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We consider the problem of extending oblivious transfers: Given a small number of oblivious transfers “for free,” can one implement a large number of oblivious transfers? Beaver has shown how to extend oblivious transfers given a one-way function. However, this protocol is inefficient in practice, in part due to its non-black-box use of the underlying one-way function.

We give efficient protocols for extending oblivious transfers in the random oracle model. We also put forward a new cryptographic primitive which can be used to instantiate the random oracle in our constructions. Our methods suggest particularly fast heuristics for oblivious transfer that may be useful in a wide range of applications.