WordNet sense 1 (having an import not apparent to the senses nor obvious to the intelligence; beyond ordinary understanding):

mystic, mystical, occult, secret

WordNet sense 2 (having a secret or hidden meaning):

cryptic

WordNet sense 3 (requiring secret or mysterious knowledge):

arcane

WordNet sense 4 (difficult to penetrate; incomprehensible to one of ordinary understanding or knowledge):

abstruse, deep, recondite