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

TL;DR

This paper introduces a new Markov model for side information in multi-source randomness extractors and proves their security against quantum adversaries within this framework, broadening the understanding of extractor security.

Contribution

The paper proposes the Markov model for side information and demonstrates that multi-source extractors are secure in this setting against quantum adversaries, with improved generality over previous models.

Findings

Multi-source extractors remain secure under the Markov model with quantum side information.

The security guarantees are weaker but applicable to a broader class of extractors.

The model generalizes previous restricted models, enhancing the robustness of extractor security proofs.

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 and the security of only some types of extractors was shown.