Better short-seed quantum-proof extractors

We construct a strong extractor against quantum storage that works for every min-entropy k, has logarithmic seed length, and outputs Ω(k) bits, provided that the quantum adversary has at most βk qubits of memory, for any β < 1 2 . The construction works by first condensing the source (with minimal entropy-loss) and then applying an extractor that works well against quantum adversaries when the source is close to uniform. We also obtain an improved construction of a strong quantum-proof extractor in the high min-entropy regime. Specifically, we construct an extractor that uses a logarithmic seed length and extracts Ω(n) bits from any source over {0, 1}n, provided that the min-entropy of the source conditioned on the quantum adversary’s state is at least (1− β)n, for any β < 1 2 .