The Mathematics of Cryptography with Dr James Grime

Explore the fascinating world of cryptography, the science of secure communication and secret messages! This comprehensive course delves into the mathematics behind codes and code breaking, revealing how secrets are protected and deciphered.

We'll begin with an accessible introduction to easy ciphers and their historical cracking, then progress to more complex systems. Discover the intricacies of the legendary Enigma machine from World War II and explore the modern internet encryption methods that safeguard our digital lives.

This course offers over 6 hours of engaging lectures, complemented by 2 hours of practical exercises and helpful solution videos.

Key topics covered include:

• Monoalphabetic Ciphers: Understand the basics of simple substitution techniques.
• Modular Arithmetic: A fundamental mathematical tool for cryptography.
• Polyalphabetic Ciphers: Explore more advanced encryption methods.
• The Enigma Machine: A deep dive into this iconic WWII encryption device.
• Public Key Cryptography: Learn about the revolutionary system of public and private keys.

Throughout the course, you'll encounter and apply crucial mathematical concepts such as:

• Sets
• Functions
• Probability
• Statistics
• Combinatorics
• Number Theory

Master essential ciphers and techniques, including:

• Substitution Ciphers: Learn how to replace letters or symbols.
• Transposition Ciphers: Discover methods of rearranging message elements.
• Commuting Ciphers: Explore ciphers with unique properties.
• Frequency Analysis: Uncover patterns in ciphertext.
• The Vigenere Cipher: A historically significant polyalphabetic cipher.
• The Kasiski Test & Index of Coincidence: Techniques for breaking polyalphabetic ciphers.
• The Friedman Test: A powerful tool for cryptanalysis.
• Diffie-Hellman: Understand key exchange protocols.
• Elliptic Curve Cryptography: Explore advanced public-key cryptography.
• RSA Internet Encryption: Learn about the widely used RSA algorithm.
• Digital Signatures: Discover how to verify message authenticity.

We'll conclude with a glimpse into the future of cryptography and its evolving landscape.

This self-contained course includes supplementary notes to guide your learning journey. Each section features exercises with solutions, allowing you to test your understanding and solidify your knowledge.

Cryptography is a captivating intersection of mathematics and security. By the end of this course, you'll have a solid foundation in fundamental mathematical ideas and a better understanding of whether truly unbreakable codes are possible.