# On the Foundations of Oblivious Transfer

## Christian Cachin

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```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
Rényi entropy of order $\alpha > 1$. For independently repeated UOT
the reduction woks even if only Bob's Shannon information is
restricted, i.e. $H(X|Y) > 0$ in
every UOT$(X, Y)$. Our protocol requires that honest Bob obtains at least
half of Alice's information $X$ without error.