# Randomness extractors from Bourgain’s breakthrough- applications?

Some exciting progress to pure mathematics is due to Bourgain

Springer - Multilinear Exponential Sums in Prime Fields Under Optimal Entropy Condition on the Sources

with applications to randomness extractors and gave the first two source extractor with min entropy rate <0.5

Since this paper there’s been other innovations and simplifications of Bourgains work, such as

An explicit two-source extractor with min-entropy rate near 4/9

This is all exciting for mathematics. Is the same true from an applied crypto perspective? For example, would it help in any way with the issues discussed here

The GCD strikes back to RSA in 2019 - Good randomness is the only solution?

Other applications/places where these theoretical breakthroughs have already been applied?

Most creditable TRGNs are based on min. entropy extraction via the Left Over Hash Lemma: $$\epsilon = 2^{-(sn-k)/2}$$ where $$s=H_{\infty}$$per bit input to the extractor. This lemma is unaffected by Bourgain.
• what is the $s$ in your equation? – kodlu May 6 '20 at 21:53