I want to know if it is possible to program such a code that could determine two distinguish, not inverse, functions, say $f$ and $g$, that is true for the below statements at a given input and output diapason?
for the diapason $(x_1,x_2,...,x_{100}), (y_1,y_2,...,y_{100})$ both statements below should be true:
1) $f(x)=y$
2) $g(y)=x$
If you already know such functions, please share with me. My aim is to find such two functions, with or without using programming.
EDIT: I have to inform that this idea if successful, will be used for app activation. The scheme will be like this:
1) App is downloaded from the web-site.
2) App creates a unique fingerprint for the computer (fp)
3) fingerprint is sent to activation server
4) activation server generates a key for the fp. ser(fp)=key
5) key is sent back to app
6) app verifies if key is valid. app(key)=fp.
The trick here must be that functions app and ser must be different and not inverse
This is possible, for example, $$f(x)=g(x)=(x-1)(x-2)(x-3)(x-4)(x-5)\cdots(x-100)+x$$
For every $x=1,2,3,4, \cdots, 100$, we have $f(x)=g(x)=x$, because there is a zero in the product. However these functions are clearly not each others inverse.