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Abstract: We construct a strong extractor against quantum storage that works for everymin-entropy $k$, has logarithmic seed length, and outputs $\Omegak$ bits,provided that the quantum adversary has at most $\beta k$ qubits of memory, forany $\beta < \half$. The construction works by first condensing the sourcewith minimal entropy-loss and then applying an extractor that works wellagainst quantum adversaries when the source is close to uniform.We also obtain an improved construction of a strong quantum-proof extractorin the high min-entropy regime. Specifically, we construct an extractor thatuses a logarithmic seed length and extracts $\Omegan$ bits from any sourceover $\B^n$, provided that the min-entropy of the source conditioned on thequantum adversary-s state is at least $1-\beta n$, for any $\beta < \half$.

Author: Avraham Ben-Aroya, Amnon Ta-Shma


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