Opposite words for private:
advertised, unrestricted, aboveboard, semipublic, straightforward, patent, national, acknowledged, avowed, prevailing, broadcast, state-supported, normal, publicized, obvious, announced, well-known, unconcealed, rife, outward, vulgar, published, proclaimed, overt, prevalent, unexclusive, communal, promulgated, open, regular, unclassified, popular, universal, generic, widespread, typical, general, disclosed, heralded, reported, current, public, in the public eye, broad, impersonal, professed, clear, enunciated, manifest, blazed, shared, undisguised, plain, evident, spotlighted, common, declared, divulged, aired.
Usage samples:
  1. With that, he turned and went out the private door.
    "Time Crime", H. Beam Piper.
  2. What about that private matter?
    "Cap'n Warren's Wards", Joseph C. Lincoln.
  3. A foster- brother as she calls the noble cripple, who is now with her in our private parlor.
    "Lily Pearl and The Mistress of Rosedale", Ida Glenwood.
  4. And sadly, Private Markwell's mother did receive this letter.
    "Complete State of the Union Addresses from 1790 to the Present", Various.