Difference between revisions of "Tables"
m |
|||
| Line 1: | Line 1: | ||
| − | + | = 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 === | |
| − | |||
| − | |||
| − | |||
* [[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)]] | ||
| − | |||
| − | |||
* [[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 16:10, 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
