Modular Arithmetic & the Caesar Cipher

The security chapters of this course are about cryptography, but they lean on math you already have: modular arithmetic (the % operator) for wrap-around, and hashing concepts from way back in the hashmap tier, now with a very different set of guarantees. Level 28 starts at the simplest possible cipher: the Caesar cipher, named for Julius Caesar, who reportedly used a shift of 3 to encode military messages.

A Caesar cipher shifts every letter forward by a fixed amount k, wrapping back to 'a' after 'z'. That wrap-around is exactly what the modulo operator is for: convert a letter to its 0-25 index, add the shift, take the result mod 26 to wrap it back into range, then convert back to a character. Decryption is the same operation with the shift negated, (index - k) % 26, which is why Python's % operator (which always returns a non-negative result for a positive modulus, unlike some other languages) matters here: it makes the negative-shift case just work without special-casing.

A Caesar cipher has exactly 26 possible keys (25 useful ones, since a shift of 0 does nothing), so brute-forcing every shift and eyeballing which one produces readable text takes a human seconds and a computer microseconds. Even without brute force, English letter-frequency analysis, 'e' and 't' are the most common letters in English text, cracks it almost as fast, since a shift preserves the relative frequency pattern. It illustrates the vocabulary real cryptography builds on, key, plaintext, ciphertext, encrypt and decrypt as inverse operations, without any of the actual security. The rest of this module builds toward algorithms where "just try every key" is computationally infeasible, not merely inconvenient.