Oblivious Transfer where neither party learns the index of the message

Question

In a traditional Oblivious Transfer setting, the sender has a list $(x_1, x_2, ... , x_n) \in G$ where $G$ is the chosen group. The receiver has $b \in \mathbb{N}$, such that engaging in the protocol the receiver is given $x_b$ and the sender does not learn $b$.

Presume I want a slightly different procedure, where the receiver gets a random $x_i$ and neither the sender nor receiver learn $i$.

Is there a name for protocols with this behavior?

Answer 1

The simplest way to do this would be to have the sender randomly shuffle the elements. The receiver chooses a random element to request. That way the receiver has no idea which of the original (before the shuffle) elements he got.