Secure two-party computation with homomorphic encryption (HE) protects data privacy with a formal security guarantee but suffers from high communication overhead. While previous works, e.g., Cheetah, Iron, etc, have proposed efficient HE-based protocols for different neural network (NN) operations, they still assume high precision, e.g., fixed point 37 bit, for the NN operations and ignore NNs' native robustness against quantization error. In this paper, we propose HEQuant, which features low-precision-quantization-aware optimization for the HE-based protocols. We observe the benefit of a naive combination of quantization and HE quickly saturates as bit precision goes down. Hence, to further improve communication efficiency, we propose a series of optimizations, including an intra-coefficient packing algorithm and a quantization-aware tiling algorithm, to simultaneously reduce the number and precision of the transferred data. Compared with prior-art HE-based protocols, e.g., CrypTFlow2, Cheetah, Iron, etc, HEQuant achieves $3.5\sim 23.4\times$ communication reduction and $3.0\sim 9.3\times$ latency reduction. Meanwhile, when compared with prior-art network optimization frameworks, e.g., SENet, SNL, etc, HEQuant also achieves $3.1\sim 3.6\times$ communication reduction.

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