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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 ==
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== 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]]
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* [[: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]]
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* [[: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)]]
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* [[Known instances of APN functions over GF(2^7)]]
* [[Known quadratic APN polynomial functions over GF(2^8)]]
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* [[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)]]
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* [[CCZ-inequivalent representatives from the known APN families for dimensions up to 11]]
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* [[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]]
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* [[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]]
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 +
== 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 18:08, 1 September 2021

Known instances of APN functions over

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