Difference between revisions of "Walsh spectra of all known APN functions over GF(2^8)"

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The tables below contain the Walsh spectra for all [[Known instances of APN functions over GF(2^8)]]. All of these 8180 functions have one of the following three Walsh spectra:
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The tables below contain the Walsh spectra for all [[known instances of APN functions over GF(2^8)]]. All of these 8180 functions have one of the following three Walsh spectra:
 
* <math>\{ -32^{2380}, -16^{20400}, 0^{16320}, 16^{23120}, 32^{3060} \}</math> (same as the Gold functions)
 
* <math>\{ -32^{2380}, -16^{20400}, 0^{16320}, 16^{23120}, 32^{3060} \}</math> (same as the Gold functions)
 
* <math>\{ -64^6, -32^{2240}, -16^{20880}, 0^{15600}, 16^{23664}, 32^{2880}, 64^{10} \}</math> (type 1)
 
* <math>\{ -64^6, -32^{2240}, -16^{20880}, 0^{15600}, 16^{23664}, 32^{2880}, 64^{10} \}</math> (type 1)

Revision as of 19:55, 9 July 2020

The tables below contain the Walsh spectra for all known instances of APN functions over GF(2^8). All of these 8180 functions have one of the following three Walsh spectra:

  • (same as the Gold functions)
  • (type 1)
  • (type 2)

There are 12 functions with a Walsh spectrum of type 2 (given in the table below), 487 functions with a Walsh spectrum of type 1, and 7681 functions with a Gold-like Walsh spectrum (not listed below due to space limitations). Magma code listing all functions with a Gold-like Walsh spectrum, a Walsh spectrum of type 1 and a Walsh spectrum of type 2 is available.


Functions with Walsh spectrum of type 2