Page 15 of the Keccak reference (PDF) explains that the $Chi$ step mapping of the Keccak-f permutation in Keccak is defined to be “nonlinear mapping”. Without this, the complete permutation would be ...
Where does the word or acronym Keccak come from? Guido Bertoni, Joan Daemen, Michael Peeters, and Gilles Van Assche. Keccak sponge function family main document. Submission to NIST (updated), 2009. ...