At CRYPTO 2018 Cramer et al. presented SPDZ 2 k , a new secret-sharing based protocol for actively secure multi-party computation against a dishonest majority, that works over rings instead of fields. Their protocol uses slightly more communication than competitive schemes working over fields. However, their approach allows for arithmetic to be carried out using native 32 or 64-bit CPU operations rather than modulo a large prime. The authors thus conjectured that the increased communication would be more than made up for by the increased efficiency of implementations.In this work we answer their conjecture in the affirmative. We do so by implementing their scheme, and designing and implementing new efficient protocols for equality test, comparison, and truncation over rings. We further show that these operations find application in the machine learning domain, and indeed significantly outperform their field-based competitors. In particular, we implement and benchmark oblivious algorithms for decision tree and support vector machine (SVM) evaluation.

Abstract. SPDZ, TinyOT and MiniMAC are a family of MPC protocols based on secret sharing with MACs, where a preprocessing stage produces multiplication triples in a finite field. This work describes new protocols for generating multiplication triples in fields of characteristic two using OT extensions. Before this work, TinyOT, which works on binary circuits, was the only protocol in this family using OT extensions. Previous SPDZ protocols for triples in large finite fields require somewhat homomorphic encryption, which leads to very inefficient runtimes in practice, while no dedicated preprocessing protocol for MiniMAC (which operates on vectors of small field elements) was previously known. Since actively secure OT extensions can be performed very efficiently using only symmetric primitives, it is highly desirable to base MPC protocols on these rather than expensive public key primitives. We analyze the practical efficiency of our protocols, showing that they should all perform favorably compared with previous works; we estimate our protocol for SPDZ triples in F 2 40 will perform around 2 orders of magnitude faster than the best known previous protocol.

We present a new constant round additively homomorphic commitment scheme with (amortized) computational and communication complexity linear in the size of the string committed to. Our scheme is based on the non-homomorphic commitment scheme of Cascudo et al. presented at PKC 2015. However, we manage to add the additive homomorphic property, while at the same time reducing the constants. In fact, when opening a large enough batch of commitments we achieve an amortized communication complexity converging to the length of the message committed to, i.e., we achieve close to rate 1 as the commitment protocol by Garay et al. from Eurocrypt 2014. A main technical improvement over the scheme mentioned above, and other schemes based on using error correcting codes for UC commitment, we develop a new technique which allows to based the extraction property on erasure decoding as opposed to error correction. This allows to use a code with significantly smaller minimal distance and allows to use codes without efficient decoding. Our scheme only relies on standard assumptions. Specifically we require a pseudorandom number generator, a linear error correcting code and an ideal oblivious transfer functionality. Based on this we prove our scheme secure in the Universal Composability (UC) framework against a static and malicious adversary corrupting any number of parties. On a practical note, our scheme improves significantly on the nonhomomorphic scheme of Cascudo et al. Based on their observations in regards to efficiency of using linear error correcting codes for commitments we conjecture that our commitment scheme might in practice be more efficient than all existing constructions of UC commitment, even non-homomorphic constructions and even constructions in the random oracle model. In particular, the amortized price of computing one of our commitments is less than that of evaluating a hash function once.

Abstract. We describe, and implement, a maliciously secure protocol for two-party computation in a parallel computational model. The protocol is based on cut-and-choose of Yao's garbled circuit and an efficient oblivious transfer extension. The implementation is done using CUDA and yields fast results in a financially feasible and practical setting by using a consumer grade CPU and GPU. Our protocol introduces a novel construction in order to verify consistency of the garbled circuit constructor's input in a parallel and maliciously secure setting.

Cryptocurrency exchange services are either trusted central entities that have been routinely hacked (losing over 8 billion USD), or decentralized services that make all orders public before they are settled. The latter allows market participants to "front run" each other, an illegal operation in most jurisdictions. We extend the "Insured MPC" approach of Baum et al. (FC 2020) to construct an efficient universally composable privacy preserving decentralized exchange where a set of servers run private cross-chain exchange order matching in an outsourced manner, while being financially incentivised to behave honestly. Our protocol allows for exchanging assets over multiple public ledgers, given that users have access to a ledger that supports standard public smart contracts. If parties behave honestly, the on-chain complexity of our construction is as low as that of performing the transactions necessary for a centralized exchange. In case malicious behavior is detected, users are automatically refunded by malicious servers at low cost. Thus, an actively corrupted majority can only mount a denial-of-service attack that makes exchanges fail, in which case the servers are publicly identified and punished, while honest clients do not to lose their funds. For the first time in this line of research, we report experimental results on the MPC building block, showing the approach is efficient enough to be used in practice.