We have a primary-order EC group. Need to perform a (sort-of) DH protocol, whereas the key is permanent, not a nonce (single-usage ephemeral key).
So we receive an arbitrary group element (EC point) from an untrusted party, and reveal it multiplied by the secret key.
Is it always safe to do that? I mean, can the attacker craft the EC point in some manner to extract some info about the key? We ensure that the EC point is indeed on the curve, and, as I mentioned, it's a primary-order group.