mystify (v.)

late 14c., mistike, "spiritually allegorical, pertaining to mysteries of faith," from Old French mistique "mysterious, full of mystery" (14c.), or directly from Latin mysticus "mystical, mystic, of secret rites" (source also of Italian mistico, Spanish mistico), from Greek mystikos "secret, mystic, connected with the mysteries," from mystes "one who has been initiated" (see mystery (n.1)).

Meaning "pertaining to occult practices or ancient religions" is recorded by 1610s. That of "hidden from or obscure to human knowledge or comprehension" is by 1630s.

word-forming element meaning "make, make into," from French -fier, from Latin -ficare, combining form of facere "to make" (from PIE root *dhe- "to set, put").