The Silmarillion answers this question pretty clearly:
"Now the Elves made many rings; but secretly Sauron made One Ring to rule all the others, and their power was bound up with it, to be subject wholly to it and to last only so long as it too should last. And much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency; and Sauron forged it in the Mountain of Fire in the Land of Shadow. And while he wore the One Ring he could precieve all the things that were done by means of the lesser rings, and he could see and govern the very thoughts of those that wore them."
and later referring to the Elves:
"...they were aware of him; and they knew him, and percieved that he would be master of them, and of all that they wrought."
and, referring to the 3 elven rings:
"...the hand of Sauron had never touched them; yet they also were subject to the One."
It is true that Sauron himself never touched the Three, but it was through his knowledge that Celebrimbor was able to craft the rings in the first place. Sauron used Celebrimbor skills and knowledge, just as Celebrimbor used Sauron's. He never touched the Three but it was through his techniques that they were forged. He surely knew what went into them and knew what would be necessary to control them when crafting his own master ring.
If that is not good enough in itself, in Tolkien's letters,
Tolkien Letter 131
"The Elves of Eregion made Three supremely beautiful and powerful rings, almost solely of their own imagination, and directed to the preservation of beauty: they did not confer invisibility. But secretly in the subterranean Fire, in his own Black Land, Sauron made One Ring, the Ruling Ring that contained the powers of all the others, and controlled them, so that its wearer could see the thoughts of all those that used the lesser rings, could govern all that they did, and in the end could utterly enslave them. He reckoned, however, without the wisdom and subtle perceptions of the Elves. The moment he assumed the One, they were aware of it, and of his secret purpose, and were afraid. They hid the Three Rings, so that not even Sauron ever discovered where they were and they remained unsullied. The others they tried to destroy."
There ya go.
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