Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 15D / a / Solution

Alice and Bob need a uniformly random secret key $K\in \{0,1{\}}^m$ known only to them. Alice publicly sends the one-time pad ciphertext $C=M\oplus K$, and Bob recovers $M=C\oplus K$. For every observed $c$ and possible message $m$ there is exactly one equally likely key $k=c\oplus m$, so $C$ is independent of $M$ and Eve learns nothing.