Alice has an item x and Bob has a set of five distinct items y1, y2, y3, y4 and y5. Design a protocol through which Alice (but not Bob) finds out whether her x equals any of Bob's five items; Alice should not find out anything other than the answer ("Yes" or "No") to the above question, and Bob should not know that answer or any secret from Alice. Do not use a hash-based solution because even though the probability of a colission is small, Alice requires that no such colission can occur (but using encryption is fine, because in that case two distinct items that are encrypted with the same key will result in two different ciphertexts). NOTE: THE SOLUTION FOR THIS SHOULD BE MATHEMATICALLY EXACT.