He said life on the mat probably had turned sunlight into energy, but probably producing "horribly smelly" sulfur instead of oxygen.
The research was published online last week in the journal Astrobiology.
NASA astrobiologist Abigail Allwood, who found slightly younger fossils a few years ago, said it is challenging to prove the fossil contained life. But Hazen said they used dozens of criteria to show that the microscopic features fit with what science knows about ancient life.
If you had walked the Australian beaches of 3.5 billion years ago, you would see this "slimy mass of purple or brown fibers emitting this stench of sulfur compounds but living very happily," Hazen said. "This is not a place you would want to go to on your summer vacation."