# Difference between revisions of "Tables"

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− | + | = Known instances of APN functions over <math>\mathbb{F}_{2^n}</math> = | |

+ | == On known families == | ||

* [[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)]] | ||

+ | * [[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 === | ||

* [[:File:1-7c.pdf|Known APN power functions over GF(2^n) with n less than or equal to 13]] | * [[:File:1-7c.pdf|Known 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 APN power permutations over GF(2^n) with n less than or equal to 129]] | ||

− | + | === Quadratic functions === | |

− | |||

− | |||

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

* [[Known quadratic APN polynomial functions over GF(2^8)]] | * [[Known quadratic APN polynomial functions over GF(2^8)]] | ||

* [[Walsh spectra of quadratic APN 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-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)]] | ||

− | |||

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* [[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]] | ||

+ | === 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]] | ||

+ | * [[Unclassified instances of APN polynomials over GF(2^n)]] | ||

* [[Lower bounds on APN-distance for all known APN functions]] | * [[Lower bounds on APN-distance for all known APN functions]] | ||

+ | |||

+ | = 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]] | ||

+ | * [[Differentially 4-uniform permutations ]] |

## Revision as of 15:10, 5 November 2019

## 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

- Known APN power functions over GF(2^n) with n less than or equal to 13
- Inverses of 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
- Unclassified instances of APN polynomials over GF(2^n)
- Lower bounds on APN-distance for all known APN functions