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Approach 1 The simplest way of doing this is for the receiver, with choice $j \in \{1,\dots,n\}$, to input $1$ in the $j$-th 1-out-of-2 OT and $0$ elsewhere. The sender, with input $(x_1, \dots, x_n)$, inputs $(0,x_i)$ in the $i$-th OT. Approach 2 An alternative protocol (that just came out of a discussion with a colleague, and seems to be actively ...


2

Sure they can, it's called the socialist millionaires problem. The most common solution is to use Yao's protocol: Alice sends a garbled circuit of the equality function to Bob, and then Alice use oblivious transfers to send the keys necessary for the evaluation of the circuit to Bob. Another option is to rely on additively homomorphic IND-CPA encryption: ...



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