"There are three general federal perjury laws. One, 18 U.S.C. 1621, outlaws presenting material false statements under oath in federal official proceedings. A second, 18 U.S.C. 1623, bars presenting material false statements under oath before or ancillary to federal court or grand jury proceedings. A third, 18 U.S.C. 1622 (subornation of perjury), prohibits inducing or procuring another to commit perjury in violation of either Section 1621 or Section 1623. In most cases, the courts abbreviate their description of the elements and state that to prove perjury in a judicial context under Section 1623 the government must establish that the defendant '(1) knowingly made a (2) false (3) material declaration (4) under oath (5) in a proceeding before or ancillary to any court or grand jury of the United States.' […] This report is an abbreviated version of CRS Report 98-808, 'Perjury Under Federal Law: A Brief Overview,' by Charles Doyle, stripped of most footnotes, quotations, citations, and bibliography."
CRS Report for Congress, 98-807