Construct an unknown yet classically intractable Simon oracle

Construct an instantiation of a Simon-problem oracle that satisfies the problem’s constraints, remains unknown to the quantum algorithm user, and does not immediately admit a faster classical solution, thereby resolving the tension between requiring the oracle to be unknown and requiring it to be implementable.

Background

Simon's algorithm requires access to an unknown but implementable unitary oracle. The oracle must remain sufficiently hidden to preserve the quantum-versus-classical complexity separation, while also being implementable so that the quantum algorithm can query it. The paper explains that this creates a fundamental tension: if the oracle implementation is known, the hidden period may be recoverable classically; if the oracle is genuinely unknown, implementing it locally is impossible. The proposed networked version addresses this tension operationally by localizing the oracle on a server, but the underlying question of constructing an oracle with the stated properties remains unresolved in the cited discussion.