Question: Is there any cryptanalytic leverage to be had from the fact that some of the 56 "raw" keybits of DES are used more & less often than others?
Observation: over the course of the 16 rounds of DES each of the eight DES S-boxes is used 16 times, so there are a total of 128 S-box "instantiations" or "instances". Each S-box instance requires six bits of the expanded and permuted 56 bit raw key, so 768 keybits are used in total.
Analysis: of the 56 "raw" keybits, 12 are used in 15 different instances; 20 are used in 14 different instances; 20 are used in 13 different instances; and four are used in only 12 different S-box instances.
Hence my question. Is there any advantage for the cryptanalyst in knowing that four of the raw keybits are only used 12 times, or that 12 are used 15 times?