A classification of differentially nonequivalent quadratic APN function in 5 and 6 variables

A vector Boolean function F from F^ to is called almost perfect nonlinear (APN) if equation F(x) ф F(x ф a) = 6 has at most 2 solutions for all vectors a, 6 E Fn, where a is non-zero. Two functions F and G are called differentially equivalent if B_a(F) = B_a(G) for all a E Fn, where B_a(F) = {F(x) ф F(x ф a) : x E F^}. A classification of differentially non-equivalent quadratic APN function in 5 and 6 variables is obtained. We prove that, for a quadratic APN function F in n variables, n ^ 6, all differentially equivalent to F quadratic functions are represented as F ф A, where A is an affine function.

Keywords

Authors

References