Abstract: Side-channel attacks (SCAs) play an important role in the security evaluation of cryptographic devices. As a form of SCAs, profiled differential power analysis (DPA) is among the most powerful and efficient by taking advantage of a profiling phase that learns features from a controlled device. Linear regression (LR) based profiling, a special profiling method proposed by Schindler et al., could be extended to generic-emulating DPA (differential power analysis) by on-the-fly profiling. The formal extension was proposed by Whitnall et al. named SLR-based method. Later, to improve SLR-based method, Wang et al. introduced a method based on ridge regression. However, the constant format of L-2 penalty still limits the performance of profiling. In this paper, we generalize the ridge-based method and propose a new strategy of using variable regularization. We then analyze from a theoretical point of view why we should not use constant penalty format for all cases. Roughly speaking, our work reveals the underlying mechanism of how different formats affect the profiling process in the context of side channel. Therefore, by selecting a proper regularization, we could push the limits of LR-based profiling. Finally, we conduct simulation-based and practical experiments to confirm our analysis. Specifically, the results of our practical experiments show that the proper formats of regularization are different among real devices.