Optimal Reduced Representatives of Quadratic APN Permutations in Odd Dimension
The paper proves that every quadratic almost perfect nonlinear permutation Q in odd dimensions $n ext{ ≥ } 5$ has an optimal linear equivalent, meaning there exist invertible linear maps L and A such that the derivative of the reduced representative of L◦Q◦A has no zero and its non-empty fibers have exactly two elements. This result is significant because it shows a specific type of permutation exists that serves as a counterexample to conjectures regarding critical points.