Abstract: Reductions among oblivious transfers have a long history in cryptography. This paper describes a (2 1)^-1-OT^k protocol that can be reduced to a single execution of UOT by using privacy amplification with extranctors. An extractor allows to efficiently isolate the randomness of some source into virtually-random bits, using a small number of perfectly-random bits as a catalyst. With extractors, less information is transmitted and the leaked information is at most 2^-n-1/2-o(1) bits. The conditions under which the protocol is unconditionally secure are investigated.

Key words: oblivious transfer, privacy amplification, extractor, unconditional security