Core Concepts
This paper presents explicit constructions of two-source and affine non-malleable extractors that match the state-of-the-art constructions of standard extractors for small entropy.
Abstract
The paper focuses on constructing explicit two-source and affine non-malleable extractors for small entropy. The main results include:
- Two-source and affine non-malleable extractors (over F2) for sources on n bits with min-entropy k ≥ log^C n and polynomially small error, matching the parameters of standard extractors.
- Two-source and affine non-malleable extractors (over F2) for sources on n bits with min-entropy k = O(log n) and constant error, also matching the parameters of standard extractors.
The authors significantly improve the entropy requirement compared to previous non-malleable extractor constructions. The key technical ideas include:
- Taking the parity of two resilient functions to obtain a non-malleable extractor.
- Generating non-oblivious bit-fixing (NOBF) sources from the inputs and their tampered counterparts.
- Handling the general case using a convex combination of subsources analysis.
The improved affine non-malleable extractors also give strong lower bounds for a certain kind of read-once linear branching programs, matching the previously best-known average-case hardness results.
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