Additional
Yes. If we push the idea beyond encryption, there is a much larger mathematical program hiding inside the Kester operator. The strongest direction is to treat it as a general theory of self-classifying operators . 15. The Kester Meta-Operator Instead of fixing the rule to continuity, define a local property P of a function: P(f,x)\in\{0,1\}. Then define \boxed{ K_{P,a}(f)(x)=a^{P(f,x)}f(x). } The original Kester operator is P(f,x)= \mathbf 1_{\{f\text{ is continuous at }x\}}, \qquad a=2. But now the same architecture can operate on completely different mathematical properties. This suggests a whole Kester operator hierarchy . 16. Differentiability Kester operator Define D_f=\{x:f\text{ is differentiable at }x\}. Then K_Df(x)= \begin{cases} 2f(x),&x\in D_f,\\ f(x),&x\notin D_f. \end{cases} Now the dynamics are controlled by differentiability rather than continuity. You can ask: D_f,\quad D_{K_Df},\quad D_{K_D^2f},\ldots Does differentiability he...