Can anyone suggest a cryptosystem for the following problem? We are working on a university research project.
Alice has multiple messages $M_i$, $i = 1,\ldots ,n$. Bob should obtain any, but exactly one $M_i$, without obtaining other $M_j$, $j \neq i$. Alice, on the other hand, shouldn't get the exact $i$, which has been selected by Bob.
Analogous physical world scenario
Alice writes each $M_i$ onto a distinct piece of paper, and puts these pieces into a hat. Then, Bob shuffles the pieces by hand without seeing them, draws one piece and, finally, burns the others. Obviously, Bob doesn't have a chance to peek into the hat. Also, Alice cannot see which piece Bob has selected (she is not able to leave secret marks in the pieces).