  The overhead of non-linear functions dominates the performance of the secure
multiparty computation (MPC) based privacy-preserving machine learning (PPML).
This work introduces a family of novel secure three-party computation (3PC)
protocols, Bicoptor, which improve the efficiency of evaluating non-linear
functions. The basis of Bicoptor 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 Bicoptor under a 3-party LAN network
over a public cloud, and achieve more than 370,000 DReLU/ReLU or 41,000 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 orders of
magnitude improvement to the state-of-the-art works, Falcon (PETS 2021) or
Edabits (CRYPTO 2020), respectively without batch processing.
