Efficient Reduction among Oblivious Transfer Protocols based on New Self-Intersecting Codes

Abstract

A 1 2-OT2 (one-out-of-two Bit Oblivious Transfer) is a technique by which a party S owning two secret bits b 0, b 1, can transfer one of them b c to another party R, who chooses c. This is done in a way that does not release any bias about b c to R nor any bias about c to S. One interesting extension of this transfer is the 1 2-OT 1 k (one-out-of-two String O.T.) in which the two secrets q 0, q 1 are elements of GF k (2) instead of bits. A reduction of 1 2-OT 1 k to 1 2-OT2 presented in [BCR86] uses O(k lo 2 3) calls to 1 2-OT2 and thus raises an interesting combinatorial question: how many calls to 1 2-OT2 are necessary and sufficient to achieve a 1 2-OT 1 k ? In the current paper we answer this question quite precisely. We accomplish this reduction using Θ(k) calls to 1 2-OT2. First, we show by probabilistic methods how to obtain such a reduction with probability essentially 1 and second, we give a deterministic polynomial time construction based on the algebraic codes of Goppa [Gop81].