Assume it's proven: "Security of protocol $\Pi$ can be deduced from hardness of problem $P$".
Is it correct to state: "Security of protocol $\Pi$ can be reduced to (hardness of) problem $P$" ?
My question is about accepted VOCABULARY in the field of cryptography with provable security.
This is a simplified version of this question, where the first of the above assertions is (I assume, rigorously) established by exhibiting an algorithm that would solve problem $P$ from an algorithm that would break protocol $\Pi$. I read two interesting answers (which I thus upvoted) concluding for one that that reduced "cannot (technically)" be used in this way but remains understandable in the context, for the other that it's "appropriate".
For a non-native speaker like me, that's far from trivial.