Deep neural network (DNN) typically involves convolutions, pooling, and activation function. Due to the growing concern about privacy, privacy-preserving DNN becomes a hot research topic. Generally, the convolution and pooling operations can be supported by additive homomorphic and secure comparison, but the secure implementation of activation functions is not so straightforward for the requirements of accuracy and efficiency, especially for the non-linear ones such as exponential, sigmoid, and tanh functions. This paper pays a special attention to the implementation of such non-linear functions in semi-honest model with two-party settings, for which SIRNN is the current state-of-the-art. Different from previous works, we proposed improved implementations for these functions by using their intrinsic features as well as worthy tiny tricks. At first, we propose a novel and efficient protocol for exponential function by using a divide-and-conquer strategy with most of the computations executed locally. Exponential protocol is widely used in machine learning tasks such as Poisson regression, and is also a key component of sigmoid and tanh functions. Next, we take advantage of the symmetry of sigmoid and Tanh, and fine-tune the inputs to reduce the 2PC building blocks, which helps to save overhead and improve performance. As a result, we implement these functions with fewer fundamental building blocks. The comprehensive evaluations show that our protocols achieve state-of-the-art precision while reducing run-time by approximately 57%, 44%, and 42% for exponential (with only negative inputs), sigmoid, and Tanh functions, respectively.

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