Good topic Kal! I like what Cheefatt said in his post. Here are some additional things to consider.
If the majority of your intent is not separate from your opponent, then it is difficult for the opponent to read yours separate from theirs. This is the "following your opponent" concept, where your intent is to follow along with what they are doing and to take advantage only of what they give you during the interaction. You do not try to impose your own movements separate from what is happening in the interaction between you and the opponent. Of course, you still control the interaction with your circle (arcing, spiraling, non-linear movements). Although the idea behind the "use four ounces to deflect your opponent's thousand pounds" concept probably only refers to physical force, I see no reason not to apply this concept to intention as well. Using only four ounces of your intent to control the opponent would be very difficult for them to detect.
Sometimes the concept of using the circle for defense and the square to issue (fajin) is stated. In practice, I find that if the circle is not only used for defense, but is also used to set up the attack, then it is more difficult for the opponent to read your intent. Defensive movements can certainly also be, or set up, offensive ones. Using arcs, spirals, curves, etc. is like water flowing around obstacles as it flows downstream. Use these non-linear paths not only to protect your own center and root, but also to flow around the opponent's strengths in order to find their center and weaken their root. The flowing to their center is like the water flowing downstream - it just goes without the intent of going around this or that obstacle. Once you have found their center in this way, it is too late for the opponent to be able to respond to an attack, and you can issue (fast if desired, but, at this point, slowly attacking will still be effective and may illustrate better when you have actually reached this situation). Linear actions are much easier to detect and interpret/understand than non-linear ones.