How do you find the inverse degree of a hash function?
Trying to express the inverse of the non-linear Chi fonction of Keccak as a multivariate polynomial of the bits of the state will yield a degree 3 polynomial. 

How to derive such inverse is explained in section 6.6.2 of Joan Daemen PhD thesis as stated page 15 of http://keccak.noekeon.org/Keccak-reference-3.0.pdf