The one cipher that is mathematically UNBREAKABLE — and the reason it’s almost never used. XOR your message with a truly random key as long as the message, use it ONCE, and the ciphertext could decrypt to ANY message of that length — so it leaks nothing. The catch: you need to share a key as long as everything you’ll ever send. Slide the message and watch it hide.
The one-time pad encrypts each message bit by XOR with a key bit: c = m ⊕ k, and decrypts m = c ⊕ k. Shannon (1949) proved it has PERFECT SECRECY — the ciphertext is statistically independent of the plaintext — PROVIDED the key is truly random, at least as long as the message, and never reused. Because every plaintext is equally consistent with a given ciphertext, no amount of computation breaks it. Its impracticality (key distribution, key length) is why modern crypto uses shorter keys with computational (not perfect) security. A fail-loud self-check throws unless c⊕k recovers m and the key length equals the message length. ◆ real cryptography, node-verified.
Perfect secrecy holds ONLY under the three conditions (random, as-long-as-message, never-reused); reusing a pad or using a pseudo-random key breaks it completely (the ‘two-time pad’ is trivially crackable). The XOR + information-theoretic argument is exact.