The state registrar of vital records shall maintain a record of the social security number of each parent whose name is recorded on any certificate of birth established or amended under this chapter on or after September 1, 1996, unless the registrar finds good cause for not requiring the number. That social security number shall be kept confidential and shall be disclosed only to the state agency responsible for administering the state’s child support enforcement program. Social security numbers obtained pursuant to this section shall not be used for any purpose other than for the establishment and enforcement of child support orders, to the extent authorized by federal law.