Lock a message with a truly random key as long as the message, and never reuse it. That is mathematically unbreakable, but you need to hand over a mountain of key in advance.
The idea: Write the message as bits and flip each bit wherever the key has a 1. If the key is truly random, every message of the same length is equally consistent with the result: the encryption of "attack at dawn" could just as well be the encryption of "retreat at six" under a different, equally likely key. So the attacker learns nothing, however much computing power they have. Reuse a key once, though, and combining the two ciphertexts cancels the key, leaving the two messages mixed together, which is often easy to untangle.
Why it matters: It proves perfect secrecy is possible, and shows why everyday encryption trades it for convenience.
Encrypt by combining (XOR) the message with a truly random key as long as the message, and never reuse the key. Shannon proved in 1949[1] that the ciphertext then reveals nothing about the message, even to an attacker with unlimited computing power.
The catch is practical: you need as much secret key as data, delivered in advance, used exactly once. Reusing pads let US codebreakers read Soviet messages (the Venona project). One-time pads are used for a few ultra-high-security links. Everyday encryption uses ciphers like AES that stretch a short key instead.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.