Whole key size
Strictly speaking, the 2 arms do not need to share a huge sequence of secret data. A very few bits once are sufficient if they initiate a known sequence, starting with the simplest, the time incremental one. Indeed, time as the hidden variable works very well.
- that we do not require strict equality for shared variables. Values shifts give smooth variations of the global outcome. Random shifts add only a little noise,
- and that at least, we require also 16 uniformly distributed different values. Ie it doesn’t work with binary variables,
Alice and Bob could agree to construct a starting shared constant, ie zero or a RSA one. Then they increment in the same way, sharing time as a presumed hidden variable. They could better use a complicated function of time while we know that it is easy to break all of them with the adequate algorithm.
Physicality of time as a hidden variable
While we can use time as the hidden variable, we don’t know if it is physical. This would need to find a cyclic real variable, itself a function of time. The question is still open and its answer is in the labs.
The effect got from the hidden variables depending mainly on their spread, sequences based on Pi digits or on any transcendantal expressions work well also. You can try the distributions with any well distributed variable.