Complexity leveraging is a proof technique in cryptography where the reduction algorithm runs in super-poly time. (see this). Many papers use complexity leveraging when there are exponentially many hybrids. Here is an example.
Suppose, we need to prove that two experiments $Expt \;0$ and $Expt \;1$ are computationally indistinguishable. Then, we come up with a sequence of hybrids $Hybrid \;1, Hybrid \;2, \ldots Hybrid \;N$ and prove
$Expt \;0 \approx_c Hybrid \;1$ assuming, say, one way functions.
$Hybrid \;i \approx_c Hybrid \;i+1$ assuming one way functions.
$Hybrid \;N \approx_c Expt \;1$ assuming one way functions.
If $N = poly(\lambda)$, then $Expt \;0 \approx_c Expt \;1$ assuming one way functions. How to apply complexity leveraging argument if $N = 2^\lambda$? (Here there are many reduction algorithms each running in poly time).