Efficient 1-out-of-n oblivious transfer schemes with universally usable parameters

Abstract

In this paper, we propose efficient and secure (string) oblivious transfer (OT(n)(1)) schemes for any n greater than or equal to 2. We build our OT(n)(1) scheme from fundamental cryptographic techniques directly. The receiver's choice is unconditionally secure and the secrecy of the unchosen secrets is based on the hardness of the decisional Diffie-Hellman problem. Some schemes achieve optimal efficiency in terms of the number of rounds and the total number of exchanged messages for the case that the receiver's choice is unconditionally secure. The distinct feature of our scheme is that the system-wide parameters are independent of n and universally usable, that is, all possible receivers and senders use the same parameters and need no trapdoors specific to each of them. We extend our OT(n)(1) schemes to distributed oblivious transfer schemes. Our distributed OT(n)(1) schemes take full advantage of the research results of secret sharing. For applications, we present a method of transforming any (single-database) PIR protocol into a symmetric PIR protocol by slightly increasing the communication cost only.