Side-Channel Leakage Analysis of Inner Product Masking

The Inner Product Masking (IPM) scheme has been shown to provide higher theoretical security guarantees than the Boolean Masking (BM). This scheme aims to increase the algebraic complexity of the coding to achieve a higher level of security. Some previous work unfolds when certain (adversarial and implementation) conditions are met, and we seek to complement these investigations by understanding what happens when these conditions deviate from their expected behaviour. In this paper, we investigate the security characteristics of IPM under different conditions. In adversarial condition, the security properties of first-order IPMs obtained through parametric characterization are preserved in the face of univariate and bivariate attacks. In implementation condition, we construct two new polynomial leakage functions to observe the nonlinear leakage of the IPM and connect the security order amplification to the nonlinear function. We observe that the security of IPM is affected by the degree and the linear component in the leakage function. In addition, the comparison experiments from the coefficients, signal-to-noise ratio (SNR) and the public parameter show that the security properties of the IPM are highly implementation-dependent.