Some Protocols require one party to send $n$ random challenges (or random values) to another party. For communication efficiency purpose, one can pick a random key for a pseudorandom function, and send only the key to the other party, instead. Given the key and the function, the recipient can generate $n$ (pseudorandom) values locally.

In here (on page 5) it's stated that we cannot prove it in the standard model but can we can do it in random oracle model. However, in here (on page 12-13) it is said we can use block cipher in the counter mode to do that. So it's a bit confusing.

Question: Why cannot we use standard primitives and assumptions to construct a provably secure scheme described above?

  • $\begingroup$ The outputs of a prf are indistinguishable from random if you do not know the key. Do you see the issue? $\endgroup$ – Maeher Oct 17 '18 at 15:06

It depends very much on what you require from the random values that are sent. If they need to be random (pseudorandom) then sending the key is a problem. However, if you just need unpredictability, then this may be enough. Bottom line, there is no one answer. It depends on the protocol and requirements, and often is only apparent when doing a formal security proof.

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