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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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Actually, it does not matter if Bobs number is greater or less than Alices number. In either case Bob can compute $n_A$ (here I denote by $n_A$ and $n_B$ the private numbers of Alice and Bob respectively). Bob could simply note the number of boxes with one pebbles in them and the number of boxes with two pebbles in them, lets call these numbers $p_1$ and ...


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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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