  We consider the problem of extracting randomness from \textit{sumset
sources}, a general class of weak sources introduced by Chattopadhyay and Li
(STOC, 2016). An $(n,k,C)$-sumset source $\mathbf{X}$ is a distribution on
$\{0,1\}^n$ of the form $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_C$,
where $\mathbf{X}_i$'s are independent sources on $n$ bits with min-entropy at
least $k$. Prior extractors either required the number of sources $C$ to be a
large constant or the min-entropy $k$ to be at least $0.51 n$.
  As our main result, we construct an explicit extractor for sumset sources in
the setting of $C=2$ for min-entropy $\mathrm{poly}(\log n)$ and polynomially
small error. We can further improve the min-entropy requirement to $(\log n)
\cdot (\log \log n)^{1 + o(1)}$ at the expense of worse error parameter of our
extractor. We find applications of our sumset extractor for extracting
randomness from other well-studied models of weak sources such as affine
sources, small-space sources, and interleaved sources.
  Interestingly, it is unknown if a random function is an extractor for sumset
sources. We use techniques from additive combinatorics to show that it is a
disperser, and further prove that an affine extractor works for an interesting
subclass of sumset sources which informally corresponds to the "low doubling"
case (i.e., the support of $\mathbf{X_1} + \mathbf{X_2}$ is not much larger
than $2^k$).
