Given a completely metrizable space $X$, a subset $A$ of $X$ is a
strongly porous set if there is a positive constant $p$ such that for any
open ball $B$ of radius $r$ smaller than 1, there is an open ball $B'$ inside
of $B$ of radius $rp$ such that $B'$ evades the set $A$. We will study the
cardinal invariants related to the $\sigma$-ideal generated by strongly porous
sets on the Cantor space and its relation with other known $\sigma$-ideals of
the real line. We will also uncover a deep connection between the
$\sigma$-ideal of the strongly porous sets and some instances of the Martin
Axiom.