WordNet sense 1 (information known only to a special group):

arcanum

WordNet sense 2 (something that baffles understanding and cannot be explained):

enigma, mystery, closed book

WordNet sense 3 (designed to elude detection):

hidden

WordNet sense 4 (hidden on any grounds for any motive):

concealed

WordNet sense 5 (confined to particular persons or groups or providing privacy):

private

WordNet sense 6 (conducted with or marked by hidden aims or methods):

clandestine, cloak-and-dagger, hush-hush, surreptitious, undercover, underground, hole-and-corner, hugger-mugger

WordNet sense 7 (secret or hidden; not openly practiced or engaged in or shown or avowed):

covert

WordNet sense 8 (hidden from general view or use):

privy, secluded

WordNet sense 9 ((of information) given in confidence or in secret):

confidential

WordNet sense 10 (having an import not apparent to the senses nor obvious to the intelligence; beyond ordinary understanding):

mysterious, mystic, mystical, occult, orphic

WordNet sense 11 (confined to and understandable by only an enlightened inner circle):

esoteric

WordNet sense 12 (official classification of information or documents; withheld from general circulation):

classified

WordNet sense 13 (not openly made known):

unavowed

WordNet sense 14 (not recognized or admitted):

unacknowledged