Code-based masking is one of the most important countermeasures to prevent side-channel attacks. Dual distance and kissing number of linear codes are critical metrics indicating the side-channel resistance of code-based masking. However, calculating the value of these indicators depends on the choice of irreducible polynomials of the corresponding finite field. Through simulation experiments, we discovered that different irreducible polynomials significantly impact the side-channel resistance. Our findings suggest that the optimal linear codes derived from a single irreducible polynomial may not be globally optimal. By going through all irreducible polynomials over GF(256), we identify the optimal linear codes for 2-Share inner product masking (IPM) and (3,1)-Shamir’s secret sharing (SSS) based masking in this field. Furthermore, we explore the application of higher-order masking defenses to the lightweight encryption scheme PRESENT. Additionally, we demonstrate through comprehensive simulation experiments that 3-share IPM provides substantial security advantages over 2-share IPM. We also extend our analysis to GF(32) and GF(64) to validate the generalizability of our approach.
Chen et al. (Sun,) studied this question.