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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)]] | ||

− | |||

− | |||

== 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 18:08, 1 September 2021

# Known instances of APN functions over

## 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

### 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)