Two-Source Extractors Secure Against Quantum Adversaries

TL;DR

This paper introduces a quantum-secure two-source extractor that remains effective even against adversaries with quantum memory and shared entanglement, advancing the understanding of randomness extraction in quantum settings.

Contribution

It presents the first two-source extractor secure against quantum adversaries, including entangled ones, matching classical parameters and addressing key challenges in quantum randomness extraction.

Findings

Extractor is secure against quantum adversaries with bounded memory.

Security holds even if adversaries share entanglement.

Parameters closely match classical extractor performance.

Abstract

We initiate the study of multi-source extractors in the quantum world. In this setting, our goal is to extract random bits from two independent weak random sources, on which two quantum adversaries store a bounded amount of information. Our main result is a two-source extractor secure against quantum adversaries, with parameters closely matching the classical case and tight in several instances. Moreover, the extractor is secure even if the adversaries share entanglement. The construction is the Chor-Goldreich [CG88] two-source inner product extractor and its multi-bit variant by Dodis et al. [DEOR04]. Previously, research in this area focused on the construction of seeded extractors secure against quantum adversaries; the multi-source setting poses new challenges, among which is the presence of entanglement that could potentially break the independence of the sources.