“What I’m saying is that if the key is truly random and full length, it will produce random ciphertext”
Whats full length? Keys come in increments of 8 with the normal key length being 256. Some software tools will use keys of over 2000.
There is not an infinite number of solutions. It is definately a finite although very high number. With todays computers it is not nearly as difficult as it once was to break a key.
“but I don’t see what else you can do.”
There is a science used to break these codes.
No, no, I’m not talking the type encryption generally done on a PC with 40-bit, or 56-bit, or 128-, or 256-, 1024-, etc, but “one-time pad”, though that can certainly be done on a PC. In that context, “full length” means if you want to encode 1000 characters of clear text, you will need 1000 truly random bytes of keytext. And — you can only use any given bit of keytext once, or you introduce a vulnerability that’s susceptible to statistical analysis, at least if the cryptanalyst knows or suspects that you may have reused keytext. And, yes, I realize I said “infinite” when I shouldn’t have.