Fully Homomorphically Encrypted Linear Regression Using CKKS

In this paper, we consider the solution of encrypted linear regression using Homomorphic Encryption. We propose a method in which each mathematical operation is performed over encrypted real numbers. This method allows the computation of linear regression in an encrypted environment without the need to modify the original dataset and does not require additional techniques for the calculation of matrix multiplications. The proposed method consists of an iterative method based on a modified Goldschmidt sequence. Numerical results on both synthetic and real data show that the method converges with minimal accuracy loss due to encryption noise, indicating that our approach is well-suited for homomorphically encrypted linear regression.