Pseudorandomness in the (Inverseless) Haar Random Oracle Model

We study the (in)feasibility of quantum pseudorandom notions in a quantum analog of the random oracle model, where all the parties, including the adversary, have oracle access to the same Haar random unitary. In this model, we show the following:

• (Unbounded-query secure) pseudorandom unitaries (PRU) exist. Moreover, the PRU construction makes two calls to the Haar oracle.

• We consider constructions of PRUs making a single call to the Haar oracle. In this setting, we show that unbounded-query security is impossible to achieve. We complement this result by showing that bounded-query secure PRUs do exist with a single query to the Haar oracle.