Because the random walk converges quickly, expander graphs
make for excellent random number generators.
They can convert “bad generators” into better ones
Rivest’s RC4 is based on expanders on permutation groups
When the nodes represent different instances of the same
problem, the random walk can sometimes be used to show that
each instance is as “difficult” as the rest.
Such “self-reducibility” is important in cryptography, because
one wants all versions of a given system to be hard to break.
Recent application (Jao, Miller, Venkatesan): ensuring security
of Microsoft’s next
(a 25 digit alpha-numeric code
one enters when installing Windows or Office).