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.