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IEEE Transactions on Information Theory

On the Oblivious-Transfer Capacity of Noisy Resources

Anderson C. A. Nascimento, Andreas Winter

Published May 29, 2008• 70 citations
Publisher

Abstract

In this paper, we deal with the task of obtaining oblivious transfer (OT) from noisy resources. We characterize which noisy channels/distributions are useful for obtaining OT. We also introduce the problem of computing the oblivious-transfer capacity of a noisy resource, which measures the optimal way of implementing OT from a noisy channel/distribution. We show that for honest-but-curious sender, the oblivious-transfer capacity of noisy resources is strictly positive. Several open questions are raised.

DOI
10.1109/tit.2008.921856

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In this paper, we deal with the task of obtaining oblivious transfer (OT) from noisy resources. We characterize which noisy channels/distributions are useful for obtaining OT. We also introduce the problem of computing the oblivious-transfer capacity of a noisy resource, which measures the optimal way of implementing OT from a noisy channel/distribution. We show that for honest-but-curious sender, the oblivious-transfer capacity of noisy resources is strictly positive. Several open questions are raised.
We deal with the task of obtaining oblivious transfer from noisy resources. We characterize which noisy channels/distributions are useful for obtaining oblivious transfer. We also introduce the problem of computing the oblivious transfer capacity of a noisy resource, which measures the optimal way of implementing oblivious transfer from a noisy channel/distribution. We show that for honest but curious sender, the oblivious transfer capacity of noisy resources is strictly positive. Several open questions are raised.
One of the most important primitives in two-party distrustful cryptography is oblivious transfer, a complete primitive for two-party computation. Recently introduced, the oblivious transfer capacity of a noisy channel measures an efficiency of information theoretical reductions from 1-out-of-k, l-string oblivious transfer to noisy channels. It is defined as the maximal achievable ratio l/n, where l is the length of the strings which are to be transferred and n is the number of times the noisy channel is invoked. This quantity is unknown in a general case. For discrete memoryless channels, it is known to be nonnegligible for honest-but-curious players, but the non-zero rates have not ever been proved achievable in the case of malicious players. Here, we show that in the particular case of the erasure channel, more precise answers can be obtained. We compute the OT capacity of the erasure channel for the case of honest-but-curious players and, for the fully malicious players, we give its lower bound.
In this paper, we study the information-theoretic limits of oblivious transfer via noisy channels. We also investigate oblivious transfer over a noisy multiple-access channel with two non-colluding senders and a single receiver. The channel is modeled through correlations among the parties, who may be honest-but-curious or, in the case of the receiver, potentially malicious. We first revisit the information-theoretic limits of two-party oblivious transfer and then extend these results to the multiple-access setting. For honest-but-curious participants, we introduce a multiparty protocol that reduces a general multiple access channel to a suitable correlation model. In scenarios with a malicious receiver, we characterize an achievable oblivious transfer rate region.
Oblivious Transfer (OT) is a broadly studied cryptographic primitive which involves two mutually distrustful users who wish to interact with each other in order to transfer messages in an oblivious manner. Noise is an important resource to realize information-theoretically secure cryptographic protocols including oblivious transfer. However, oftentimes these noisy channels may be poorly characterized and the complete channel characteristics might be unknown to both users. Such channels are studied in the literature through the lens of compound channels. We study 1-out-of-2 oblivious transfer over a compound binary erasure channel (compound-BEC) and characterize the oblivious transfer capacity of compound-BEC. Our OT capacity characterization involves a general alphabet compound-DMC converse, subsequently specialized to compound-BEC along with an optimal and computationally-efficient achievability scheme for honest-but-curious users.
We consider the problem of oblivious transfer (OT) over OFDM and MIMO wireless communication systems where only the receiver knows the channel state information. The sender and receiver also have unlimited access to a noise-free real channel. Using a physical layer approach, based on the properties of the noisy fading channel, we propose a scheme for honest-but-curious parties that enables the transmitter to send obliviously one-of-two files, i.e., without knowing which one has been actually requested by the receiver, while also ensuring that the receiver does not get any information about the other file.
Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy channels have to be considered in the scenario where a cheating party has some degree of control over the channel characteristics. Damgård et al. (EUROCRYPT 1999) proposed a more realistic model where such level of control is permitted to an adversary, the so called unfair noisy channels, and proved that they can be used to obtain commitment and oblivious transfer protocols. Given that noisy channels are a precious resource for cryptographic purposes, one important question is determining the optimal rate in which they can be used. The commitment capacity has already been determined for the cases of discrete memoryless channels and Gaussian channels. In this work we address the problem of determining the commitment capacity of unfair noisy channels. We compute a single-letter characterization of the commitment capacity of unfair noisy channels. In the case where an adversary has no control over the channel (the fair case) our capacity reduces to the well-known capacity of a discrete memoryless binary symmetric channel.