In a stream cipher, encrypting the ciphertext should always give the plaintext
That's true for the appropriate definition of "ciphertext", which implies it is the same size as the plaintext; and the same Initialisation Vector (the "random number" I guess, hereafter IV) is used.
I suspect the experiment that attempts encrypting the ...
Is the following cryptosystem possible:
The length of the key is generally much less than the length of the input text
I will assume that the plaintexts are essentially incompressable; that is, they are allowed to be arbitrary bit patterns.
If so, then if you are allowed to select the keys based on what the plaintexts are, then it is possible, but only if ...