Do police have the legal authority to randomly force somone to identify themselves?

The answer to your question is "no" the police can not at random conduct a search of a person - (demanding ID is a form of search and seizure) without - at least - a reasonable suspicion of criminal activity. The U.S. Constitution - Amendment IV - "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable search and seizures ..." An officer has no right to demand (at random) identification - but a citizen does have a duty - under certain circumstances - to produce proper identification.