Homomorphic encryption (HE) is considered as one of the most powerful solutions to securely protect clients' data from malicious users and even severs in the cloud computing. However, though it is known that HE can protect the data in theory, it has not been well utilized because many operations of HE are too slow, especially multiplication. In addition, existing data mining research studies using encrypted data focus on implementing only speci c algorithms without addressing the fundamental problem of HE. In this paper, we propose a fundamental design and implementation of data mining algorithm through logical gates. In order to do this, we design various logic of atomic operations in encrypted domain and nally apply these logic to wellknown data mining algorithms. We also analyze the execution time of atomic and advanced algorithms.

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Secure computation, a methodology of computing on encrypted data, has become a key factor in machine learning. Homomorphic encryption (HE) enables computation on encrypted data without leaking any information to untrusted servers. In machine learning, the model selection method is a crucial algorithm that determines the performance and reduces the fitting problem. Despite the importance of finding the optimal model, none of the previous studies have considered model selection when performing data analysis through the HE scheme. The HE-based model selection we proposed finds the optimal complexity that best describes given data that is encrypted and whose distribution is unknown. Since this process requires a matrix calculation, we constructed the matrix multiplication and inverse of the matrix based on the bitwise operation. Based on these, we designed the model selection of the HE cross-validation approach and the HE Bayesian approach for homomorphic machine learning. Our focus was on evidence approximation for linear models to find goodness-of-fit that maximizes the evidence. We conducted an experiment on a dataset of age and Body Mass Index (BMI) from Kaggle to compare the capabilities and our model showed that encrypted data can regress homomorphically without decrypting it.

Homomorphic encryption (HE) is notable for enabling computation on encrypted data as well as guaranteeing high-level security based on the hardness of the lattice problem. In this sense, the advantage of HE has facilitated research that can perform data analysis in an encrypted state as a purpose of achieving security and privacy for both clients and the cloud. However, much of the literature is centered around building a network that only provides an encrypted prediction result rather than constructing a system that can learn from the encrypted data to provide more accurate answers for the clients. Moreover, their research uses simple polynomial approximations to design an activation function causing a possibly significant error in prediction results. Conversely, our approach is more fundamental; we present t-BMPNet which is a neural network over fully homomorphic encryption scheme that is built upon primitive gates and fundamental bitwise homomorphic operations. Thus, our model can tackle the nonlinearity problem of approximating the activation function in a more sophisticated way. Moreover, we show that our t-BMPNet can perform training—backpropagation and feedforward algorithms—in the encrypted domain, unlike other literature. Last, we apply our approach to a small dataset to demonstrate the feasibility of our model.