How can alpha-information theory formally prove that your sensitive circuits are protected against side-channel attacks?

Cryptographic algorithms are ubiquitous in our digital society. Principles (such as Kerckhoffs’) and mathematical techniques for securing data against cryptanalysis are well established, even with future quantum computers: the best attacks of this type are essentially brute force, which takes several times the age of the universe.

However, one real threat is that algorithm implementations are vulnerable to side-channel attacks, that exploit sensitive information leaks to recover the secret in a “divide and conquer” approach. Some attacks only require a few queries (leakage measurements). Thus, the question is not whether you are secure or not, since it is only a matter of time. The question is how much you can be secure, e.g. with a protected implementation that use data masking. For that, we need a formal evaluation.

In this talk, I present such a formal evaluation using alpha-information theory, based on Rényi alpha-divergence and alpha-entropy, and Sibson’s alpha-information. The parameter alpha can be positive or negative, and the limiting case alpha = minus infinity is related to the important notion of Doeblin coefficient, which can be used to reduce the noisy leakage model to a random probing model. Fano and data processing inequalities, as well as Mrs. Gerber’s lemma in the case of additive masking, are used to establish lower bounds on the number of queries that any attacker has to make to achieve a given level of success. In this way, it is possible to be proactive, for example with ephemeral keys, to maintain the security of an implementation.

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Bio: Olivier Rioul (https://perso.telecom-paristech.fr/rioul/) is full Professor at the Department of Communication and Electronics at Télécom Paris, Institut Polytechnique de Paris, France. He graduated from École Polytechnique and from École Nationale Supérieure des Télécommunications, Paris, France, where he obtained his PhD degree. His research interests are in applied mathematics and include various, sometimes unconventional, applications of information theory such as inequalities in statistics, hardware security, and experimental psychology. He has been teaching information theory and statistics at various universities for twenty years and has published a textbook which has become a classical French reference in the field.