DEEP-FRI: Sampling outside the box improves soundness

@article{BenSasson2019DEEPFRISO,
  title={DEEP-FRI: Sampling outside the box improves soundness},
  author={E. Ben-Sasson and Lior Goldberg and Swastik Kopparty and S. Saraf},
  journal={IACR Cryptol. ePrint Arch.},
  year={2019},
  volume={2019},
  pages={336}
}
Motivated by the quest for scalable and succinct zero knowledge arguments, we revisit worst-case-to-average-case reductions for linear spaces, raised by [Rothblum, Vadhan, Wigderson, STOC 2013]. We first show a sharp quantitative form of a theorem which says that if an affine space $U$ is $\delta$-far in relative Hamming distance from a linear code $V$ - this is the worst-case assumption - then most elements of $U$ are almost $\delta$-far from $V$ - this is the average case. This leads to an… Expand
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