  We propose the use of natural minerals as detectors to study the past flux of
cosmic rays. This novel application of the \textit{paleo-detector} technique
requires a specific approach as it needs samples that have been exposed to
secondary cosmic rays for a well defined period of time. We suggest here the
use of the evaporites formed during the desiccation of the Mediterranean sea
${\sim}6$ Myr ago. These minerals have been created and exposed to the air or
under a shallow water basin for ${\sim}500$ kyr before being quickly submerged
again by a km-scale overburden of water. We show that, by looking at the
damages left in the minerals by muons in cosmic ray showers, we could detect
differences in the primary cosmic ray flux during that period, as the ones
expected from nearby supernova explosions, below the percent-level. We show
also that little to no background from radioactive contamination and other
astroparticles is expected for this kind of analysis.
