What can Information Guess? Guessing Advantage vs. Rényi Entropy for Small Leakages

We leverage the Gibbs inequality and its natural generalization to Rényi entropies to derive closed-form parametric expressions of the optimal lower bounds of \rho \text{th} -order guessing entropy (guessing moment) of a secret taking values on a finite set, in terms of the Rényi-Arimoto \alpha -ent...

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Bibliographic Details
Published in2024 IEEE International Symposium on Information Theory (ISIT) pp. 2963 - 2968
Main Authors Beguinot, Julien, Rioul, Olivier
Format Conference Proceeding
LanguageEnglish
Published IEEE 07.07.2024
Subjects
Additive noise
Analytical models
Entropy
Hamming weight
Random variables
Side-channel attacks
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Summary:We leverage the Gibbs inequality and its natural generalization to Rényi entropies to derive closed-form parametric expressions of the optimal lower bounds of \rho \text{th} -order guessing entropy (guessing moment) of a secret taking values on a finite set, in terms of the Rényi-Arimoto \alpha -entropy. This is carried out in an non-asymptotic regime when side information may be available. The resulting bounds yield a theoretical solution to a fundamental problem in side-channel analysis: Ensure that an adversary will not gain much guessing advantage when the leakage information is sufficiently weakened by proper countermeasures in a given cryptographic implementation. Practical evaluation for classical leakage models show that the proposed bounds greatly improve previous ones for analyzing the capability of an adversary to perform side-channel attacks.
ISSN:2157-8117
DOI:10.1109/ISIT57864.2024.10619150