Paper 2020/1053

Circuit Amortization Friendly Encodings and their Application to Statistically Secure Multiparty Computation

Anders Dalskov, Eysa Lee, and Eduardo Soria-Vazquez

Abstract

At CRYPTO 2018, Cascudo et al. introduced Reverse Multiplication Friendly Embeddings (RMFEs). These are a mechanism to compute $$ parallel evaluations of the same arithmetic circuit over a field $$ at the cost of a single evaluation of that circuit in $$, where $$. Due to this inequality, RMFEs are a useful tool when protocols require to work over $$ but one is only interested in computing over $$. In this work we introduce Circuit Amortization Friendly Encodings (CAFEs), which generalize RMFEs while having concrete efficiency in mind. For a Galois Ring $$, CAFEs allow to compute certain circuits over $$ at the cost of a single secure multiplication in $$. We present three CAFE instantiations, which we apply to the protocol for MPC over $$ 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 $$ and $$ 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 $$ followed by bit-wise operations. From an implementation of our techniques, we estimate that an SVM can be evaluated on 250 images in parallel up to $$ more efficiently using our techniques, compared to the protocol from Abspoel et al. (TCC 2019).