Caesar Cipher Shifter

The Caesar cipher operates on modular arithmetic, substituting each letter in the plaintext with a letter a fixed number of positions down the alphabet. For encryption, given a letter's numerical index $x$ (where A=0, B=1, ... Z=25), a shift $s$, and alphabet size $n$ (usually 26): E(x) = (x + s) mod n. For decryption, the formula reverses the operation: D(x) = (x - s) mod n. If the resulting index falls outside the 0 to 25 range, the modulo operator wraps it back around to keep it within the alphabet bounds.

Let's encrypt the message "HELLO" using a shift value of 3. First, convert each letter to its standard 0-indexed alphabet position: H is 7, E is 4, L is 11, L is 11, and O is 14. Next, add the shift of 3 to each index using modulo 26 arithmetic. For H: (7 + 3) mod 26 = 10, which corresponds to 'K'. For E: (4 + 3) mod 26 = 7, which corresponds to 'H'. Repeating this for the remaining letters transforms "HELLO" into "KHOOR". To decode, simply subtract 3 from each letter's index, wrapping around in reverse to recover the original text.

Always verify your alphabet set before shifting, as including spaces, punctuation, or numbers can either alter the index counts or cause unexpected formatting shifts depending on your mode settings. Remember that because the standard English alphabet has 26 letters, shifting by 26 results in the exact same plaintext, while a shift of 13 is identical to the famous ROT13 transformation. When practicing cryptography, test both encryption and decryption modes to ensure your shift key is symmetrical and error-free.