The Constitution grants to Congress only limited powers to make criminal laws. These powers fall into five categories:
a) those made pursuant to express authorizations for four specific crimes;
b) those made under the “necessary and proper” clause;
c) those made for the few tiny geographical areas over which Congress has “exclusive Legislation”;
d) those governing the military; and
e) those made pursuant to two of the Amendments to the Constitution.
OVERVIEW OF EACH CATEGORY
a) Art. I, § 8 grants to Congress authority to define & punish counterfeiting, piracies and felonies committed on the high seas, & offenses against “the Laws of Nations”.  Article III, §3 grants to Congress a restricted power to declare the punishment of Treason.
b) Art. I, §8, last clause, grants to Congress the power “to make all Laws which shall be necessary and proper for carrying into Execution …all …Powers vested by this Constitution in the Government of the United States…”. This necessary and proper clause allows Congress to make criminal laws when necessary to enforce powers vested by the Constitution in the federal government. This worried people, so Madison & Hamilton explained it:
In Federalist No. 44, Madison said, regarding the peoples’ fears of usurpations by Congress:
what is to be the consequence, in case the Congress shall misconstrue this part of the Constitution and exercise powers not warranted by its true meaning, I answer the same as if they should misconstrue or enlarge any other power vested in them…the success of the usurpation will depend on the executive and judiciary departments,  which are to expound and give effect to the legislative acts; and in the last resort a remedy must be obtained from the people, who can, by the election of more faithful representatives, annul the acts of the usurpers (17th Para).
In Federalist No. 33, Hamilton cited Art. VI, cl.2, as showing that laws which are not pursuant to the Constitution are merely acts of usurpation and deserve to be treated as such (7th Para). He also said:
If the federal government should overpass the just bounds of its authority and make a tyrannical use of its powers, the people, whose creature it is, must appeal to the standard they have formed, and take such measures to redress the injury done to the Constitution as the exigency may suggest and prudence justify. (6thPara)
Congress has authority under the necessary and proper clause to make criminal laws enforcing the “Taxes, Duties, Imposts and Excises” authorized by Art. I, §8, cl.1; to make criminal laws prohibiting the filing of false statements or claims in Bankruptcy Court (Art. I, §8, cl. 4); and to make criminal laws forbidding the importation of slaves after 1808 (Art. I, §9, cl. 1). Article II, §4 mentions impeachment of civil officers for, among other things, “bribery”; so by implication, Congress is authorized to pass a criminal statute prohibiting the accepting of bribes by civil officers of the United States.
The main duty of the federal judiciary created by Art. III is to conduct trials [in the limited category of cases which they are permitted to hear], and that means parties & witnesses. Parties & witnesses must be required to tell the Truth. So, it would be necessary and proper for Congress to make laws declaring perjury and lying under oath in federal court criminal offenses.
These examples are not exclusive – there are doubtless additional criminal laws which would be appropriate exercises of the necessary and proper clause. But it is important to note that private citizens would rarely, if ever, be in situations where these criminal laws would apply to them!
c) Article I, §8, next to last clause, authorizes Congress to exercise “exclusive legislation in all Cases whatsoever” over small defined geographical areas: the seat of the government of the United States [not to exceed ten squares miles], forts, dock-yards, magazines, arsenals, and the like.
As Madison said in Federalist No. 43 (4th –6th Paras), it is necessary for the government of the United States to have “complete authority” at the seat of government, and over forts, dock-yards, etc. This means that over these limited geographical areas, Congress has authority to make the full range of laws criminalizing murder, robbery, extortion, arson, rape, kidnapping, etc.
It is important to note that private citizens would not be affected by these laws unless they are inside the District of Columbia, military bases, dock-yards, and the like. 
d) Article I, §8, cl. 14 authorizes Congress “To make Rules for the Government and Regulation of the land and naval Forces.” Under this grant of authority, Congress has properly enacted The Uniform Code of Military Justice, the criminal code which governs members of our military forces.
This covers all the “standard” criminal offenses plus additional crimes uniquely appropriate to those in the military: failure to obey a lawful order, dereliction of duty, absent without leave, desertion, conduct unbecoming an officer, etc. Again, it is important to note that civilians are not affected by the criminal code which governs our military forces.
e) Some of the Amendments to the Constitution authorize Congress to enact laws to enforce them: The 13th Amendment would authorize Congress to make laws criminally punishing those who keep slaves. The 16thAmendment presumably authorizes Congress to make criminal laws to enforce the “income” tax. The 18th Amendment (now repealed) authorized Congress & the States to make laws criminally punishing those who manufactured or trafficked in intoxicating liquors. The 14th, 15th, 19th, 24th, & 26th Amendments restrict only States &/or the federal government. The other Amendments (after the original Ten) address “housekeeping” issues.
So, Congress’ criminal jurisdiction over private citizens under all Amendments is limited to those who keep slaves or don’t pay “income” taxes (whatever “income” meant when the Amendment was adopted).
TODAY’S FEDERAL CRIMINAL CODE
Much of the federal criminal code of today consists of “laws” which are mere usurpations and deserve to be treated as such. They are not “laws”, because they are outside the legislative powers granted to Congress by the Constitution. Excepting members of the military, and outside the tiny geographical areas (the District of Columbia, military bases, dock-yards, etc., and any Territories) where Congress has “exclusive legislation”; Congress has no general authority to pass criminal laws.
Thus, laws which purport to be of general application throughout the several States criminalizing acts respecting firearms, ammunition, hate crimes, environmental crimes, economic crimes, banking crimes, computer crimes, murder, kidnapping, narcotics, arson, extortion, etc., are all unconstitutional usurpations.
Lest you think this is astonishing, remember that before the 18th Amendment was ratified in 1919, everybody knew that Congress didn’t have the power to make laws criminalizing the manufacture or distribution of intoxicating beverages. Congress needed an Amendment to the Constitution to authorize them to make the laws giving effect to prohibition!. But today, Congress is lawless & filled with usurpers; and the federal prisons are filled with inmates convicted under unconstitutional laws/
Do we have a remedy for these usurpations by Congress? As Madison, quoted above, said,
the success of the usurpation will depend on the executive and judiciary departments, which are to expound and give effect to the legislative acts.
Thus, when Congress makes a criminal law for which it lacks constitutional authority, the Executive Branch (in the person of the U.S. Attorney) has the power & duty to refuse to prosecute the violation. If that check fails, the Judicial Branch has the power to declare the statute unconstitutional.  If the U.S. attorneys and federal judges both fail in their obligations to enforce the Constitution, Madison said, as quoted above,
…in the last resort a remedy must be obtained from the people, who can, by the election of more faithful representatives, annul the acts of the usurpers…
Hamilton said, as quoted above,
If the federal government should overpass the just bounds of its authority and make a tyrannical use of its powers, the people, whose creature it is, must appeal to the standard they have formed, and take such measures to redress the injury done to the Constitution as the exigency may suggest and prudence justify.
Did you get that? Hamilton said that when our ”creature”, i.e., the federal government, usurps power, we are to judge the conduct by the standard of the Constitution, and we are to take appropriate action to “redress the injury done to the Constitution.”
This includes demands for impeachment, recall petitions, defeating faithless representatives in the next election, nullification by states, jury nullification, non-violent civil disobedience, ignoring unconstitutional “laws” because an unconstitutional “law” is a “mere usurpation and deserves to be treated as such” – and the like.
Alexander Hamilton considered the people to be “the natural guardians of the Constitution” – and contemplated “a people enlightened enough to distinguish between a legal exercise and an illegal usurpation of authority.” (The Federalist, No. 16, 10th Para). 
One expects Hamilton would be disappointed in “the People” of today.  It is our responsibility to learn the Constitution, to educate the people in our spheres of influence, and to take this country back from the faithless usurpers who have betrayed us.
THE STATES AND CRIMINAL CODES
Did the Framers of the Constitution advocate anarchy? No way!
The legislatures of the States have whatever authority granted to them by their State Constitutions to enact criminal codes applicable to those within the borders of their States. Madison said it all in Federalist No. 45 (9th Para):
The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and internal order, improvement, and prosperity of the State.
It is up to the States to enact the criminal codes which apply to the people within their borders.
Webster’s American Dictionary (1828) defines “laws of nations” as, “the rules that regulate the mutual intercourse of nations or states. These rules depend on natural law, or the principles of justice which spring from the social state; or they are founded on customs, compacts, treaties, leagues and agreements between independent communities.”
Here is one example of a “law of nations” based on custom: From antiquity to modern times, envoys between warring armies have been entitled to safe conduct while on their missions. In the [excellent!] movie, “300”, it was a shocking thing when the Spartan King, Leonidas, killed the envoys of the Persian King Xerxes. Our concept of “diplomatic immunity” is thus an ancient one.
 Madison here illustrates checks which the Executive & Judicial Branches have over Congress. We all know that Courts may declare an act of Congress unconstitutional; but most don’t know that the President should refuse to enforce an Act of Congress which the President, in the exercise of his thoughtful & independent judgment, deems unconstitutional. The President’s Oath is to “…preserve, protect and defend the Constitution…” (Art II, § 1, last cl.). It is not to “go along with” Congress – it is not to “obey” the Courts. The President must make his own independent determinations. He may notproperly abdicate this duty in favor of another Branch! The Executive Branch is to function as a check on the other two! The check on the President is impeachment & removal from office.
 Article IV, §3, cl. 2 also granted to Congress authority to dispose of and make all needful Rules and Regulations respecting the Territories belonging to the United States [such as the Western Territories before they became States – Federalist No. 43, 11th Para]. This gave Congress authority to make the full range of criminal laws to govern those Territories until such time as they became States. When they became States, jurisdiction to enact criminal laws would be transferred TO the new State.
 It is the responsibility of defense counsel to raise the issue of the unconstitutionality of the statute under which defendant is charged. But lawyers, like everybody else in our modern culture, have been indoctrinated into statism; and likeeverybody else, are often unaware that Congress must be authorized by the Constitution to enact a criminal law before the law is valid. The judge has an independent responsibility to raise the unconstitutionality of the statute; but like defense counsel and everybody else, they often don’t know that Congress must have constitutional authority for their Acts.
 Hamilton also knew that “an illegal usurpation of authority”, to be successful, “would require not merely a factious majority in the legislature, but the concurrence of the courts of justice and of the body of the people.” Federalist No. 16, 10th Para. [emphasis added]. Thus, the people, as the natural guardians of the Constitution, have a duty to protestwhen the authorities act lawlessly! If they don’t, they will suffer the consequences, as in Europe during the last century &, as we may soon see, in our own once blessed country.
 Hamilton contemplated “…the most vigilant and careful attention of the people…” (Federalist No. 23, next to last Para). In speaking of power disputes between the federal and state governments, Hamilton said that if the rights of the people “…are invaded by either, they can make use of the other as the instrument of redress.” (Federalist No. 28 7th Para).
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