Probabilistic truncation has been widely used in a broad range of privacy-preserving machine learning (PPML) platforms, such as EdaBits (Crypto 20), ABY 2.0 (Usenix 21), Crypten (NIPS 21), Piranha-Falcon (Usenix 22), and Bicoptor (S&P 23), etc. In this work, we examine the problems of common probabilistic truncation protocols in PPML, and propose solutions from the perspectives of accuracy and efficiency. With regard to accuracy, we found the recommended precision parameters in many existing works are incorrect, leading to extremely low inference accuracy. We conducted a thorough analysis of their open-source code and found that their errors were mainly caused by simplified implementation; more specifically, random numbers are not correctly sampled in probabilistic truncation protocols. Based on this, we provide a detailed theoretical analysis to validate our views. With regard to efficiency, we identify limitations in the state-of-the-art secure comparison, Bicoptor’s (S&P 2023) DReLU protocol, which relies on the probabilistic truncation and is heavily constrained by the security parameter to eliminate errors, significantly impacting its performance. To address these challenges, we introduce a non-interactive deterministic truncation technique, replacing the original probabilistic truncation. Additionally, we propose a new technique for speeding up the ReLU/DReLU evaluation, which can be applied to the other non-linear functions as well. When the input size of DReLU is reduced to 7 bits, we can speed up approximately 5x the ReLU protocols w.r.t. ABY3, ABY2.0, EdaBits, and Bicoptor without compromising model accuracy. The improved protocol can complete a ReLU evaluation within 2 rounds and 704 bits overall communication when the input/output is secretly shared over the 64-bit ring, which yields a 92% communication reduction on original Bicoptor. Compared to existing PPML platforms with GPU acceleration, our benchmark indicates a 10x improvement in the DReLU protocol, and a 6x improvement in the ReLU protocol over Piranha-Falcon and a 3.7x improvement over Bicoptor. As a result, the overall PPML model inference could be sped up by 3-4 times.

Abstract Actively secure two-party computation (2PC) is one of the canonical building blocks in modern cryptography. One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we make significant progress in closing this gap by proposing two new actively secure constant-round 2PC protocols, one with one-way communication of $$2\kappa +5$$ 2 κ + 5 bits per AND gate (for $$\kappa $$ κ -bit computational security and any statistical security) and one with total communication of $$2\kappa +\rho +5$$ 2 κ + ρ + 5 bits per AND gate (for $$\rho $$ ρ -bit statistical security). In particular, our first protocol essentially matches the one-way communication of semi-honest half-gates protocol. Our optimization is achieved by three new techniques: The recent compression technique by Dittmer et al. (Crypto 13510:57–87, 2022) shows that a relaxed preprocessing is sufficient for authenticated garbling that does not reveal masked wire values to the garbler. We introduce a new form of authenticated bits and propose a new technique of generating authenticated AND triples to reduce the one-way communication of preprocessing from $$5\rho +1$$ 5 ρ + 1 bits to 2 bits per AND gate for $$\rho $$ ρ -bit statistical security. Unfortunately, the above compressing technique is only compatible with a less compact authenticated garbled circuit of size $$2\kappa +3\rho $$ 2 κ + 3 ρ bits per AND gate. We designed a new authenticated garbling that does not use information-theoretic MACs but rather dual execution without leakage to authenticate wire values in the circuit. This allows us to use a more compact half-gates based authenticated garbled circuit of size $$2\kappa +1$$ 2 κ + 1 bits per AND gate, and meanwhile keep compatible with the compression technique. Our new technique can achieve one-way communication of $$2\kappa +5$$ 2 κ + 5 bits per AND gate. In terms of total communication, we notice that the communication overhead of the consistency checking method by Dittmer et al. (Crypto 13510:57–87, 2022) can be optimized by adding one-round of interaction and utilizing the Free-XOR property. This reduces the online communication from $$2\kappa +3\rho $$ 2 κ + 3 ρ bits down to $$2\kappa +\rho +1$$ 2 κ + ρ + 1 bits per AND gate. Combined with our first contribution, this yields total amortized communication of $$2\kappa +\rho +5$$ 2 κ + ρ + 5 bits.

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.