We present a secure multiparty computation (MPC) protocol based on garbled circuits which is both actively secure and supports the free-XOR technique, and which has communication complexity $O(n)$ per party. This improves on a protocol of Ben-Efraim, Lindell and Omri which only achieved passive security, without support for free-XOR. Our construction is based on a new variant of LPN-based encryption, but has the drawback of requiring a rather expensive garbling phase. To address this issue we present a second protocol that assumes at least $n/c$ of the parties are honest (for an arbitrary fixed value $c$). This second protocol allows for a significantly lighter preprocessing, at the cost of a small sacrifice in online efficiency. We demonstrate the practicality of our evaluation phase with a implementation.

At CRYPTO 2018, Cascudo et al. introduced Reverse Multiplication Friendly Embeddings (RMFEs). These are a mechanism to compute $\delta$ parallel evaluations of the same arithmetic circuit over a field $F_q$ at the cost of a single evaluation of that circuit in $F_{q^d}$, where $\delta < d$. Due to this inequality, RMFEs are a useful tool when protocols require to work over $F_{q^d}$ but one is only interested in computing over $F_q$. In this work we introduce Circuit Amortization Friendly Encoding (CAFEs), which generalize RMFEs while having concrete efficiency in mind. For a Galois Ring $R = GR(2^k,d)$, CAFEs allow to compute certain circuits over $Z_{2^k}$ at the cost of a single secure multiplication in $R$. We present three CAFE instantiations, which we apply to the protocol for MPC over $Z_{2^k}$ via Galois Rings by Abspoel et al. (TCC 2019). Our protocols allow for efficient switching between the different CAFEs, as well as between computation over $R = GR(2^k,d)$ and $F_{2^{d}}$ in a way that preserves the CAFE in both rings. This adaptability leads to efficiency gains for e.g. Machine Learning applications, which can be represented as highly parallel circuits over $Z_{2^k}$ followed by bit-wise operations. From an implementation of our techniques, we estimate that an SVM can be evaluated on 250 images in parallel up to $\times 7$ more efficiently using our techniques, compared to the protocol from Abspoel et al. (TCC 2019).

Recent years have seen a tremendous growth in the interest in secure multiparty computation (MPC) and its applications. While much progress has been made concerning its efficiency, many current, state-of-the-art protocols are vulnerable to Denial of Service attacks, where a cheating party may prevent the honest parties from learning the output of the computation, whilst remaining anonymous. The security model of identifiable abort aims to prevent these attacks, by allowing honest parties to agree upon the identity of a cheating party, who can then be excluded in the future. Several existing MPC protocols offer security with identifiable abort against a dishonest majority of corrupted parties. However, all of these protocols have a round complexity that scales linearly with the depth of the circuit (and are therefore unsuitable for use in high latency networks) or use cryptographic primitives or techniques that have a high computational overhead.

In this work, we present the first efficient MPC protocols with identifiable abort in the dishonest majority setting, which run in a constant number of rounds and make only black-box use of cryptographic primitives. Our main construction is built from highly efficient primitives in a careful way to achieve identifiability at a low cost. In particular, we avoid the use of public-key operations outside of a setup phase, incurring a relatively low overhead on top of the fastest currently known constant-round MPC protocols based on garbled circuits. Our construction also avoids the use of adaptively secure primitives and heavy zero-knowledge machinery, which was inherent in previous works. In addition, we show how to upgrade our protocol to achieve public verifiability using a public bulletin board, allowing any external party to verify correctness of the computation or identify a cheating party.

In this work we develop a new theory for concretely efficient, large-scale MPC with active security. Current practical techniques are mostly in the strong setting of all-but-one corruptions, which leads to protocols that scale badly with the number of parties. To work around this issue, we consider a large-scale scenario where a small minority out of many parties is honest and design scalable, more efficient MPC protocols for this setting. Our results are achieved by introducing new techniques for information-theoretic MACs with short keys and extending the work of Hazay et al. (CRYPTO 2018), which developed new passively secure MPC protocols in the same context. We further demonstrate the usefulness of this theory in practice by analyzing the concrete communication overhead of our protocols, which improve upon the most efficient previous works.