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arXiv:1504.01101 · IEEE International Symposium on Information Theory (ISIT)

Private data transfer over a broadcast channel

Manoj Mishra, Tanmay Sharma, Bikash Kumar Dey, Vinod M. Prabhakaran

Published Jun 1, 2015• 2 citations
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Abstract

We study the following private data transfer problem: Alice has a database of files. Bob and Cathy want to access a file each from this database (which may or may not be the same file), but each of them wants to ensure that their choices of file do not get revealed even if Alice colludes with the other user. Alice, on the other hand, wants to make sure that each of Bob and Cathy does not learn any more information from the database than the files they demand (the identities of which will be unknown to her). Moreover, they should not learn any information about the other files even if they collude. It turns out that it is impossible to accomplish this if Alice, Bob, and Cathy have access only to private randomness and noiseless communication links. We consider this problem when a binary erasure broadcast channel with independent erasures is available from Alice to Bob and Cathy in addition to a noiseless public discussion channel. We study the file-length-per-broadcast-channel-use rate in the honest-but-curious model. We focus on the case when the database consists of two files, and obtain the optimal rate. We then extend to the case of larger databases, and give upper and lower bounds on the optimal rate.

DOI
10.1109/isit.2015.7282676

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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).
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We formulate and study a cryptographic problem relevant to wireless: a sender, Alice, wants to transmit private messages to two receivers, Bob and Calvin, using unreliable wireless broadcast transmissions and short public feedback from Bob and Calvin. We ask, at what rates can we broadcast the private messages if we also provide (information-theoretic) unconditional security guarantees that Bob and Calvin do not learn each-other's message? We characterize the largest transmission rates to the two receivers, for any protocol that provides unconditional security guarantees. We design a protocol that operates at any rate-pair within the above region, uses very simple interactions and operations, and is robust to misbehaving users.
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Both the oblivious transfer (OT) problem and the symmetric private information retrieval (SPIR) problem studies the scenario where a client retrieves information privately and securely from databases, i.e., the privacy of the client is protected from the databases, and the undesired information is protected from the client. The OT problem studies the case of one database plus additional noisy resources between the database and the client. The SPIR problem studies the case of multiple replicated and non-colluding databases. In this paper, we combine the two models and propose a new problem of oblivious transfer (OT) with two replicated databases and a binary erasure multiple access channel connecting the databases and the client. We first provide an upper bound on the OT capacity. We then propose a protocol which achieves the upper bound. Therefore, we obtain the capacity of OT for this model. In our achievability and converse proofs, we utilized the techniques from both traditional OT and PIR. Compared to schemes that utilizes only techniques from OT, we see a 100% increase in the achieved OT rate.