Privacy in machine learning has been widely recognized as an essential ethical and legal issue, because the data used for machine learning may contain sensitive information. Homomorphic encryption has recently attracted attention as a key solution to preserve privacy in machine learning applications. However, current approaches on the training of encrypted machine learning have relied heavily on hyperparameter selection, which should be avoided owing to the extreme difficulty of conducting validation on encrypted data. In this study, we propose an effective privacy-preserving logistic regression method that is free from the approximation of the sigmoid function and hyperparameter selection. In our framework, a logistic regression model can be transformed into the corresponding ridge regression for the logit function. We provide a theoretical background for our framework by suggesting a new generalization error bound on the encrypted data. Experiments on various real-world data show that our framework achieves better classification results while reducing latency by $\sim68\%$, compared to the previous models.