Tables

Known instances of APN functions over $\mathbb {F} _{2^{n}}$

Known families of APN functions

• Known infinite families of APN power functions over GF(2^n)
• Known infinite families of quadratic APN polynomials over GF(2^n)

On known instances in small dimensions

Power functions

• APN power functions over GF(2^n) with n less than or equal to 13
• Inverses of known APN power permutations over GF(2^n) with n less than or equal to 129

Quadratic functions

• Known instances of APN functions over GF(2^7)
• Known instances of APN functions over GF(2^8)

Equivalences, inequivalences and invariants

• CCZ-inequivalent representatives from the known APN families for dimensions up to 11
• Walsh spectra of all known APN functions over GF(2^8)
• CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)
• CCZ-invariants for all known APN functions in dimension 7
• CCZ-invariants for all known APN functions in dimension 8
• Sigma multiplicities for APN functions in dimensions up to 10

Other instances

• Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8
• Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1
• APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials
• Lower bounds on APN-distance for all known APN functions

Misceallaneous results

• Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)
• Some APN functions CCZ-equivalent to x^3 + tr_n(x^9) and CCZ-inequivalent to the Gold functions over GF(2^n)

On other differential uniformities

• Differential uniformity of all power functions over GF(2^n) with n less than or equal to 13
• Differentially 4-uniform permutations