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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 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)]]
* [[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 ==
=== 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|Known APN 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]]
* [[: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 APN power permutations over GF(2^n) with n less than or equal to 129]]
* [[Known infinite families of quadratic APN polynomials over GF(2^n)]]
=== Quadratic functions ===
* [[Unclassified instances of APN polynomials over GF(2^n)]]
* [[Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8]]
* [[CCZ-inequivalent APN functions from the known APN classes over GF(2^n) (for n between 6 and 11)]]
* [[Known quadratic APN polynomial functions over GF(2^7)]]
* [[Known quadratic APN polynomial functions over GF(2^7)]]
* [[Known quadratic APN polynomial functions over GF(2^8)]]
* [[Known quadratic APN polynomial functions over GF(2^8)]]
* [[Walsh spectra of quadratic APN functions over GF(2^8)]]
* [[Walsh spectra of quadratic APN functions over GF(2^8)]]
* [[Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)]]
=== Equivalences, inequivalences and invariants ===
* [[Some APN functions CCZ-equivalent to x^3 + tr_n(x^9) and CCZ-inequivalent to the Gold functions over GF(2^n)]]
* [[CCZ-inequivalent APN functions from the known APN classes over GF(2^n) (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-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)]]
* [[Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1]]
* [[Differentially 4-uniform permutations ]]
* [[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]]
=== 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]]
* [[Unclassified instances of APN polynomials over GF(2^n)]]
* [[Lower bounds on APN-distance for all known APN functions]]
* [[Lower bounds on APN-distance for all known APN functions]]
= 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]]
* [[Differentially 4-uniform permutations ]]

Revision as of 14:10, 5 November 2019

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

On known families

On known instances in small dimensions

Power functions

Quadratic functions

Equivalences, inequivalences and invariants

Other instances

On other differential uniformities