This is a 32-bit feedback shift register to encrypt some message. The register shifts circularly by 4 bits. Before each shift the S-box takes the last 4 bits and feeds the 4-bit output back into the four bits just next to them (as shown above). This cryptosystem is keyed by the contents of the S-box. The questions are:
If the S-box is not invertible, how many bits of information does it contain? And what if the S-box is invertible but entries selected randomly without replacement?
So what I'm confused about is: why is this cryptosystem "keyed by the contents of the S-box"? How to decrypt the ciphertext if we know the S-box (and times the register shifted if necessary)? And what does "information contained by the S-box" mean? How does the invertibility of the S-box affect the bits of information it contains?
I know that the initial value of an FSR is called the "seed" and from that the register can generate some pseudorandom keys to be used in some cryptosystems. But in this problem it seems that the seed itself is the plaintext to be encrypted and the ciphertext is one of its successors. Also, I know an S-box is used to perform substitution but I've never heard something about "the information it contains".
Hope that I've described this problem clearly. Thank you guys in advance :)