Bicoptor: Two-round Secure Three-party Non-linear Computation without Preprocessing for Privacy-preserving Machine Learning

The overhead of non-linear functions dominates the performance of the secure multiparty computation (MPC) based privacy-preserving machine learning (PPML). This work introduces two sets of novel secure three-party computation (3PC) protocols, using additive and replicated secret sharing schemes respectively. We name the whole family of protocols as Bicoptor, its basis is a new sign determination protocol, which relies on a clever use of the truncation protocol proposed in SecureML (S&P 2017). Our 3PC sign determination protocol only requires two communication rounds, and does not involve any preprocessing. Such sign determination protocol is well-suited for computing non-linear functions in PPML, e.g. the activation function ReLU, Maxpool, and their variants. We develop suitable protocols for these non-linear functions, which form a family of GPU-friendly protocols, Bicoptor. All Bicoptor protocols only require two communication rounds without preprocessing. We evaluate the protocols using additive secret sharing under a 3-party LAN network over a public cloud, and achieve 90,000 DReLU/ReLU or 3,200 Maxpool (find the maximum value of nine inputs) operations per second. Under the same settings and environment, our ReLU protocol has a one or even two order(s) of magnitude improvement to the state-of-the-art works, Edabits (CRYPTO 2020) or Falcon (PETS 2021), respectively without batch processing.