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Formal Security Proofs via Doeblin Coefficients: Optimal Side-channel Factorization from Noisy Leakage to Random Probing
Authors: Julien Béguinot, Wei Cheng, Sylvain Guilley, Olivier RioulAbstract:
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 Euro-
crypt’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 over-
come these flaws. In fact, it yields optimal reductions from noisy leakage
to random probing, thereby providing a correct and usable metric to
properly 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.
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