A gemstone passed down the line of Hamon masters.
There are naturally created gemstone that can reflect light a million times and release it as a powerful beam, these gemstones are called "Red Stones of Aja". Kars needs them to supply the spines in a Stone Mask with enough energy so it can fully pierce a Pillar Men's immortal brain, unlocking all of their power. But, the normal red stones can't give enough energy, and thus in order to power a Stone Mask one would need a "Super Aja", a completely flawless red stone.
The Roman Empire had a Super Aja in its possessions, that's why the Pillar Men set out for Rome. They were opposed by the Hamon clan, who couldn't destroy the stone because of a legend that dictates that the Pillar Men's defeat would be even more difficult to accomplish if the stone was destroyed. The Hamon clan was annihilated by the Pillar Men, but the survivors hid the stone away from them. And from then on, the stone was passed down along the line of Hamon masters to keep it hidden.