Fast two-party secure computation with minimal assumptions

Almost all existing protocols for secure two-party computation require a specific hardness assumption, such as DDH, discrete logarithm, or a random oracle, even after assuming oracle access to the oblivious transfer functionality for their correctness and/or efficiency. We propose and implement a Yao-based protocol that is secure against malicious adversaries and enjoys the following benefits: it requires the minimal hardness assumption, i.e., OTs; it uses 10 rounds of communication plus OT rounds; it has the optimal overhead complexity (for an approach that uses the circuit-level cut-and-choose technique); and it is embarrassingly parallelizable in the sense that each circuit can be processed in a pipelined manner, and all circuits can be processed in parallel. To achieve these properties, we describe novel solutions for the three main obstacles for achieving security against malicious adversaries in a cut-and-choose garbled-circuit protocol. We propose an efficient proof to establish the generator's output authenticity; we suggest the use of an auxiliary circuit that computes a hash to ensure the generator's input consistency; and we advance the performance of Pinkas and Lindell's state-of-the-art approach for handling the selective failure attack. Not only does our protocol require weaker cryptographic assumptions, but our implementation of this protocol also demonstrates a several factor improvement over the best prior work which relies on specific number-theoretic assumptions. Thus, we show that performance does not require specific algebraic assumptions.