Masking is one of the most popular countermeasures to protect cryptographic implementations against side-channel analysis since it is provably secure and can be deployed at the algorithm level. To strengthen the original Boolean masking scheme, several works have suggested using schemes with high algebraic complexity. The Inner Product Masking (IPM) is one of those. In this paper, we propose a unified framework to quantitatively assess the side-channel security of the IPM in a coding-theoretic approach. Specifically, starting from the expression of IPM in a coded form, we use two defining parameters of the code to characterize its side-channel resistance. In order to validate the framework, we then connect it to two leakage metrics (namely signal-to-noise ratio and mutual information, from an information-theoretic aspect) and one typical attack metric (success rate, from a practical aspect) to build a firm foundation for our framework. As an application, our results provide ultimate explanations on the observations made by Balasch et al. at EUROCRYPT'15 and at ASIACRYPT'17, Wang et al. at CARDIS'16 and Poussier et al. at CARDIS'17 regarding the parameter effects in IPM, like higher security order in bounded moment model. Furthermore, we show how to systematically choose optimal codes (in the sense of a concrete security level) to optimize IPM by using this framework. Eventually, we present a simple but effective algorithm for choosing optimal codes for IPM, which is of special interest for designers when selecting optimal parameters for IPM.

The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring $\mathcal{R}:={\mathbb{F}}_4\left[v\right]/⟨v^3⟩$. We show an association between the codons and the elements of $\mathcal{R}$ using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.

Code-based masking is a recent line of research on masking schemes aiming at provably counteracting side-channel attacks. It generalizes and unifies many masking schemes within a coding-theoretic formalization. In code-based masking schemes, the tuning parameters are the underlying linear codes, whose choice significantly affects the side-channel resilience. In this paper, we investigate the exploitability of the information leakage in code-based masking and present attack-based evaluation results of higher-order optimal distinguisher (HOOD). Particularly, we consider two representative instances of code-based masking, namely inner product masking (IPM) and Shamir’s secret sharing (SSS) based masking. Our results do confirm the state-of-the-art theoretical derivatives in an empirical manner with numerically simulated measurements. Specifically, theoretical results are based on quantifying information leakage; we further complete the panorama with attack-based evaluations by investigating the exploitability of the leakage. Moreover, we classify all possible candidates of linear codes in IPM with 2 and 3 shares and (3, 1)-SSS based masking, and highlight both optimal and worst codes for them. Relying on our empirical evaluations, we therefore recommend investigating the coding-theoretic properties to find the best linear codes in strengthening instances of code-based masking. As for applications, our attack-based evaluation directly empowers designers, by employing optimal linear codes, to enhance the protection of code-based masking. Our framework leverages simulated leakage traces, hence allowing for source code validation or patching in case it is found to be attackable.