ConstantRound Oblivious Transfer in the Bounded S

Authors: Yan Zong Ding Danny Harnik Alon Rosen Ronen Shaltiel

Publish Date: 2007/03/21

Volume: 20, Issue: 2, Pages: 165-202

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Abstract

We present the first constantround protocol for Oblivious Transfer in Maurers bounded storage model In this model a long random string R is initially transmitted and each of the parties stores only a small portion of R Even though the portions stored by the honest parties are small security is guaranteed against any malicious party that remembers almost the entire string R but not all of it Previous constructions for oblivious transfer in the bounded storage model required polynomially many rounds of interaction In contrast our protocol uses only five messages In addition we also improve other parameters such as the number of bits transferred and the probability of immaturely aborting the protocol due to failure Our techniques utilize explicit constructions from the theory of derandomization In particular we achieve the constant round complexity of our oblivious transfer protocol by constructing a novel fourmessage protocol for Interactive Hashing in place of the wellknown protocol by Naor et al known as the NOVY protocol which involves many rounds of interaction Our fourmessage interactive hashing protocol is constructed by use of twise independent permutations and may be of independent interest For achieving constantround complexity we also construct a new subset encoding scheme that is dense namely guarantees that almost every string in the image of the encoding function has a preimage Other tools we employ include randomness extractors and averaging samplers

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