MIke Stay: That's not RSA, that's just a strange one-time pad.
--no, it (RSA for secret key use) is a secret key cryptosystem. It is much more secure against repeated use, than a 1-time pad. I just pointed out, it is much less secure than the usual secret key systems are generally thought to be.
At this point, it seems to me this has become a discussion for sci.crypt. You'll need to post your own cryptanalysis with the design (e.g. prove it's secure against differential, linear, saturation, boomerang, and whatever number-theoretic attacks you can come up with), as well as explain why anyone should care about it.
--the recursive system I described was more a skeleton of a design, than a design. I have no idea how secure it is against those attacks. The reason anybody should care about it, is this skeleton permits the design of very simple cryptosystems. Can you be more precise about what "sci.crypt" is?