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arXiv:2207.06363 · IEEE Transactions on Information Theory

Capacity Results for the Wiretapped Oblivious Transfer

Tianyou Pei, Wei Kang, Nan Liu

Published Oct 28, 2024• 2 citations
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Abstract

In this paper, we study the problem of the 1-of-2 string oblivious transfer (OT) between Alice and Bob in the presence of a passive eavesdropper Eve. The eavesdropper Eve is not allowed to get any information about the private data of Alice or Bob. When Alice and Bob are honest-but-curious users, we propose a protocol that satisfies 1-private (neither Alice nor Bob colludes with Eve) OT requirements for the binary erasure symmetric broadcast channel, in which the channel provides dependent erasure patterns to Bob and Eve. We find that when the erasure probabilities of the channel are within a certain range, the derived lower and upper bounds on the wiretapped OT capacity meet. Our results generalize and improve upon the results on 1-private wiretapped OT capacity by Mishra et al. Finally, we propose a protocol for a larger class of wiretapped channels and derive a lower bound on the wiretapped OT capacity.

DOI
10.1109/tit.2024.3487218

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In this paper, we study the problem of the 1-of-2 string oblivious transfer (OT) between Alice and Bob in the presence of a passive eavesdropper Eve. The eavesdropper Eve is not allowed to get any information about the private data of Alice or Bob. When Alice and Bob are honest-but-curious users, we propose a protocol that satisfies 1-private (neither Alice nor Bob colludes with Eve) OT requirements for the binary erasure symmetric broadcast channel, in which the channel provides dependent erasure patterns to Bob and Eve. We find that when the erasure probabilities of the channel are within a certain range, the derived lower and upper bounds on the wiretapped OT capacity meet. Our results generalize and improve upon the results on 1-private wiretapped OT capacity by Mishra et al. Finally, we propose a protocol for a larger class of wiretapped channels and derive a lower bound on the wiretapped OT capacity.
In this paper, we study the problem of obtaining 1-of-2 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the 1-of-2 string OT capacity for both 2-privacy (when Eve can collude with either Alice or Bob) and 1-privacy (when no such collusion is allowed). We generalize these capacity results to 1-of-N string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and 1-of-2 string OT is desired between Alice and Bob with 1-privacy. For this setup, we derive an upper and lower bound on the 1-of-2 string OT capacity which match in one of two possible parameter regimes.
We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).
We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.
We propose the problem of wiretapped commitment, where two parties, say committer Alice and receiver Bob, engage in a commitment protocol using a noisy channel as a resource, in the presence of an eavesdropper, say Eve. Noisy versions of Alice's transmission over the wiretap channel are received by both Bob and Eve. We seek to determine the maximum commitment throughput in the presence of eavesdropper, i.e., wiretapped commitment capacity, where in addition to the standard security requirements for two-party commitment, one seeks to ensure that Eve doesn't learn about the commit string. A key interest in this work is to explore the effect of collusion (or lack of it) between the eavesdropper Eve and either Alice or Bob. Toward the same, we present results on the wiretapped commitment capacity under the so-called Y-private regime (when Alice or Bob cannot collude with Eve) and the 2-private regime (when Alice or Bob may collude with Eve).
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.