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 Omega(k) bits, provided that the quantum adversary has at most beta k qubits of memory, for any beta < 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 Omega(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 - beta)n, for any beta < 1/2. (C) 2011 Elsevier B.V. All rights reserved.