# What does $x^{1/e}$ mean in cryptography in this open butterfly structure?

I am currently reading a research paper that introduces this thing called a butterfly structure.

I am confused about the structure of the open butterfly in this paper which has the equation $$H^{\alpha}_{e}(x,y)=(R^{-1}_{R_y[e,\alpha](x)}(y),R_y[e,\alpha](x))$$ where $$R_k[e,\alpha](x)=(x+\alpha k)^e+k^e$$ and a corresponding structure as seen below:

I am confused as to how the structure of the butterfly above, relates to the equation. Furthermore, I don't really understand what $$x^{1/e}$$ in the butterfly structure means. It would be great if someone could explain this. The paper is Cryptanalysis of a Theorem Decomposing the only Known solution to the big APN problem.

Squeamish Ossifrage is correct. This is the power map $$x\rightarrow x^t$$ where $$te\equiv 1 \pmod{2^n-1}$$ and the underlying field is $$GF(2^n).$$