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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> = | ||
== | == 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)]] | ||
* [[ | * [[Known infinite families of APN functions]] | ||
== On known instances in small dimensions == | == On known instances in small dimensions == | ||
=== Power functions === | === Power functions === | ||
* [[:File:1-7c.pdf| | * [[: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 | * [[Known instances of APN functions over GF(2^7)]] | ||
* [[Known | * [[Known instances of APN functions over GF(2^8)]] | ||
=== Equivalences, inequivalences and invariants === | === Equivalences, inequivalences and invariants === | ||
* [[CCZ-inequivalent | * [[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]] | ||
* [[ | * [[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 09:28, 16 October 2024
Known instances of APN functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math]
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)
- Known infinite families of APN functions
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
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
- 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
- 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)