To add two numbers, for example, it constructs the midpoint between them, then doubles the distance from the origin.

It’s basically a self-defined system of arithmetic, with no actual numbers. e.g. rather than 1 + 2 = 3, you have [radius of unit circle A] + [radius of 2 unit circle B] = [length of 3 unit line C]. I’ll confess I don’t totally understand how you can extend that to the point that it can correctly implement RSA, but I believe it can be done based on other achievements with unquantified geometry I’ve witnessed in the past.

For example, this excellent video about constructing flags using only the shape drawing tools of PowerPoint without ever applying external measurements to the shapes.