# 1-out-of-2 OT, chosen 1-out-of-2 OT and Random 1-out-of-2 OT

I'm studying some concepts about Oblivious Transfer(OT), and would like to know what is the 1-out-of-2 OT, chosen 1-out-of-2 OT and Random 1-out-of-2 OT, and wonder the relation and difference between these concepts, thank!

• 1-out-of-2 OT: In this case, Alice inputs two bits, $$b_0$$ and $$b_1$$, and Bob inputs nothing. Bob receives two bits, $$c$$, chosen with uniform probability, and $$b_c$$. Crucially, he doesn't choose the value $$c$$, it's an output of the functionality [1].
• Chosen 1-out-of-2 OT: Alice again has inputs $$b_0$$ and $$b_1$$, but now Bob can select $$c$$ himself, and receive $$b_c$$ [1].
• Randomized 1-out-of-2: In this case, neither Alice nor Bob have inputs to the protocol. Instead, they interact as prescribed by the protocol, and as a result, Alice receives bits $$b_0, b_1$$ both chosen uniformly at random, and Bob learns $$c$$ and $$b_c$$ [2].