Provide asymptotic time complexity analysis of the following algorithm. Also, identify what problem does the below algorithm solve.

Func FOO$(a$ :integer, $b$ :integer$)$

if $b==0$ :

return $1$

temp :$=$ FOO $(a,\frac{b}{2})$;

if $b$ is even:

return temp$*$ temp;

else:

return temp $*$ temp $*$ a;