryption, solving the key distribution problem.

"Two keys? What's wrong with one key? I only need one key for my truck!" - Eustace on public key cryptography

Small RSA Example:

Try with small primes (educational purposes only):

RSA demonstration will appear here...

Chapter 4: Advanced Cryptographic Concepts

Exploring cutting-edge cryptographic techniques and emerging technologies.

4.1 Digital Signatures

Digital signatures provide authentication, non-repudiation, and integrity for digital documents.

How Digital Signatures Work:

Create hash of the document
Encrypt hash with sender's private key
Attach encrypted hash (signature) to document
Recipient decrypts signature with sender's public key
Compare decrypted hash with computed hash of document

4.2 Zero-Knowledge Proofs

Allow one party to prove they know a secret without revealing the secret itself.

Simple Zero-Knowledge Example:

Ali Baba's Cave: Prove you know the magic word without revealing it.

Zero-knowledge proof simulation...

Cryptography Mastery Course