Does there exist any sorts of algebraic relationship between Original and Sub Key of DES? I understand that by solving K-Maps of 64-bit Input/48-bit Output, I can get 16 algebraic relationships relating each sub key with the original key. Has someone done it already? Can this be of any use in exploiting the vulnerabilities of DES?
Laurie Brown and Jeniffer Seberry (see paper here performed a comprehensive analysis of the key schedule of DES, published in AUSCRYPT90 (conference series which later on turned into ASIACRYPT), and suggested some changes to strengthen the key schedule.
This is a good starting point to start hunting citations, and see what else has been done since then.