Efficient Multi-party Computation: From Passive to Active Security via Secure SIMD Circuits

A central problem in cryptography is that of converting protocols that offer security against passive (or semi-honest) adversaries into ones that offer security against active (or malicious) adversaries. This problem has been the topic of a large body of work in the area of secure multiparty computation (MPC). Despite these efforts, there are still big efficiency gaps between the best protocols in these two settings. In two recent works, Genkin et al. (STOC 2014) and Ikarashi et al. (ePrint 2014) suggested the following new paradigm for efficiently transforming passive-secure MPC protocols into active-secure ones. They start by observing that in several natural information-theoretic MPC protocols, an arbitrary active attack on the protocol can be perfectly simulated in an ideal model that allows for additive attacks on the arithmetic circuit being evaluated. That is, the simulator is allowed to (blindly) modify the original circuit by adding an arbitrary field element to each wire. To protect against such attacks, the original circuit is replaced by a so-called AMD circuit, which can offer protection against such attacks with constant multiplicative overhead to the size.