On what Bill of Rights protections does the Supreme Court base the right to privacy?

Constitution right

The First Amendment protects the privacy of beliefs

The Third Amendment protects the privacy of the home against the use of it for housing soldiers

The Fourth Amendment protects privacy against unreasonable searches

The Fifth Amendment protects against self-incrimination, which in turn protects the privacy of personal information

The Ninth Amendment says that the "enumeration in the Constitution of certain rights shall not be construed to deny or disparage other rights retained by the people." This has been interpreted as justification for broadly reading the Bill of Rights to protect privacy in ways not specifically provided in the first eight amendments.