The first APN polynomials EA-inequivalent to power functions have been constructed in [7, 8] by applying CCZ-equivalence to the Gold APN functions. It is a natural question whether it is possible to construct APN polynomials EA-inequivalent to power functions by using only EA-equivalence and inverse transformation on a power APN function: this would be the simplest method to construct APN polyn...

In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z2n−1, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function Invd (n), which for a fixed positive integer d maps integers n ≥ 1 to the least positive residue of the inverse of d modulo 2n − 1, if it exists. In particular, we showe...

We find a one to one correspondence between quadratic APN functions without linear and constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On F27 , we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which...

In this extended abstract, we computationally check and list the CCZ-inequivalent APN functions from infinite families on F2n for n from 6 to 11. These functions are selected with simplest coefficients from CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence between any APN function and infinite APN families.

We give all the polynomials functions of degree 20 which are APN over an infinity of field extensions and show they are all CCZ-equivalent to the function x, which is a new step in proving the conjecture of Aubry, McGuire and Rodier.

The paper proposes multi-operation blank localization to fit final product geometries into near net shape blanks. Groups of machining features are located subject tolerance intervals on their relative positions and a lower bound the allowance which accommodates for uncertainties measurement machining. error, i.e., deviation resulting dimensions from center is minimized. problem formulated as co...

In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodier. Vectorial Boolean function and Almost Perfect Non-linear functions and Algebraic surface and CCZ equivalence

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n with n = 4k and k odd. We prove that these functions are CCZinequivalent to known APN power functions when k 6= 1. In particular it means that for n = 12, 20, 28, they are CCZ-inequivalent to any power function.

Given two families of sets F and G, the F separability problem for G asks whether for two given sets U, V ∈ G there exists a set S ∈ F , such that U is included in S and V is disjoint with S. We consider two families of sets F : modular sets S ⊆ N, defined as unions of equivalence classes modulo some natural number n ∈ N, and unary sets. Our main result is decidability of modular and unary sepa...