Abstract

We define the following problem termed ${n}\boldsymbol \times $ 1-out-of- ${n}$ oblivious transfer ( ${n}\boldsymbol \times $ 1-out-of- ${n}$ OT): in a system with one server and ${n}$ clients, how to securely and efficiently assign ${n}$ secrets to ${n}$ clients by the server, with each client getting a unique secret from the server, and the server and clients remain unknown of how the secrets are distributed? This is a novel problem that is fundamentally different than 1-out-of- ${n}$ OT repeated ${n}$ times, and is different than ${k}$ -out-of- ${n}$ OT as well. Nevertheless, the proposed OT has many practical applications such as privacy-preserving data aggregation in smart grids. It can also be employed to design crypto protocols for anonymous communications and group signatures. In this paper, we propose the first algorithm to efficiently and effectively implement the ${n}\boldsymbol \times $ 1-out-of- ${n}$ OT. We construct hidden permutation circuits to obliviously assign ${n}$ secrets to ${n}$ clients by the server within ${O}$ (lg( ${n}$ )) time. A rigorous theoretical analysis is also carried out to investigate the security strength and performance of the protocol.

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