Tallonian crystals were precious gemstones from the Tallonian homeworld.
They were illegal anywhere but on the Tallonian homeworld. To determine the purity of Tallonian crystals, a type 4 Tallonian microscanner is needed.
Quark tried to purchase Tallonian crystals from Regana Tosh in 2372, but was apprehended by Odo. (DS9: "Hippocratic Oath")