Paper 2009/327

Simple Adaptive Oblivious Transfer Without Random Oracle

Kaoru Kurosawa and Ryo Nojima

Abstract

Adaptive oblivious transfer (adaptive OT) schemes have wide applications such as oblivious database searches, secure multiparty computation and etc. It is a two-party protocol which simulates an ideal world such that the sender sends $M_1, \cdots, M_n$ to the trusted third party (TTP) first, and then the receiver receives $M_{\sigma_i}$ from TTP adaptively for $i=1,2,\cdots k$. In the standard model, however, the fully simulatable schemes known so far had to rely on dynamic assumptions such as $q$-strong DH assumption, $q$-PDDH assumption and $q$-hidden LRSW assumption. This paper shows two fully simulatable adaptive OT schemes which do not rely on dynamic assumptions in the standard model. Our first scheme holds under the DDH assumption and our second scheme holds under the Paillier's decisional $N$th residuosity assumption, respectively.