In this paper they change the $AES$ S-box to a uniformly random one and answer the questions:
How does the security of AES change when the S-box is changed by a secret S-box?
Would it be safe to reduce the number of rounds?
I have tried reading the paper but there are some things I do not understand.
- Are the S-boxes they are considering just random permutations of bytes that fit into an $8 \times 8$ table? How might they have chosen all the entries to get the S-box?
- Are they choosing a random S-box and then leaving it unchanged thereafter?
- In Section $3.1$ they state differential cryptanalysis will not pose a threat to variants of $AES$ where the S-box is replaced by a randomly chosen $8$-bit box. This is confusing. Do they mean one $8$-bit element in the S-box? I thought the S-box was $256$-bit, not $8$.
- Still referring to Section $3.1$. If a random S-box is secure against DCA and LCA, why make such an effort to design the one currently in use?
- How does a random S-box cause the secret information to go from $128$ to $256$ bits (depending on the key size) to $1812$ to $1940$. I understand there is now more secret information owing to the secret S-box but I cannot see where these numbers ($1812$ to $1940$) come from.