Better short-seed quantum-proof extractors

TL;DR

This paper presents new quantum-proof extractors that efficiently generate nearly uniform randomness from sources with high min-entropy, even against quantum adversaries with limited quantum memory.

Contribution

The authors introduce strong quantum-proof extractors with logarithmic seed length that work for all min-entropy levels and quantum memory constraints, improving previous constructions.

Findings

Constructed extractors with logarithmic seed length and high output bits.

Achieved security against quantum adversaries with up to half of the source entropy in qubits.

Enhanced extractor performance in high min-entropy regimes.

Abstract

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 $\beta < \half$. 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 $\B^n$, provided that the min-entropy of the source conditioned on the quantum adversary's state is at least $(1-\beta) n$, for any $\beta < \half$.