We show that oblivious transfer can be based on a very general notion of asymmetric information difference. We investigate a Universal Oblivious Transfer, denoted UOT(X, Y), that gives Bob the freedom to access Alice's input X in an arbitrary way as long as he does not obtain full information about X. Alice does not learn which information Bob has chosen. We show that oblivious transfer can be reduced to a single execution of UOT(X, Y) with Bob's knowledge Y restricted in terms of Renyi entropy of order α > 1. For independently repeated UOT the reduction works even if only Bob's Shannon information is restricted, i.e. if H(X¦Y) > 0 in every UOT(X, Y). Our protocol requires that honest Bob obtains at least half of Alice's information X without error.