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Lecture notes in computer science

An Information-Theoretically Secure Threshold Distributed Oblivious Transfer Protocol

Christian L. F. Corniaux, Hossein Ghodosi

Published Jan 1, 2013• 5 citations
Publisher
DOI
10.1007/978-3-642-37682-5_14

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In this paper, we present a new application for , n 1 oblivious transfer, which i s a n i n teractive protocol between two parties Alice and Bob, where Alice has n secrets and Bob has a query i.A t the end of the protocol Bob has the ith secret and no other information about Alice's other secrets, while Alice does not get any information about i.This new application is the Secure Database Access problem.Motivated by this application, we propose an OT scheme which a c hieves low communication complexity and information theoretic security.We use a distributed model for , n 1 oblivious transfer, where Bob interacts with multiple \Alices".In this model, we base our scheme on any PIR scheme, which i s a s c heme where only the privacy of Bob is considered, and use it to construct an OT scheme, private for both parties, without paying too much i n communication complexity.This results in the rst sublinear information theoretic scheme for , n 1 OT.Further motivated by the application of , n 1 OT for polynomial n, w e raise the issue of repetition in , n 1 OT, where both security and eciency are important.We show that previous protocols for , n 1 oblivious transfer fail in this setting.

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We consider the problem of basing Oblivious Transfer (OT) and Bit Commitment (BC), with information theoretic security, on seemingly weaker primitives.We introduce a general model for describing such primitives, called Weak Generic Transfer (WGT). This model includes as important special cases Weak Oblivious Transfer (WOT), where both the sender and receiver may learn too much about the other party's input, and a new, more realistic model of noisy channels, called unfair noisy channels. An unfair noisy channel has a known range of possible noise levels; protocols must work for any level within this range against adversaries who know the actual noise level. We give a precise characterization for when one can base OT on WOT. When the deviation of the WOT from the ideal is above a certain threshold, we show that no information-theoretic reductions from OT (even against passive adversaries) and BC exist; when the deviation is below this threshold, we give a reduction from OT (and hence BC) that is information-theoretically secure against active adversaries. For unfair noisy channels we show a similar threshold phenomenon for bit commitment. If the upper bound on the noise is above a threshold (given as function of the lower bound) then no information-theoretic reduction from OT (even against passive adversaries) or BC exist; when it is below this threshold we give a reduction from BC. As a partial result, we give a reduction from OT to UNC for smaller noise intervals.
In this paper, we present a new application for , n 1 oblivious transfer, which i s a n i n teractive protocol between two parties Alice and Bob, where Alice has n secrets and Bob has a query i.A t the end of the protocol Bob has the ith secret and no other information about Alice's other secrets, while Alice does not get any information about i.This new application is the Secure Database Access problem.Motivated by this application, we propose an OT scheme which a c hieves low communication complexity and information theoretic security.We use a distributed model for , n 1 oblivious transfer, where Bob interacts with multiple \Alices".In this model, we base our scheme on any PIR scheme, which i s a s c heme where only the privacy of Bob is considered, and use it to construct an OT scheme, private for both parties, without paying too much i n communication complexity.This results in the rst sublinear information theoretic scheme for , n 1 OT.Further motivated by the application of , n 1 OT for polynomial n, w e raise the issue of repetition in , n 1 OT, where both security and eciency are important.We show that previous protocols for , n 1 oblivious transfer fail in this setting.