🔐 Modular Arithmetic Cryptography Project

Part 1: Personalized Message Encryption

Choose a personally meaningful message (8–15 words). Convert it to uppercase, remove non-alphabetic characters, and encrypt it using the Affine Cipher:

E(x) = (ax + b) mod 26

• Pick a value of a that is coprime with 26.
• Show hand calculations for at least 5 letters.
• Explain why you chose the message and keys.

Part 2: Mathematical Explanation

• Define what it means for two numbers to be coprime.
• Show how to find the modular inverse of your chosen a.
• Explain how the inverse is used in decryption.

Part 3: Programming with ASCII

Write a program (Python/Java/JS) that encrypts/decrypts using mod 95 for ASCII printable characters. This allows for punctuation, spaces, and symbols.

If you have extensive programming experience, you are free to make your program as sophisticated as you like. Consider encrypting pairs of letters instead of single letters. How might your modulus need to change? Consider adding a nice user interface (either command-line or gui). If you are relatively new to programming, keep it simple! Ask for guidance if you'd like some ideas.

Explain: How does using mod 95 change your logic?

Part 4: Error Exploration & Edge Cases

• Choose an a not coprime with 26 and try decrypting. Explain why it fails.
• Bonus: Add a checksum or mod-based error detection to your encrypted message.

Part 5: Reflection (Choose 2–3)

• What concept was most difficult for you?
• What surprised you about modular arithmetic?
• How could someone attack or improve your cipher?
• How would you explain this topic to a younger student?