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Whoever knowingly makes any false statement under oath, in any case, proceeding, or matter relating to, or under, or by virtue of any law of the United States relating to naturalization, citizenship, or registry of aliens; or Whoever knowingly, with intent to avoid any duty or liability imposed or required by law, denies that he has been naturalized or admitted to be a citizen, after having been so naturalized or admitted; or Whoever uses or attempts to use any certificate of arrival, declaration of intention, certificate of naturalization, certificate of citizenship or other documentary evidence of naturalization or of citizenship, or any duplicate or copy thereof, knowing the same to have been procured by fraud or false evidence or without required appearance or hearing of the applicant in court or otherwise unlawfully obtained; or Whoever knowingly makes any false certificate, acknowledgment or statement concerning the appearance before him or the taking of an oath or affirmation or the signature, attestation or execution by any person with respect to any application, declaration, petition, affidavit, deposition, certificate of naturalization, certificate of citizenship or other paper or writing required or authorized by the laws relating to immigration, naturalization, citizenship, or registry of aliens; or Whoever knowingly makes any false statement or claim that he is, or at any time has been, a citizen or national of the United States, with the intent to obtain on behalf of himself, or any other person, any Federal or State benefit or service, or to engage unlawfully in employment in the United States; or Whoever knowingly makes any false statement or claim that he is a citizen of the United States in order to register to vote or to vote in any Federal, State, or local election (including an initiative, recall, or referendum)— Shall be fined under this title or imprisoned not more than five years, or both. Subsection (f) does not apply to an alien if each natural parent of the alien (or, in the case of an adopted alien, each adoptive parent of the alien) is or was a citizen (whether by birth or naturalization), the alien permanently resided in the United States prior to attaining the age of 16, and the alien reasonably believed at the time of making the false statement or claim that he or she was a citizen of the United States.