Efficient computational oblivious transfer using interactive hashing

Abstract

We present two protocols for reducing oblivious transfer (OT) to the security of trapdoor permutations and to the hardness of some coding problems, respectively. The first protocol is the most efficient known to date, while the second one is a theoretical proof-of-concept. Our constructions leverage the power of Interactive Hashing (IH). The first protocol can be viewed as a simple modification of the well-known OT construction by Even, Goldreich and Lem-pel (1985), in which a receiver must send a random domain element to a sender through IH. Alternatively, our protocol can be viewed as a simple modification of the construction by Ostrovsky, Venkatesan and Yung (1993), in which the players substitute the one-way permutation with a trapdoor permutation. We use a similar approach to derive a second OT protocol based on coding assumptions related to security of the McEliece cryptosystem. In our second construction, the receiver inputs a public key into IH while privately keeping the corresponding secret key. Two different versions of IH are used: the computationally secure one in the first protocol, and the information-theoretically secure one in the second.