Categorizing all linear codes of IPM over F28\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb {F}}_{2^{8}}$\end{document}

Inner Product Masking (IPM) is a generalization of several masking schemes including the Boolean one to protect cryptographic implementation against side-channel analysis. The core competitiveness of IPM is that it provides higher side-channel resistance than Boolean masking with the same number of shares. In this paper, we follow a coding theoretic approach and categorize all linear codes of IPM with n = 2 shares over the finite field F28\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb {F}}_{2^{8}}$\end{document} in terms of side-channel resistance. We focus on 2-share masking schemes, as they provide, at bit-level, as high as 3rd-order security (much higher than the 1st-order security of Boolean masking). We present the optimal codes for IPM in the sense of side-channel resistance assessed by the signal-to-noise ratio (SNR) and the mutual information (MI). We also show that IPM with equivalent linear codes have comparable level of side-channel resistance. Furthermore, we take the Best Known Linear Codes into consideration for comparison. The numerical results of SNR and MI confirm the effectiveness of our proposal for categorizing.