Where does “carmin” come from?

carmin (French) comes from Medieval Latin carminium, from Arabic قِرْمِز, from Persian کرمست, from Sanskrit कृमिज, from Sanskrit कृमि, from Proto-Indo-Aryan kŕ̥miṣ, from Proto-Indo-Iranian kŕ̥miš, from Proto-Indo-European kʷŕ̥mis — worm.

carmin (French): carmine, crimson; cochineal, carmine; cinnabar...