# Secure Convolution Neural Network Inference Based on Homomorphic Encryption
## 1 Introduction  
Due to its high efficiency, automation, and wide coverage, deep learning technology is widely used in many fields such as computer vision, natural language processing, and automatic driving. In real life, computing power is mainly concentrated in some cloud service providers. As a result, the combination of cloud computing and deep learning is also developing rapidly. Local users and enterprises can upload their personal data to the cloud, and use the computing power of the cloud service provider for model training and inference. For example, a furniture company can upload the type and price distribution of furniture purchased by different users to the cloud in the past year, and customize a model on the cloud to predict the possibility and quantity of residents in the area to buy different types of furniture in the next period of time. This forecasting model can obtain the minimum inventory quantity that the enterprise should keep at a relatively low cost, which is conducive to the turnover of the capital chain and also forecasts the future development direction of the enterprise. At the same time, the user's private data will also be leaked to the cloud. If the cloud uses these private data maliciously, such as using home address, phone number, and purchase tendency, the interests of these data providers are likely to be violated. In September 2022, the security company SOCRadar found that an improperly configured Azure Blob Storage server of Microsoft had a great possibility of information leakage. This sensitive information was associated with more than 65,000 corporate customers in 111 countries (regions). If information is leaked, users could face illegal activities such as extortion.  
In order to protect the privacy data of these users, researchers focus their research on statistical techniques and cryptography techniques. In recent years, with the introduction of Differential Privacy (DP) [1], some researchers combined it with various machine learningmodels and proposed various privacy protection schemes suitable for machine learning. The main protection point of this technology focuses on the private data used to train the model. Cryptography technologies such as Homomorphic Encryption (HE) and some Secure Multi-Party Computation (SMC) protocols are combined with the model reasoning stage, and some application solutions have emerged. However, these schemes require adding noise to the original messages, which has a significant impact on the final inference accuracy. Homomorphic encryption schemes can be traced back to 1978 when [PERSON] et al. [2] proposed the idea of processing data without revealing the information by using large prime factorization to ensure the security of the information. In 1982, [PERSON] proposed garbled circuits [3], and many homomorphic encryption schemes were based on garbled circuits construction. However, these schemes had poor usability and large communication overhead, making them difficult to use in practice. It was not until 2009 when [PERSON] proposed the bootstrapping process that the first fully homomorphic encryption scheme was constructed [4], ushering in a new stage of development and expanding the usage scenarios of homomorphic encryption. In recent years, according to the mathematical problems on which the schemes are based and the differences in construction processes, homomorphic encryption schemes have been divided into four generations, which will be explained in Section 3.3.