# Difference between revisions of "Tables"

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== 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 quadratic APN polynomial functions over GF(2^7)]] | * [[Known quadratic APN polynomial functions over GF(2^7)]] |

## Revision as of 13:46, 23 June 2020

## Contents

# Known instances of APN functions over

## On known families

- 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

- 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