I'm not an expert in constitutional law but as I understand it, the constitution grants the Federal government "To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;"
And simultaneously restricts powers on the states "No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts;"
Article 1, sections 8 and 10.
But note that this doesn't say "only the federal government can authorize" as you have stated it, it only restricts "states". I'm sure you recall that historically banks issued their own bank notes (perhaps a grey area) and the federal government didn't start printing currency until 1862. But it looks to me like there is nothing to restrict individuals, organizations, etc. from coining or printing (or digitally generating) their own money. I do find it very interesting and would enjoy hearing from someone more knowledgeable.