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= Known instances of APN functions over <math>\mathbb{F}_{2^n}</math> =
= Known instances of APN functions over <math>\mathbb{F}_{2^n}</math> =
== On known families ==
== Known families of APN functions ==
* [[Known infinite families of APN power functions over GF(2^n)]]
* [[Known infinite families of APN power functions over GF(2^n)]]
* [[Known infinite families of quadratic APN polynomials over GF(2^n)]]
* [[Known infinite families of quadratic APN polynomials over GF(2^n)]]
* [[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 known instances in small dimensions ==
== On known instances in small dimensions ==
=== Power functions ===
=== Power functions ===
* [[:File:1-7c.pdf|Known APN power functions over GF(2^n) with n less than or equal to 13]]
* [[:File:1-7c.pdf|APN power functions over GF(2^n) with n less than or equal to 13]]
* [[:File:inv.pdf|Inverses of APN power permutations over GF(2^n) with n less than or equal to 129]]
* [[:File:inv.pdf|Inverses of known APN power permutations over GF(2^n) with n less than or equal to 129]]
=== Quadratic functions ===
=== Quadratic functions ===
* [[Known quadratic APN polynomial functions over GF(2^7)]]
* [[Known instances of APN functions over GF(2^7)]]
* [[Known quadratic APN polynomial functions over GF(2^8)]]
* [[Known instances of APN functions over GF(2^8)]]
* [[Walsh spectra of quadratic APN functions over GF(2^8)]]
=== Equivalences, inequivalences and invariants ===
=== Equivalences, inequivalences and invariants ===
* [[CCZ-inequivalent APN functions from the known APN classes over GF(2^n) (for n between 6 and 11)]]
* [[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-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 7]]
* [[CCZ-invariants for all known APN functions in dimension 8]]
* [[CCZ-invariants for all known APN functions in dimension 8]]
* [[Sigma multiplicities for APN functions in dimensions up to 10]]
=== Other instances ===
=== Other instances ===
* [[Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8]]
* [[Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8]]
* [[APN functions obtained via polynomial expansion in small dimensions]]
* [[Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1]]
* [[Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1]]
* [[Non-quadratic APN polynomials over GF(2^n)]]
* [[APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials]]
* [[Lower bounds on APN-distance for all known APN functions]]
* [[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 =
= On other differential uniformities =
* [[:File:a.pdf|Differential uniformity of all power functions over GF(2^n) with n less than or equal to 13]]
* [[:File:a.pdf|Differential uniformity of all power functions over GF(2^n) with n less than or equal to 13]]
* [[Differentially 4-uniform permutations ]]
* [[Differentially 4-uniform permutations ]]

Latest revision as of 16:15, 3 January 2023

Known instances of APN functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math]

Known families of APN functions

On known instances in small dimensions

Power functions

Quadratic functions

Equivalences, inequivalences and invariants

Other instances

Misceallaneous results

On other differential uniformities