A Black-Box Construction of Fully-Simulatable, Round-Optimal Oblivious Transfer from Strongly Uniform Key Agreement

We show how to construct maliciously secure oblivious transfer (M-OT) from a strengthening of key agreement (KA) which we call strongly uniform KA (SU-KA), where the latter roughly means that the messages sent by one party are computationally close to uniform, even if the other party is malicious. Our transformation is black-box, almost round preserving (adding only a constant overhead of up to two rounds), and achieves standard simulation-based security in the plain model. As we show, 2-round SU-KA can be realized from cryptographic assumptions such as low-noise LPN, high-noise LWE, Subset Sum, DDH, CDH and RSA—all with polynomial hardness—thus yielding a black-box construction of fully-simulatable, round-optimal, M-OT from the same set of assumptions (some of which were not known before).