We give the first explicit construction of deterministic extractors for affine sources over F_2, with entropy k \geq \log^C n for some large enough constant C, where n is the length of the source. Previously the best known results are by Bourgain \cite{Bourgain07}, Yehudayoff \cite{Yehudayoff10} and Li \cite{Li11a}, which require the affine source to have entropy at least \Omega(n/\sqrt{\log \log n}). Our extractor outputs one bit with error n^{-\Omega(1)}.

Our construction is obtained by reducing an affine source to a non-oblivious bit-fixing source, and then applying a deterministic extractor for such sources in the recent breakthrough result of two-source extractors by Chattopadhyay and Zuckerman \cite{CZ15}. To reduce an affine source to a non-oblivious bit-fixing source, we adapt the alternating extraction based approach in previous work on independent source extractors \cite{Li13b} to the affine setting.