Paul Christiano writes (source):
I’ll assume that we have some 256 bit cryptographic hash function F [...] The first important observation is that a 256-bit shared secret allows Alice and Bob to talk for as long as they want, by just using their secret to create a new pseudorandom pad for each message. That is, if Alice and Bob share a secret s, then Alice can send a message m by picking k at random, and sending the pair (k, F(sk) ⊕ m). It’s easy to confirm that Bob can still get the message, and if F is random then this is secure.
This is confusing to me. I was under the impression that there is no way of using a one time pad based on a shared secret of $n$ bits to transmit securely more than $n$ bits but this seems to imply it is possible by sending messages with $k=1,2,\dots$
What am I misunderstanding?