Almost Optimal Oblivious Transfer from QA-NIZK

We show how to build a UC-Secure Oblivious Transfer in the presence of Adaptive Corruptions from Quasi-Adaptive Non-Interactive Zero-Knowledge proofs. Our result is based on the work of Jutla and Roy at Asiacrypt 2015, where the authors proposed a constant-size very e cient PAKE scheme. As a stepping stone, we rst show how a twoow PAKE scheme can be generically transformed in an optimized way, in order to achieve an e cient threeow Oblivious-Transfer scheme. We then compare our generic transformations to existing OT constructions and see that we manage to gain at least a factor 2 to the best known constructions. To the best of our knowledge, our scheme is the rst UC-secure Oblivious Transfer with a constant size ow from the receiver, and nearly optimal size for the server.