# Difference between revisions of "Tables"

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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 == | ||

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* [[APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions]] | * [[APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions]] | ||

* [[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 ]] |

## Revision as of 18:29, 9 July 2020

# 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

- Known quadratic APN polynomial functions over GF(2^7)
- Known quadratic APN polynomial functions over GF(2^8)
- Walsh spectra of quadratic APN functions over GF(2^8)

### Equivalences, inequivalences and invariants

- 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-invariants for all known APN functions in dimension 7
- 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
- APN polynomials over GF(2^n) CCZ-inequivalent to quadratic 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)