## 2 Related Work
### Privacy Preservation  
Current solutions for privacy preservation in medical wearables use ordinary encryption technologies (e.g., symmetric-key encryption, public-key encryption) to protect sensitive patient well-being data only when the data are stored on the server or in transit. Any manipulation of the data at rest requires the data to be first decrypted. This, however, leads to sensitive information leakage issues. A promising solution is based on homomorphic encryption. This specific form of encryption allows data to be encrypted while it is being manipulated. The data can remain private on the server by enabling data processing without revealing the underlying information. Since the mathematical properties of the data are preserved in the encrypted form, homomorphic encryption becomes a viable option to guarantee anonymity while providing sufficient utility. While homomorphic encryption represents a promising high-level option for privacy-preserving computations, certain practical challenges remain to be addressed, including enhanced security, shorter runtime, and improved accuracy. A variety of new homomorphic encryption schemes with different capabilities and constraints have recently appeared in the field of homomorphic encryption [8; 9]. Most of these schemes have significant practical limitations due to their high computational complexity, lack of direct support for floating-point data, and the constraint of performing a limited number of operationson homomorphically encrypted data to avoid losing the underlying information through noise accumulation. The first important work that tackles the idea of privacy-preserving neural networks through homomorphic encryption was suggested by [PERSON] et al. [10] in 2007. The encryption scheme considered therein allowed only a few basic operations to be performed in the encrypted domain. Hence, interactions between the data owner and the server were required for the remaining operations. CryptoNets [11] eliminates the interaction between the involved parties using a Fully Homomorphic Encryption (FHE) scheme in combination with the polynomial approximation of non-linear activation functions. A performance limitation that restricts usability is encountered when handling large networks, due to the computational complexity of FHE. [PERSON] et al. [12] have further enhanced the capabilities of CryptoNets and introduced a low-degree polynomial approximation for the ReLU function which, in addition to the batch normalization technique, has been shown to reduce the depth limits of FHE to some extent. Focusing on improving the efficiency of neural networks when operating on encrypted data, [PERSON] [13] proposed to approximate sigmoid and tanh functions with low-degree polynomials. [PERSON] [14] suggested a different approach by combining additive homomorphic encryption with garbled circuit techniques (e.g., functions expressed as circuits of logical gates). None of these techniques, however, address the issue of privacy-preserving training for deep neural network models. Most, if not all, standard encryption schemes are based on modular arithmetic, and their security relies on the difficulty of factoring large numbers. This makes standard encryption schemes exceptionally secure. The key downside of most of the privacy-preserving neural network solutions is the computational overhead: deeper networks need more computations, resulting in longer running times. In addition, an encoding strategy for floating point numbers has been typically used to empower computations on real-world data. Not only does the encoding strategy explicitly restrict the utility of these methods, but it also has a direct impact on the outcome of the computations. The attempt to address the non-linearity property in neural network models through an approximation mechanism does not necessarily result in better performance. In fact, most of these homomorphic solutions fail to maintain the highest prediction accuracy due to the polynomially approximated activation functions.