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Here is a concrete example of how the receiver could extract information about the senders input: Assume the circuit to be evaluated is the simple circuit computing $(x \oplus (y \wedge z)) = w$, where $x, y$ is the input of the sender and $z$ the input of the receiver. Note, that $w$ and $z$ alone does not reveal the value of $y$ (you can write down the ...

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The problem is because sender has provided the receiver with a garbled circuit in which the sender's inputs are hard coded (or has provided keys for those inputs, which is morally the same). If the receiver has both keys for each input wire then it is trivial to narrow down the possible values of the sender's input. Consider a concrete example, the ...

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Not a real answer, but some hints: Single DB PIR schemes (ones that don't need several non-colluding DB) have had serious efficiency problems for a long time. See paper 'on the computational practicality of private information retrieval' by Sion and Carbunar arguing that all schemes at that time (2007) were less efficient than downloading the whole DB (most ...

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There's a new really simple OT protocol based on DH. It's even practical. Watch this video. For the paper and source code, go here.

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They could use 1 out of 2 oblivious transfer. Alice offers the messages $0$ and $a$ and Bob uses $b$ as his choice bit (I.e., choosing the first message if $b = 0$ and the second if $b = 1$.). It should be easy to see that Bob now receives $a \land b$ (if in doubt write down the truth-table). Now Bob can send the result to Alice (or they can do the protocol ...

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