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International Journal of Theoretical Physics

Quantum Oblivious Transfer Based on a Quantum Symmetrically Private Information Retrieval Protocol

Yu‐Guang Yang, Si-Jia Sun, Yan Wang

Published Aug 8, 2014• 18 citations
Publisher
DOI
10.1007/s10773-014-2286-3

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We describe efficient constructions for two oblivious twoparty computation problems: l-out-of-N Oblivious Transfer &d 'Oblivious Poly&nial Evaluation.The oblivious polynomial evaluation protocol is based on a new intractability assumption which is closely related to noisy polynomial re construction.A direct corollary of the l-out-of-N OT protccol is an efficient transformation of any Private Information Retrieval (PIR) protocol to a Symmetric PIR (SPIR) prc-tow1 without increasing the number of databases.The new construction for l-out-of-N OT is highly efficient -it requires only log N executions of a l-out-of-2 OT protocol.We also present a construction for k-out-of-N OT which is more efficient than k repetitions of l-out-of-N OT.The efficiency of the new OT protocols makes them useful for a variety of applications.These include oblivious sampling which can be used to securely compare the sizes of web search engines, protocols for privately solving the list intersection problem and for mutually authenticated key exchange based on (possibly weak) passwords, and protocols for anonymity preserving web usage metering.
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.
Oblivious Transfer protocol (OTP) is a paramount important primitive tool in modern cryptography. Essentially, OTP can be used to construct a secure multi-party computation protocol and distributed oblivious transfer protocol (DOTP). DOTP is the general OTP in the distributed setting. Private information retrieval (PIR) and symmetric private information retrieval (SPIR) problems are also analogous to those of the OTP. Due to its importance, the task of constructing efficient and secure OTP has attracted a lot interests. In this paper, a paradigm of OPT protocol and a practical fully-simulatable OTP protocol based on blind GDH (Gap Diffie-Hellman) signature are presented. The proposed schemes can achieve higher efficiency and better security than the popular Malkhi & Sella scheme. The salient property of short signature length of GDH signature scheme enables our proposals applicable to low-bandwidth communication environments.