Quantum-proof multi-source randomness extractors in the Markov model

Abstract

Randomness extractors, widely used in classical and quantum cryptography and other fields of computer science, e.g., derandomization, are functions which generate almost uniform randomness from weak sources of randomness. In the quantum setting one must take into account the quantum side information held by an adversary which might be used to break the security of the extractor. In the case of seeded extractors the presence of quantum side information has been extensively studied. For multi-source extractors one can easily see that high conditional min-entropy is not sufficient to guarantee security against arbitrary side information, even in the classical case. Hence, the interesting question is under which models of (both quantum and classical) side information multi-source extractors remain secure. In this work we suggest a natural model of side information, which we call the Markov model, and prove that any multi-source extractor remains secure in the presence of quantum side information of this type (albeit with weaker parameters). This improves on previous results in which more restricted models were considered or the security of only some types of extractors was shown.

Physical Security in the Post-quantum Era: A Survey on Side-channel Analysis, Random Number Generators, and Physically Unclonable Functions

“…This model can be considered as a generalization of models studied in [Kasher and Kempe 2012] in the sense that limits have been imposed on neither how the side-channels from different sources are combined nor the amount of information stored by the adversary cf. [Arnon- Friedman et al 2015]. The latter condition is known as the "bounded-storage" model, widely applied in work related to the design of randomness extractors, see, e.g., [De et al 2012;Ta-Shma 2011].…”