One-time pad

How it works

The one-time pad adds a random key letter to every message letter: $c_i = (p_i + k_i) \bmod 26$. Gilbert Vernam built the same idea with XOR on teleprinter tape in 1917, and Joseph Mauborgne added the rule that makes it work: the key is truly random, as long as the message, and used only once.

Then it cannot be broken, even with unlimited computing power. Claude Shannon proved in 1949 that the ciphertext gives no information about the message besides its length: for every possible plaintext of that length there is exactly one key that produces the ciphertext, and all keys are equally likely.

The price is the key: as much secret random material as there will ever be messages, delivered safely in advance. Reusing it is fatal, because $c_i - c'_i \equiv p_i - p'_i$ cancels the key; the Venona project read thousands of Soviet messages for exactly this reason.