Art I, Sect 8 says, among other powers: The Congress shall have Power ....To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;"
Bingo!
You are correct!
Naturalization.
Congress has the power of "naturalization." Only.
They do not have the Constitutional authority to make laws to determine who may be a "natural born Citizen." And it's a darn good thing they don't have that authority.
Naturalization. Only.
Since Ted Cruz's birth status in a foreign land is fully dependant upon what Congress said at the time (via laws they passed), foreign born Ted Cruz could not be a "natural born Citizen."
To define who needs to be naturalized means you have to define who is already a citizen. That is covered at the end of section 8, where it says: “To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof. “
Ted Cruz did not have to be naturalized because he was already declared to be an automatic citizen at birth.
The law says so. And the Constitution gives Congress the power to decide.