One-time Pad

One-time pad: given any plaintext, the key is a string of equal length to the message. We use a self-inverting function such as XOR, $C$ transforms each $s_i$ into $s_i\oplus k_i$. Capable of perfect secrecy but requires a large amount of key material and key distribution is a big problem.

One-time pad is an improvement to the Vernam cipher except:

• we use a truly random key that is as long as the message, so the key need not be repeated
• we use the key to encrypt and decrypt a single message, then we discard it

Each new message $P$ requires a new key of the same length as $P$. Produces random output with no statistical relation to plaintext.

It is unbreakable: $C$ contains no information whatsoever about $P$. This is the only cryptosystem that exhibits perfect secrecy.