International Association
for Cryptologic Research

Masking is one of the most popular countermeasures to side- channel attacks, because it can offer provable security. However, depend- ing on the adversary’s model, useful security guarantees can be hard to provide. At first, masking has been shown secure against t-threshold probing adversaries by Ishai et al. at Crypto’03. It has then been shown secure in the more generic random probing model by Duc et al. at Euro- crypt’14. Prouff and Rivain have introduced the noisy leakage model to capture more realistic leakage at Eurocrypt’13. Reduction from noisy leakage to random probing has been introduced by Duc et al. at Eu- rocrypt’14, and security guarantees were improved for both models by Prest et al. at Crypto’19, Duc et al. in Eurocrypt’15/J. Cryptol’19, and Masure and Standaert at Crypto’23. Unfortunately, as it turns out, we found that previous proofs in either random probing or noisy leakage models are flawed, and such flaws do not appear easy to fix. In this work, we show that the Doeblin coefficient allows one to overcome these flaws. In fact, it yields optimal reductions from noisy leakage to random probing, thereby providing a correct and usable metric to prop- erly ground security proofs. This shows the inherent inevitable cost of a reduction from the noisy leakages to the random probing model. We show that it can also be used to derive direct formal security proofs using the subsequence decomposition of Prouff and Rivain.

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.

Using information-theoretic tools, this paper establishes a mathematical link between the probability of success of a side-channel attack and the minimum number of queries to reach a given success rate, valid for any possible distinguishing rule and with the best possible knowledge on the attacker’s side. This link is a lower bound on the number of queries highly depends on Shannon’s mutual information between the traces and the secret key. This leads us to derive upper bounds on the mutual information that are as tight as possible and can be easily calculated. It turns out that, in the case of an additive white Gaussian noise, the bound on the probability of success of any attack is directly related to the signal to noise ratio. This leads to very easy computations and predictions of the success rate in any leakage model.