Improved Two-source Extractors against Quantum Side Information
Jakob Miller, Martin Sandfuchs, Carla Ferradini
TL;DR
The paper addresses the security of two-source extractors against quantum side information, focusing on the Dodis et al. deor_A construction. It introduces a modular approach via a novel measured XOR-Lemma that reduces quantum security to classical single-bit security and combines this with a non-modular, matrix-analytic method to substantially improve extractor performance, including achieving the same security as no side information for product-type quantum knowledge and extending these guarantees to the quantum Markov model. The main contributions are twofold: a general reduction yielding the √(2^m ε) error bound for generic extractors, and a 5x improvement in output length for deor_A against quantum product-type side information, plus Markov-model extensions with minimal losses. These results significantly strengthen the practicality of two-source extractors in quantum-adversarial settings and open avenues for applying the measured XOR-Lemma to a wider class of extractors.
Abstract
Two-source extractors aim to extract randomness from two independent sources of weak randomness. It has been shown that any two-source extractor which is secure against classical side information remains secure against quantum side information. Unfortunately, this generic reduction comes with a significant penalty to the performance of the extractor. In this paper, we show that the two-source extractor from Dodis et al. performs equally well against quantum side information as in the classical realm, surpassing previously known results about this extractor. Additionally, we derive a new quantum XOR-Lemma which allows us to re-derive the generic reduction but also allows for improvements for a large class of extractors.