Paper 2024/1274

Generation of Authenticated Secret-Shared Scaled Unit Vectors for Beaver Triples

Abstract

For secure multi-party computation in the line of the secret-sharing based SPDZ protocol, actively secure multiplications consume correlated randomness in the form of authenticated Beaver triples, which need to be generated in advance. Although it is a well-studied problem, the generation of Beaver triples is still a bottleneck in practice. In the two-party setting, the best solution with low communication overhead is the protocol by Boyle et al. (Crypto 2020), which is derived from the recent primitive of Pseudorandom Correlation Generators (PCGs) (Crypto 2019). Their protocol requires less than 2 MB of communication to generate about 100 MB of Beaver triples (per party). In this work, we improve their protocol in terms of communication (7%), computation (20% for its interactive phase), and the amount of correlated randomness consumed by internal secure two-party computations (11% storage). To achieve our improvements, we propose a novel actively secure protocol for the efficient generation of (authenticated) secret-shared scaled unit vectors, which in general are the main building blocks of current PCG protocols.