International Association
for Cryptologic Research

Code-based masking is a highly generalized type of masking schemes, which can be instantiated into specific cases by assigning different encoders. It captivates by its side-channel resistance against higher-order attacks and the potential to withstand fault injection attacks. However, similar to other algebraically-involved masking schemes, code-based masking is also burdened with expensive computational overhead. To mitigate such cost and make it efficient, we contribute to several improvements to the original scheme proposed by Wang et al. in TCHES 2020. Specifically, we devise a computationally friendly encoder and accordingly accelerate masked gadgets to leverage efficient implementations. In addition, we highlight that the amortization technique introduced by Wang et al. does not always lead to efficient implementations as expected, but actually decreases the efficiency in some cases.From the perspective of practical security, we carry out an extensive evaluation of the concrete security of code-based masking in the real world. On one hand, we select three representative variations of code-based masking as targets for an extensive evaluation. On the other hand, we aim at security assessment of both encoding and computations to investigate whether the state-of-the-art computational framework for code-based masking reaches the security of the corresponding encoding. By leveraging both leakage assessment tool and side-channel attacks, we verify the existence of “security order amplification” in practice and validate the reliability of the leakage quantification method proposed by Cheng et al. in TCHES 2021. In addition, we also study the security decrease caused by the “cost amortization” technique and redundancy of code-based masking. We identify a security bottleneck in the gadgets computations which limits the whole masked implementation. To the best of our knowledge, this is the first time that allows us to narrow down the gap between the theoretical security order under the probing model (sometimes with simulation experiments) and the concrete side-channel security level of protected implementations by code-based masking in practice.

Block ciphers are protected against side-channel attacks by masking. On one hand, when the leakage model is unknown, second-order correlation attacks are typically used. On the other hand, when the leakage model can be profiled, template attacks are prescribed. But what if the profiled model does not exactly match that of the attacked device?One solution consists in regressing on-the-fly the scaling parameters from the model. In this paper, we leverage an Expectation-Maximization (EM) algorithm to implement such an attack. The resulting unprofiled EM attack, termed U-EM, is shown to be both efficient (in terms of number of traces) and effective (computationally speaking). Based on synthetic and real traces, we introduce variants of our U-EM attack to optimize its performance, depending on trade-offs between model complexity and epistemic noise. We show that the approach is flexible, in that it can easily be adapted to refinements such as different points of interest and number of parameters in the leakage model.

This paper presents a unified approach to quantifying the information leakages in the most general code-based masking schemes. Specifically, by utilizing a uniform representation, we highlight first that all code-based masking schemes’ side-channel resistance can be quantified by an all-in-one framework consisting of two easy-tocompute parameters (the dual distance and the number of conditioned codewords) from a coding-theoretic perspective. In particular, we use signal-to-noise ratio (SNR) and mutual information (MI) as two complementary metrics, where a closed-form expression of SNR and an approximation of MI are proposed by connecting both metrics to the two coding-theoretic parameters. Secondly, considering the connection between Reed-Solomon code and SSS (Shamir’s Secret Sharing) scheme, the SSS-based masking is viewed as a particular case of generalized code-based masking. Hence as a straightforward application, we evaluate the impact of public points on the side-channel security of SSS-based masking schemes, namely the polynomial masking, and enhance the SSS-based masking by choosing optimal public points for it. Interestingly, we show that given a specific security order, more shares in SSS-based masking leak more information on secrets in an information-theoretic sense. Finally, our approach provides a systematic method for optimizing the side-channel resistance of every code-based masking. More precisely, this approach enables us to select optimal linear codes (parameters) for the generalized code-based masking by choosing appropriate codes according to the two coding-theoretic parameters. Summing up, we provide a best-practice guideline for the application of code-based masking to protect cryptographic implementations.

Addition chain is a well-known approach for implementing higher-order masked SBoxes. However, this approach induces more computations of intermediate monomials over F2n, which in turn leak more information related to the sensitive variables and may decrease its side-channel resistance consequently. In this paper, we introduce a new notion named polygon degree to measure the resistance of monomial computations. With the help of this notion, we select several typical addition chain implementations with the strongest or the weakest resistance. In practical experiments based on an ARM Cortex-M4 architecture, we collect power and electromagnetic traces in consideration of different noise levels. The results show that the resistance of the weakest masked SBox implementation is close to that of an unprotected implementation, while the strongest one can also be broken with fewer than 1,500 traces due to extra leakages. Moreover, we study the resistance of addition chain implementations against profiled attacks. We find that some monomials with smaller output size leak more information than the SBox output. The work by Duc et al. at JOC 2019 showed that for a balanced function, the smaller the output size is, the less information is leaked. Thus, our attacks demonstrate that this property of balanced functions does not apply to unbalanced functions.