Recovering or Testing Extended-Affine Equivalence

Extended Affine (EA) equivalence is the relation between two vectorial Boolean functions $F$ and notation="LaTeX">$G$ such that there exist affine permutations notation="LaTeX">$A$ , notation="LaTeX">$B$ an function notation="LaTeX">$C$ satisfying notation="LaTeX">$G = A \circ F B + C$ . While problem has a simple formulation, it very difficult in practice to test whether are EA-equivalent. This variants: EA-partitioning deals with partitioning set of into disjoint EA-equivalence classes, xmlns:xlink="http://www.w3.org/1999/xlink">EA-recovery about recovering tuple notation="LaTeX">$(A,B,C)$ if exists. In this paper, we present new algorithm efficiently solves EA-recovery for quadratic functions. Although its worst-case complexity occurs when dealing APN functions, supersedes, terms performance, all previously known algorithms solving any dimension, even case approach based on Jacobian matrix tool whose study context can be independent interest. The best EA-partitioning mainly relies class invariants. We provide overview invariants along one xmlns:xlink="http://www.w3.org/1999/xlink">ortho-derivative invariant applicable specific type great interest, which tens thousands need sorted distinct EA-classes. Our ortho-derivative-based fast compute, practically always distinguishes EA-inequivalent