Article 1, Section 10, of the Constitution, which is a restriction on the power of the states, states, "No State shall … coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts…."
What were "bills of credit"? That was the term used at that time for paper money. Through that provision in the Constitution, the Framers expressly prohibited the states from issuing paper money. It prohibited them from making anything but gold coins and silver coins legal tender or official money. It prohibited the states from issuing their own coins, leaving that power and responsibility to the federal government.
With respect to the federal government, Article 1, Section 8, states, "The Congress shall have Power …To coin Money, regulate the value thereof, and of foreign Coin…. To provide for the Punishment of counterfeiting the Securities and current Coin of the United States."
Why wasn't there an express prohibition on the power of the federal government to emit "bills of credit" or paper money? The reason is that the Constitution established a government of limited, enumerated powers. The federal government's powers were limited to those listed in the Constitution. If a power wasn't enumerated, it couldn't be exercised. Since there was no power to issue paper money given to the federal government, it couldn't exercise such power.