Modular Arithmetic & Cryptography Basics: From Caesar to Toy RSA

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Split game times into hours and minutes with QUOTIENT and MOD, then use MOD to wrap a 24-hour clock and a letter wheel.
• Turn the word VAULTKEY into numbers, encrypt it with a Caesar shift and an affine key, and decrypt it again with the modular inverse.
• Count every letter of an intercepted message with COUNTIF, chart the counts, find the most frequent letter and work out the Caesar shift.
• Run Euclid's algorithm step by step for a 1,092 × 852 cm floor, read off the greatest common divisor and confirm it with GCD.
• Find the inverse of 17 modulo 3,120 with an extended-Euclid step table: quotients, remainders and the coefficient t that becomes the private key d.
• Compute 2790^2753 mod 3233 with a 12-row square-and-multiply table: the bits of the exponent, repeated squaring and the running result.
• Build a complete toy RSA key from p = 17 and q = 11, encrypt the message 88 with e = 7 and decrypt it again with d = 23, multiplying step by step mod n.
• Compute the check digit of an ISBN-13 with alternating weights and the Luhn check digit of a ticket number, the same MOD 10 idea used on payment cards.