Paper 2026/1201

Silentium revisited: Pseudorandom Beaver Triple Expansion

Abstract

In the line of the SPDZ protocol for secure multi-party computation, the generation of Beaver triples is the most expensive task. Silentium (Rieder, PrivCryp 25) is the implementation of a Pseudorandom Correlation Generator (PCG) for Beaver triples (Boyle et al., Crypto 20). PCGs focus on low-communication costs., e.g. their PCG reduces the communication by one order of magnitude compared to protocols in MP-SPDZ. Silentium is an implementation of their PCG, achieving similar running times than MP-SPDZ. We make three theoretical contributions to Silentium, including an implementation. First, we make a practical proposal how to generate Beaver triples over binary fields F2λ, which extends the previous setting over prime fields. For this, we propose a suitable instantiation of the Number Theoretic Transform. Second, we show how to use the binary triples to construct what we call a Beaver triple expansion scheme, that is we construct a scheme that expands a small batch of Beaver triples into a large batch of Beaver triples, in the sense of recently established oblivious transfer extension schemes. This feature enables an efficient preprocessing stage for the PCG, closing a practical issue of Silentium. Finally, we provide details about the Silentium implementation, by clearing a technical bug in the initial theoretical protocol description.