  Efficient derandomization has long been a goal in complexity theory, and a
major recent result by Yanyi Liu and Rafael Pass identifies a new class of
hardness assumption under which it is possible to perform time-bounded
derandomization efficiently: that of ''leakage-resilient hardness.'' They
identify a specific form of this assumption which is $\textit{equivalent}$ to
$\mathsf{prP} = \mathsf{prBPP}$. In this paper, we pursue an equivalence to
derandomization of $\mathsf{prBP{\cdot}L}$ (logspace promise problems with
two-way randomness) through techniques analogous to Liu and Pass. We are able
to obtain an equivalence between a similar ''leakage-resilient hardness''
assumption and a slightly stronger statement than derandomization of
$\mathsf{prBP{\cdot}L}$, that of finding ''non-no'' instances of ''promise
search problems.''
