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:
 
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)
+
* <span class="htmlMath">{ -32<sup>2380</sup>, -16<sup>20400</sup>, 0<sup>16320</sup>, 16<sup>23120</sup>, 32<sup>3060</sup> }</span> (same as the Gold functions)
* <math>\{ -64^6, -32^{2240}, -16^{20880}, 0^{15600}, 16^{23664}, 32^{2880}, 64^{10} \}</math> (type 1)
+
* <span class="htmlMath">{ -64<sup>6</sup>, -32<sup>2240</sup>, -16<sup>20880</sup>, 0<sup>15600</sup>, 16<sup>23664</sup>, 32<sup>2880</sup>, 64<sup>10</sup> }</span> (type 1)
* <math>\{ -64^{12}, -32^{2100}, -16^{21360}, 0^{14880}, 16^{24208}, 32^{2700}, 64^{20} \}</math> (type 2)
+
* <span class="htmlMath">{ -64<sup>12</sup>, -32<sup>2100</sup>, -16<sup>21360</sup>, 0<sup>14880</sup>, 16<sup>24208</sup>, 32<sup>2700</sup>, 64<sup>20</sup> }</span> (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 [[: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]] is available.
 
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]] is available.

Revision as of 18:26, 11 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:

  • { -322380, -1620400, 016320, 1623120, 323060 } (same as the Gold functions)
  • { -646, -322240, -1620880, 015600, 1623664, 322880, 6410 } (type 1)
  • { -6412, -322100, -1621360, 014880, 1624208, 322700, 6420 } (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
g130x192 + g160x160 + g117x144 + g230x136 + g228x132 + g162x130 + g25x129 + g79x96 + g204x80 + g83x72 + g159x68 + g234x66 + g36x65 + g67x48 + g151x40 + g17x36 + g81x34 + g52x33 + g9x24 + g116x20 + g102x18 + g97x17 + g74x12 + g48x10 + g144x9 + g58x6 + g146x5 + g123x3
g154x192 + g36x160 + g83x144 + g160x136 + g253x132 + g215x130 + g221x129 + g76x96 + g137x80 + g206x72 + g185x68 + g165x66 + g201x65 + g226x48 + g25x40 + g65x36 + g11x33 + g170x24 + g247x20 + g155x18 + gx17 + g146x12 + g204x10 + g121x9 + g202x6 + g246x5 + g170x3
g183x192 + g178x160 + g103x144 + g97x136 + g37x132 + g172x130 + g102x129 + g62x96 + g145x80 + g96x72 + g132x68 + g210x66 + g69x65 + g69x48 + g11x40 +x36 + g4x34 + g76x33 + g122x24 + g6x20 + g145x18 + g155x17 + g41x12 + g40x10 + g106x9 + g144x6 + g102x5 + g246x3
g22x192 + g167x160 + g178x144 + g84x136 + g219x132 + g248x130 + g130x129 + g221x96 + g84x80 + g123x72 + g140x68 + g26x66 + g108x65 + g50x48 + g15x40 + g211x36 + g116x34 + g19x33 + g228x24 + g176x20 + g42x18 + g80x17 + g180x12 + g203x10 + g104x9 + g72x6 + g151x5 + g247x3
g156x192 + g25x160 + g158x144 + g20x136 + g50x132 + g140x130 + g203x129 + g184x96 + g152x80 + g228x72 + g194x68 + g203x66 + g131x65 + g25x48 + g192x40 + g191x36 + g125x34 + g136x33 + g132x24 + g85x20 + g191x18 + g120x17 + g212x12 + g244x10 + g133x9 + g78x6 + g161x5 + gx3
g193x192 + g33x160 + g22x144 + g204x136 + g173x132 + g50x130 + g66x129 + g42x96 + g69x80 + g175x72 + g230x68 + g253x66 + g16x65 + g52x48 + g54x40 + g9x36 + g177x34 + g99x33 + g12x24 + g37x20 + g83x18 + g230x17 + g78x12 + gx10 + g64x9 + g225x6 + g68x5 + g204x3
g88x192 + g8x160 + g11x144 + g121x136 + g205x132 + g165x130 + g206x129 + g164x96 + g235x80 + g94x72 + g173x68 + g142x66 + g238x65 + g102x48 + g113x40 + g183x36 + g187x34 + g157x33 + g2x24 + g23x20 + g122x18 + g21x17 + g154x12 + g78x10 + g117x9 + g177x6 + g111x5 + g60x3
g212x192 + g198x160 + g175x144 + g80x136 + g196x132 + g167x130 + g2x129 + g65x96 + g243x80 + g91x72 + g171x68 + g211x66 + g182x65 + g247x48 + g86x40 + g89x36 + g87x34 + g83x33 + g138x24 + g45x20 + g149x18 + g100x17 + g188x12 + g17x10 + g243x9 + g237x6 + g112x5 + g137x3
g117x192 + g61x160 + g230x144 + g105x136 + g191x132 + g113x130 + g245x129 + g139x96 + g166x80 + g210x72 + g221x68 + g138x66 + g146x65 + g120x48 + g124x40 + g252x36 + g182x34 + g5x33 + g8x24 + g136x20 + g235x18 + g61x17 + g45x12 + g149x10 + g158x9 + g13x6 + g169x5 + g121x3
g34x192 + g57x160 + g187x144 + g36x136 + g137x132 + g63x130 + g98x129 + g236x96 + g161x80 + g66x72 + g191x68 + g117x66 + g241x65 + g7x48 + g9x40 + g153x36 + g118x34 + g154x33 + g194x24 + g157x20 + g14x18 + g116x17 + g119x12 + g113x10 + g13x9 + g138x6 + g143x5 + g35x3
g140x192 + g233x160 + g150x144 + g146x136 + g99x132 + g249x130 + g211x129 + g66x96 + g37x80 + g35x72 + g199x68 + g170x66 + g2x65 + g217x48 + g2x40 + g192x36 + g32x34 + g229x33 + g241x24 + g200x20 + g63x18 + g17x17 + g251x12 + g44x10 + g106x9 + g25x6 + g174x5 + g127x3
g237x192 + g133x160 + g204x144 + g169x136 + g30x132 + g127x130 + g41x129 + g12x96 + g198x80 + g151x72 + g252x68 + g29x66 + g144x65 + g120x48 + g72x40 + g123x36 + g170x34 + g159x33 + g77x24 + g227x20 + g161x18 + g231x17 + g159x12 + g253x10 + g56x9 + g35x6 + g251x5 + g99x3