[Legate of Amon Lanc]

Originally Posted by Raynor

Hm, I would say that Sauron would be able to differentiate between an Elf Lord/Gandalf and the One Ring, with which he had a special relation. I don't think he was able to spot elves or istari by pure subtle perception, from miles away, but given the episode of Frodo at the Amon Lhaw, he was capable of perceiving the worn Ring from a far greater distance.

Well, but then you are definitely saying that Sauron knew the Ring was in Mordor. Which is something I just cannot agree with. Yes, he could sense, in general, the Ring - sometimes. But he was not 100% precise. I imagine it as being inside a room where there are many people talking. Among them are people like Galadriel, Saruman, Gandalf, Frodo, Denethor... All of them are important to Sauron. Suddenly, Sauron hears a raised voice from Osgiliath. He looks around - and it takes him a little to focus and then he notices it's only Denethor marching his armies to Osgiliath. Then he hears another shout from Rivendell - and sees that it's his Nazgul being splashed at the Bruinen Fords. Then he hears another shout, and sees that it's coming from Amon Hen. Looks there, but suddenly another, stronger shout comes from other place and he looks over there and so he doesn't notice Frodo.
I would say Sauron knew about some power in Mordor. But he did not know where the Ring is. He could have thought Aragorn has it, or Gandalf, or anyone else. Later, when Shagrat brought the mithril-coat and the dagger and the cloak to Barad-Dur, Sauron would have known there was some sort of "spy from the Shire" there, and if he were to believe Shagrat, he would have known there was also "the great elf warrior" with him, who is still running around somewhere. Ergo, if he knew the Ring is in Mordor, he would make all effort to catch that "great elf warrior" - mainly, he would have the clear information now: there is a great elf warrior with MY ring running around at Mordor. No, this is, in my opinion, not what Sauron could have thought in the slightest.

Also, consider this (emphasise mine):

Originally Posted by Mount Doom

And far away, as Frodo put on the Ring and claimed it for his own, even in Sammath Naur the very heart of his realm, the Power in Barad-dur was shaken, and the Tower trembled from its foundations to its proud and bitter crown. The Dark Lord was suddenly aware of him, and his Eye piercing all shadows looked across the plain to the door that he had made; and the magnitude of his own folly was revealed to him in a blinding flash, and all the devices of his enemies were at last laid bare.

Sauron did not expect it. Not in the slightest. He did not even think that the Ring could appear in Mordor. The Mouth of Sauron presumes that Frodo was "spying" in Mordor. This is probably the opinion of Sauron himself. So, no Ring inside Mordor. Even if Frodo's mysterious companion had it, Sauron would have acted differently. When he sent the Nine to the Shire, why wouldn't he made all effort to get the Ring inside his own realm? No, he just thought that there are some spies with no magic Rings. Yes, it will be good to catch them, but the war with Gondor was far more important.

Originally Posted by Raynor

I would guess that, given the importance of their coalition, the elves did not keep their secrets concerning the rings from Saruman, esspecially considering his developing interest in them. As for the taboo about them, I believe it applies only to those outside the White Council.

Not entirely sure. It is only one of the possibilities. As I said, it will be for another thread. But why did not then Gandalf tell Saruman about Narya? It is said that

Originally Posted by Unfinished Tales, The Istari

And the Grey Messenger took the Ring, and kept it ever secret; yet the White Messenger (who was skilled to uncover all secrets) after a time became aware of this gift, and begrudged it

I believe that the Three were taboo even among those in the Council. Also, we are told that Galadriel's view of Saruman was not as trustworthy. It could be that originally, the Rings were hidden, Saruman discovered Gandalf's, and that was before the first Council even met. And later, at the Council, they all agreed to tell about the Rings to each other. That would be explainable. But, was that really even needed? The Three were made "for protection and healing", and they did not have much of a strategic value in the Council's plans. "My Ring and Lórien are my own business, I will take care of it. Now let's focus on other things that bother us outside our own realms." That could be, in short, the motto of the Ring-bearers on the Council.