[Ibrîniðilpathânezel]

As Inziladun said, the smiths of Eregion learned the craft of making rings of power from Sauron; thus, he knew how they worked at a very fundamental level. It was said, of the inscription on Sauron's ring during the Council of Elrond, that when Sauron finished forging the One Ring, he spoke the words of the ring-verse, which the smiths of Eregion heard and "knew they had been betrayed." If the speaking of those words was enough to constitute a betrayal (which also prompted the Elves to immediately remove their rings), it would appear that it was actually the "spell" by which Sauron sealed the plan which he had initiated when he went to the smiths as Annatar and taught them this craft. Celebrimbor was able to make the Three useful in ways that did not have the corrupting influence of those rings Sauron helped to forge, but he apparently could not avoid incorporating aspects of the basic "blueprint" of which Sauron was able to take advantage, rendering them useless so long as he held the master ring.

And Sauron clearly did have knowledge of their making. The words of ring verse are what the smiths heard when Sauron "activated" the One Ring, Sauron spoke them, and the full verse mentions the Three. Since the elves who held them took them off the instant they knew of their betrayal, they were not used and Sauron did not know who had them; he tortured Celebrimbor to death, trying to force him to reveal that secret, which he kept till his death. But it seems apparent to me that Sauron knew of their existence, both before and after he finished the One.