  We present a new dynamic matching sparsification scheme. From this scheme we
derive a framework for dynamically rounding fractional matchings against
\emph{adaptive adversaries}. Plugging in known dynamic fractional matching
algorithms into our framework, we obtain numerous randomized dynamic matching
algorithms which work against adaptive adversaries (the first such algorithms,
as all previous randomized algorithms for this problem assumed an
\emph{oblivious} adversary). In particular, for any constant $\epsilon>0$, our
framework yields $(2+\epsilon)$-approximate algorithms with constant update
time or polylog worst-case update time, as well as $(2-\delta)$-approximate
algorithms in bipartite graphs with arbitrarily-small polynomial update time,
with all these algorithms' guarantees holding against adaptive adversaries. All
these results achieve \emph{polynomially} better update time to approximation
tradeoffs than previously known to be achievable against adaptive adversaries.
