Reaching the Limit of Nonprofiling DPA

Many profiling differential power analysis (DPA) attacks estimate the multivariate probability distribution using a profiling step, and thus, can optimally combine the leakages of multiple sample points. Though there exist several approaches like filtering or principal component analysis for combining the leakages of multiple sample points in nonprofiling DPA, their optimality has been rarely studied. We study the issue of optimally combining the leakages of multiple sample points in nonprofiling DPA attacks using a linear function. In this paper, we introduce a multivariate leakage model based on some observations obtained by profiling the power traces of Advanced Encryption Standard (AES) encryption on Virtex-5 field programmable gate array (FPGA) device. Then, we use the introduced multivariate leakage model to propose optimal combining functions for nonprofiling DPA. The theoretical claims are supported by experimental evidence. We have also discussed different sides of the proposed combining functions in various practical scenarios.