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 socalled AMD circuit, which can offer protection against such attacks with constant multiplicative overhead to the size. Our motivating observation is that in the most efficient known information-theoretic MPC protocols, which are based on packed secret sharing, it is not the case that general attacks reduce to additive attacks. Instead, the corresponding ideal attack can include limited forms of linear combinations of wire values. We extend the AMD circuit methodology to so-called secure SIMD circuits, which offer protection against this more general class of attacks. We apply secure SIMD circuits to obtain several asymptotic and concrete efficiency improvements over the current state of the art. In particular, we improve the additive per-layer overhead of the current best protocols from O(n²) to O(n), where n is the number of parties, and obtain the first protocols based on packed secret sharing that “natively” achieve near-optimal security without incurring the high concrete cost of Bracha’s committee-based security amplification method. Our analysis is based on a new modular framework for proving reductions from general attacks to algebraic attacks. This framework allows us to reprove previous results in a conceptually simpler and more unified way, as well as obtain our new results.