We put forth a new paradigm for secure multi-party computation (MPC) in the preprocessing model, where a feasible one-time setup can enable a lifetime of efficient online secure computations. Our protocols match the security guarantees and low costs of the cheapest category of MPC solutions, namely 3-party protocols (3PC) secure against a single malicious party, with the qualitative advantages that one party communicates data sublinear in the circuit size, and can go offline after its initial messages. This “2+ 1“-party structure can alternatively be instantiated between 2 parties with the aid of an (untrusted) dealer. Within such existing protocols, we provide comparable online performance while improving the storage and offline dealer-to-party communication requirements by more than 3 orders of magnitude. At the technical level, we build on the Fully Linear Interactive Oracle Proof (FLIOP)-based protocol design of Boyle et al. (CRYPTO 2021). We provide an extensive assortment of algorithmic and implementation-level optimizations, design efficient distributed proofs of well-formedness of complex FLIOP correlations, and make them circuit-independent. We implement and benchmark our end-to-end system against the state of the art in the 2+1 regime, a dealer-aided variant of SPDZ for Boolean circuits. We additionally extend our techniques to the$(n+1)$party setting, where a dealer aids general dishonest-majority MPC, and provide a variant of the protocol which further achieves security with “identifiable abort.”

A Distributed Point Function (DPF) is a crypto-graphic primitive used for compressing additive secret shares of a secret unit vector across two parties. Many DPF applications require compressed shares of a sparse weight- t vector, namely a Distributed Multi-Point Function (DMPF). Despite the strong motivation and prior optimization efforts, in most use cases the best practical implementation of DMPF is still a simple brute-force combination of$t$independent DPFs. We present new constructions and optimized implementations of DMPFs in different parameter regimes, providing significant efficiency savings over existing approaches. We showcase our new constructions within applications of pseu-dorandom correlation generators (PCGs) and 2-server private set intersection (PSI). Incorporating our tools into the state-of-the-art PCG for “silent” generation of binary multiplication triples (FOLEAGE, Bombar et al, ePrint'24) yields a x2.68 improvement in throughput, with only x 1.4 blowup in the seed size. On a single core of our benchmark machine, our implementation silently generates up to 22.1 million triples per second, outperforming even the best “non-silent” protocol (Roy, CRYPTO'22), which generates 16 million triples per second.

Finite fields of characteristic 2 -- "binary fields" -- are used in a variety of applications in cryptography and data storage. Multiplication of two finite field elements is a fundamental operation and a well-known computational bottleneck in many of these applications, as they often require multiplication of a large number of elements. In this work we focus on accelerating multiplication in "large" binary fields of sizes greater than 232. We devise a new parallel algorithm optimized for execution on GPUs. This algorithm makes it possible to multiply large number of finite field elements, and achieves high performance via bit-slicing and fine-grained parallelization.