[Rune Son of Bjarne]

What Sauron could not know was wether Gil-Galad and Galadriel had passed them on. . .well, Galadriel probably wouldn't unless she had two.

I know that it says that Saruman became aware of the ring, but for some reason I have alwas thought of it as if he suspected it, but did not know it. That could also explain why the ring was not taken from Gandalf during his imprissonment.

It is clear that Sauron did not know who had the rings, but meerly suspected sertain people. Now this either means that Saruman did not know either or that he found it convinient to keep Sauron in the dark about this. . .

I guess one just have to decide what is most plausible.