As an update, I am still working on the security of the POW problem. A lot of security issues arise because I want to design a POW that incentivizes the construction of the reversible computer in the best possible way. For R5, I will use reversible linear cellular automata of dimensions 1 and 2. However,
I can list several security anomalies that arise from the use of linear cellular automata of dimension 1 including the following:
1. Suppose that f,g are involutions which are related to each other in some way. Then the composition fg is a permutation with cycles of an exceptionally low period. I so far have not been able to explain this phenomenon.
2. Cryptosystems require a large amount of non-linearity in order to thwart linear algebraic attacks. My POW problems however need to have as much linearity as possible since the CNOT gates (which are reversible and linear) will be much easier to construct than other reversible gates.
3. Reversible linear cellular automata over Z_2 of dimensions 1 or 2 over the torus of size 2^n x 2^n or circle of length 2^n have exceptionally low periods.
4. Reversible linear cellular automata over Z_2 of dimensions 1 or 2 have a Sierpinski triangle structure which indicates that these functions are not disorderly enough for cryptographic use.
Of course, I can solve these issues simply by basing my POW problems on something other than reversible linear cellular automata of dimension 1 or 2, but I do not want to do that because these reversible linear cellular automata are literally the simplest reversible objects that I can use, and I need my POW problem to be simple enough so that it will be as easy as possible for reversible computing manufacturers to construct machinery to solve these POW problems.
I hope you are doing fine and keep making progress.
Just wanted to drop by and give you some positive vibes
Would love to hear about any new stuff you got.