  We construct several explicit quantum secure non-malleable-extractors. All
the quantum secure non-malleable-extractors we construct are based on the
constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015].
  1) We construct the first explicit quantum secure non-malleable-extractor for
(source) min-entropy $k \geq \textsf{poly}\left(\log \left( \frac{n}{\epsilon}
\right)\right)$ ($n$ is the length of the source and $\epsilon$ is the error
parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that
the inner-product based non-malleable-extractor proposed by Li [2012] is
quantum secure, however it required linear (in $n$) min-entropy and seed
length.
  Using the connection between non-malleable-extractors and privacy
amplification (established first in the quantum setting by Cohen and Vidick
[2017]), we get a $2$-round privacy amplification protocol that is secure
against active quantum adversaries with communication $\textsf{poly}\left(\log
\left( \frac{n}{\epsilon} \right)\right)$, exponentially improving upon the
linear communication required by the protocol due to [2019].
  2) We construct an explicit quantum secure $2$-source non-malleable-extractor
for min-entropy $k \geq n- n^{\Omega(1)}$, with an output of size
$n^{\Omega(1)}$ and error $2^{- n^{\Omega(1)}}$.
  3) We also study their natural extensions when the tampering of the inputs is
performed $t$-times. We construct explicit quantum secure
$t$-non-malleable-extractors for both seeded ($t=d^{\Omega(1)}$) as well as
$2$-source case ($t=n^{\Omega(1)}$).
