# Reducing String Oblivious Transfer to Universal Oblivious Transfer

## Stefan Wolf

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```This paper is concerned with information-theoretic reductions of
1-out-of-2 chosen string oblivious transfer to other primitives that
are as weak as possible. At Eurocrypt '97, Brassard and Crepeau
presented a reduction to so-called generalized bit oblivious transfer,
a primitive in which the sender inputs a pair of bits of which the
receiver can choose to obtain at most one bit of deterministic
information (e.g., one of the two bits, the XOR or AND function of the
bits, and so on). It was stated as an open problem how this can be
generalized to probabilistic information (where the receiver for
instance obtains noisy versions of the bits). We show that the most
optimistic answer to this question is the correct one: Whenever the
so-called universal oblivious transfer is such that Bob does not
obtain full information about the bits sent, then string oblivious
transfer can be reduced to it in linear time, where an exponentially
small failure probability must be tolerated. The new technique applied
in the analysis uses specific side information provided to the
receiver by an oracle and allows to simplify the argumentation