We first provide a four-round two-party protocol for coin-tossing that achieves 1/p-simulation security (i.e. simulation fails with probability at most 1/p+\ngl), in the presence of malicious corruptions. Next, we provide a four-round two-party protocol for general functionalities, where both parties receive the output, that achieves 1/p-security in the presence of malicious adversaries corrupting one of the parties, and full security in the presence of non-aborting malicious adversaries corrupting the other party.
Next, we provide a three-round oblivious-transfer protocol, that achieves 1/p-simulation security against arbitrary malicious senders, while simultaneously guaranteeing a meaningful notion of privacy against malicious corruptions of either party.
Finally, we show that the simulation-based security guarantees for our three-round protocols are optimal by proving that 1/p-simulation security is impossible to achieve against both parties in three rounds or less when requiring some minimal guarantees on the privacy of their inputs.Category / Keywords: Secure Computation, Coin-Tossing, Oblivious Transfer, Round Complexity Original Publication (with minor differences): SCN 2016 Date: received 8 Aug 2015, last revised 24 Aug 2016 Contact author: carmit hazay at biu ac il Available format(s): PDF | BibTeX Citation Note: The revised version of October 17,2015 includes a new protocol for oblivious transfer that achieves the strongest security notion achievable in three rounds, namely, it provides full privacy against both parties and 1/p security against a malicious sender. It also includes a new result that proves optimality of this new construction by providing a matching lower bound. Version: 20160824:192718 (All versions of this report) Short URL: ia.cr/2015/797 Discussion forum: Show discussion | Start new discussion