Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study two variants of seeded randomness extractors. The first one, as studied by Goldreich et al. \cite{goldreich2015randomness}, is seeded extractors that can be computed by AC0 circuits. The second one, as introduced by Bogdanov and Guo \cite{bogdanov2013sparse}, is (strong) extractor families that consist of sparse transformations, i.e., functions that have a small number of overall input-output dependencies (called \emph{sparse extractor families}). #R##N#In the AC0 extractor case, our main results substantially improve the positive results in \cite{goldreich2015randomness}.  give constructions of strong seeded extractors for $k=\delta n \geq n/poly(\log n)$, with seed length $d=O(\log n)$, output length $m=k^{\Omega(1)}$, and error any $1/poly(n)$.  can then boost the output length to $\Omega(\delta k)$ with seed length $d=O(\log n)$, or to $(1-\gamma)k$ for any constant $0<\gamma<1$ with $d=O(\frac{1}{\delta}\log n)$.  give two applications of such extractors to the constructions of pseudorandom generators in AC0 that are cryptographically secure, and that fool small space computation. #R##N#In the case of sparse extractor families,for min-entropy $k=\Omega(\log^2 n)$ and error $\epsilon \geq 2^{-k^{\Omega(1)}}$,  give a strong seeded extractor with seed length $d = O(k)$, $m = (1-\gamma)k$ and locality $\frac{n}{k}\log^2 (1/\epsilon) (\log n)poly(\log k)$.
['Kuan Cheng', 'Xin Li']
I am writing a research paper on a idea Randomness Extraction in AC0 and with Small Locality
[{"from": "human", "value": "I am writing a research paper on a idea Randomness Extraction in AC0 and with Small Locality"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study two variants of seeded randomness extractors. The first one, as studied by Goldreich et al. \\cite{goldreich2015randomness}, is seeded extractors that can be computed by AC0 circuits. The second one, as introduced by Bogdanov and Guo \\cite{bogdanov2013sparse}, is (strong) extractor families that consist of sparse transformations, i.e., functions that have a small number of overall input-output dependencies (called \\emph{sparse extractor families}). #R##N#In the AC0 extractor case, our main results substantially improve the positive results in \\cite{goldreich2015randomness}.  give constructions of strong seeded extractors for $k=\\delta n \\geq n/poly(\\log n)$, with seed length $d=O(\\log n)$, output length $m=k^{\\Omega(1)}$, and error any $1/poly(n)$.  can then boost the output length to $\\Omega(\\delta k)$ with seed length $d=O(\\log n)$, or to $(1-\\gamma)k$ for any constant $0<\\gamma<1$ with $d=O(\\frac{1}{\\delta}\\log n)$.  give two applications of such extractors to the constructions of pseudorandom generators in AC0 that are cryptographically secure, and that fool small space computation. #R##N#In the case of sparse extractor families,for min-entropy $k=\\Omega(\\log^2 n)$ and error $\\epsilon \\geq 2^{-k^{\\Omega(1)}}$,  give a strong seeded extractor with seed length $d = O(k)$, $m = (1-\\gamma)k$ and locality $\\frac{n}{k}\\log^2 (1/\\epsilon) (\\log n)poly(\\log k)$."}]