Generalizations of ChiChi: Families of Low-Latency Permutations in Any Even Dimension

At Eurocrypt’25, Belkheyar et al. introduced a new non-linear layer called ChiChi or χχ. ChiChi is built based on Daemen’s χ function, but crucially gives a permutation in even dimension divisible by four.In this work, we generalize their construction in multiple ways, prove their open conjecture regarding the algebraic degree of the inverse of ChiChi, and investigate the properties of it against key recovery attacks.