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

We propose efficient and secure (string) oblivious transfer (OT¹_n) schemes for any n≥2. We build our OT¹_n 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 OT¹_n schemes to distributed oblivious transfer schemes. Our distributed OT¹_n 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.