Data from the ESA ExoMars Rover Mission will provide invaluable input for further studies in astro/exobiology. The search for mineral products as indicators of present and/or past biogenetic activities in Mars' surface and subsurface samples is the main objective of the compact Raman-laser-induced breakdown spectroscopy (LIBS) instrument. The inherent features of Raman spectroscopy and LIBS make the combined instrument a unique and very powerful tool in the search for biomarkers and hence it is regarded as the highest priority instrument for mineral analysis within the mission. We have developed a software package for the on-board processing of the instrument's data outputs, including spectral conditioning and search-match characterization of mineral phases and biomarkers. In this paper we show the mathematical and physical basis of the software package.