Gamma-ray measurements can be used to detect Inter-Galactic Magnetic Fields (IGMF) in the voids of Large Scale Structure. We explore the possibility of identifying the inflationary origin of the IGMF and measuring its parameters with gamma-ray astronomy methods. We developed new CRbeam Monte-Carlo code for the precision of the modelling of the secondary gamma-ray emission and compared it with publicly available Monte-Carlo codes ELMAG and CRPropa. We demonstrated that after eliminating the inaccuracies found in ELMAG and CRPropa, the difference between the three codes is reduced to 10% when modelling nearby sources with z ∼ 0.1 (inaccuracies was taken into account and removed by developers of ELMAG and CRPropa in new
versions of their codes). Finally, we argue that the new CRbeam code produce reliable predictions when modelling both nearby and distant sources with z ∼ 1 and thus provide relevant precision for the prospective CTA studies of gamma-ray sources and IGMF. The large correlation length inflationary field is expected to impose a characteristic asymmetry of extended secondary gamma-ray emission that is correlated between different sources on the sky. New gamma-ray observatory, Cherenkov Telescope Array (CTA), will provide an increase of sensitivity and angular resolution compared to the current generation of telescopes. We show that CTA observations can be used
for the test of inflationary origin of the IGMF.