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

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(Replaced content with "The tables below contain the Walsh spectra for all quadratic APN functions of dimension 8 as given in the appendix of [https://eprint.iacr.org/2013/007.pdf "A Matrix Appro...")
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* <math>\{ -64^{12}, -32^{2100}, -16^{21360}, 0^{14880}, 16^{24208}, 32^{2700}, 64^{20} \}</math> (type 2)
 
* <math>\{ -64^{12}, -32^{2100}, -16^{21360}, 0^{14880}, 16^{24208}, 32^{2700}, 64^{20} \}</math> (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).
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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 [[:File:Gold spectra.txt|Gold-like Walsh spectrum]], a [[:File:T1 spectra.txt|Walsh spectrum of type 1]] and a [[:File:T2 spectra.txt|Walsh spectrum of type 2]] are available.
  
  

Revision as of 21:30, 19 December 2018

The tables below contain the Walsh spectra for all quadratic APN functions of dimension 8 as given in the appendix of "A Matrix Approach for Constructing Quadratic APN Functions". All 8180 functions listed in the appendix 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 are available.


Functions with Walsh spectrum of type 2