  Quantum-proof randomness extraction is essential for handling quantum side
information possessed by a quantum adversary, which is widely applied in
various quantum cryptography tasks. In this study, we introduce a real-time
two-source quantum randomness extractor against quantum side information. Our
extractor is tailored for forward block sources, a novel category of
min-entropy sources introduced in this work. These sources retain the
flexibility to accommodate a broad range of quantum random number generators.
Our online algorithms demonstrate the extraction of a constant fraction of
min-entropy from two infinitely long independent forward block sources.
Moreover, our extractor is inherently block-wise parallelizable, presenting a
practical and efficient solution for the timely extraction of high-quality
randomness. Applying our extractors to the raw data of one of the most commonly
used quantum random number generators, we achieve a simulated extraction speed
as high as 64 Gbps.
