Bit constants are often added to the key schedule to reduce slide attacks. I have reviewed David Wagner's work, where he showed that the increased rounds in a Feistel network do not help if you have key symmetry. I have been trying to find some work that describes if a round-based bit-constant stream could be used to reduce the rounds and not hinder the safety margin.
For instance, let's say that you had a cipher that had 36 rounds, and you can attack 32 of them, where the key schedule contained a round-based constant stream based on an LFSR. Could round-constants be used in different places to allow the same fundamental architecture to be used in 32 rounds where you can attack up to 28? I've been unsuccessful in finding something like this in literature.
My motivation behind this is that there are a lot of ciphers out there, and some of them would be better for actual hardware implementation if they were a few rounds shorter. If I have a 32-round cipher, I can easily just use a shift register to control the rounds.
The question: has anyone looked at taking a cipher that existed and decreased the round requirements without ruining the cryptographic performance by the addition of bit constants per round?
Addendum 1: I've been exploring this question a little bit as continued literature searches haven't found anything that's helpful. Slide attacks invalidate the idea that even simple round functions are strong even with many rounds. I looked at this with SIMON32/64 because it has the simplest round function that I know combined with the fact that I wrote a simulation framework for them so I could tweak the code.
Firstly, it makes me wonder why slide attacks weren't invented earlier, as the image above shows how wonderfully symmetric the simple key schedule just happens to be with the LFSR input. Secondly, as the strength of the cipher largely depends on the key rounds, it makes me more convinced that someone has looked at reducing rounds in already existing ciphers by modifying the key schedule a bit.