I've seen a few questions here on fixed-points in ciphers, most asking about the possibility and existence. Most of the answers however pointed out that fixed points are not exactly a security threat. Googling about it didn't fetch me much. All I found was this book, which stated it well but does not go on and explain it why!
My thoughts (from an attacker's perspective)
If I find out that the block that I captured is a fixed-point, I know the
pText as well as
eText for this key. So it'd certainly help me crack it faster (both chosen-plaintext-attack and chosen-ciphertext-attack). Additionally, I know that the number of keys that result in such a fixed-point are very few. So maybe there is a way for me to get the possible keys given the fixed-point.
My assumption was that it'd be easy for the attacker to find out that the captured block is a fixed-point because it retains all of the original message's pattern. Also I assumed that the relation from fixed-point to key is quite obvious.
So it seems this attack is not considered a threat because my assumptions are wrong (one or both). What am I missing?