I wonder if the way that Mill's constant is defined could provide a good data encapsulation and encryption method if instead of encapsulating primes, for instance a simple ASCII message is encapsulated into the intervals generated by Mill's method. Mill's constant is always associated to the initial original idea of encapsulating an infinite set of primes, but: what if the constant is used to encapsulate a finite set of values required for some calculation or safe communication?
This is an example: for small messages it is totally possible to encapsulate each character of an ASCII message in a Mill's (-demonstration like) $[N^2,(N+1)^2]$ interval using each ASCII code of each character (in this case we can use a power of two interval because there is no restriction regarding the existence of the values we store in the interval).
For instance, the ASCII value of $A$ is $65$, $B$ is $66$, ..., $Z$ is $90$, etc. so it is possible to encapsulate each single character of the message inside $[N^2,(N+1)^2]$ intervals as $C_n=N^2+V$, where $V$ is the ASCII value of the character. The only restriction is that the interval must be big enough to handle an ASCII code: small intervals like $[1^2,2^2],[2^2,3^3]...[9^2,10^2]$ are not valid because the ASCII value plus the lower bound of the interval, $N^2$, is greater than the upper bound $(N+1)^2$, but for instance, any interval $[N^2,(N+1)^2]$ greater than $[20^2,21^2]$ would be fine to encapsulate an ASCII character in the way explained above.
The generation of the Mill's constant would be done as usual. For instance after encapsulating a message of $5$ characters, the Mill's constant $A_{5}$ is generated. That constant is able to generate the characters back, by using the character representing-function $C_n=\lfloor A^{2^n} \rfloor - (\lfloor A^{2^{n-1}} \rfloor)^2 $, $n \in [0..5]$.
Example: message = "Hello"
$N_{0}=20^2, C_{0}=20^2+Ascii(H)$
$N_{1}=C_{0}^2, C_{1}=N_{1}+Ascii(e)$
$N_{2}=C_{1}^2, C_{2}=N_{2}+Ascii(l)$
$N_{3}=C_{2}^2, C_{3}=N_{3}+Ascii(l)$
$N_{4}=C_{3}^2, C_{4}=N_{4}+Ascii(o)$
Then the Mill's constant is $A=A_{4}=C_{4}^{\frac{1}{2^4}}$. With this constant is possible to recalculate each $C_{n}=\lfloor A^{2^n} \rfloor$ and then recover the ASCII values $V_n=C_n-C_{n-1}^2$
Finally:
message$=V_0.V_1.V_2.V_3.V_4=H.e.l.l.o="Hello"$ where "." means concatenation of characters.
Probably the cost of the generation of the constant makes this theoretically possible but impossible to perform due to the accuracy required (decimals required to know about the constant to encrypt properly a very long message).
I would like to ask the following questions:
Has this approach been tried before? Are there references to this kind of "encryption by constant" method?
Would it be useful for some kind of encoding scheme? e.g.: it might be possible to encrypt a path of a graph in a constant, using the value of the nodes as the value encapsulated on each iteration and then "decode" the value and use the path for some decision tree. Thank you!