Access control problem in oblivious transfer I am not sure whether the title is proper or not, but this question comes to my mind when I was reading $k-n$ oblivious transfers.

In a $k-n$ oblivious transfer (OT) protocol, a party A has $n$ messages and another party B wants to retrieve $k$ of them. There are two basic requirements for OT:


A should not know which $k$ messages are retrieved by B.
B should not know other messages besides the $k$ messages. 


Then, does B have access right to all the $n$ messages?

If B does not have the access right, B can retrieve any $k$ messages. In this case, B can actually retrieve all the $n$ messages.

If B does have the access right, why do we need OT. B can simply retrieve all the $n$ messages, since existing OT schemes require $O(n)$ communication overhead.

With this question in mind, it is hard for me to think of any practical scenarios where OT can be utilized. Can anyone give some application examples of OT?

EDIT: I found that there are some research papers about access control in OT. Still, the problem I asked above is mainly in the scenario of information retrieve where access control seems very important. I am interested in other possible applications where OT without access control can be utilized.
OT is typically not used as an application in its own right. In the context of access control, OT limits the number of messages received by B but not which messages. I don't know of any real applications for this (you could talk about a subscription where B has purchased the right to read any $k$ articles, but this is pretty artificial in my opinion).

However, OT is a very important and basic building block used in constructing secure computation protocols. It is used in generic protocols like Yao and GMW, and is often used in specific protocols for things like secure set intersection and others.