Difference between revisions of "Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8"

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Line 346: Line 346:
 
<td rowspan="23"><math>8</math></td>
 
<td rowspan="23"><math>8</math></td>
 
<td>1.1</td>
 
<td>1.1</td>
<td><math>
+
<td>
x^{3}
+
<span class="htmlMath">x<sup>3</sup></span>
</math></td>
+
</td>
 
<td>11818</td>
 
<td>11818</td>
 
<td>420</td>
 
<td>420</td>
Line 356: Line 356:
 
<tr>
 
<tr>
 
<td>1.2</td>
 
<td>1.2</td>
<td><math>
+
<td>
x^{9}
+
<span class="htmlMath">x<sup>9</sup></span>
</math></td>
+
</td>
 
<td>12370</td>
 
<td>12370</td>
 
<td>420</td>
 
<td>420</td>
Line 366: Line 366:
 
<tr>
 
<tr>
 
<td>1.3</td>
 
<td>1.3</td>
<td><math>
+
<td>
x^{3}+{\rm Tr}(x^{9})
+
<span class="htmlMath">x<sup>3</sup>+Tr(x<sup>9</sup>)</span>
</math></td>
+
</td>
 
<td>13800</td>
 
<td>13800</td>
 
<td>432</td>
 
<td>432</td>
Line 376: Line 376:
 
<tr>
 
<tr>
 
<td>1.4</td>
 
<td>1.4</td>
<td><math>
+
<td>
x^{9}+{\rm Tr}(x^{3})
+
<span class="htmlMath">x<sup>9</sup>+Tr(x<sup>3</sup>)</span>
</math></td>
+
</td>
 
<td>13804</td>
 
<td>13804</td>
 
<td>434</td>
 
<td>434</td>
Line 386: Line 386:
 
<tr>
 
<tr>
 
<td>1.5</td>
 
<td>1.5</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+u<sup>245</sup>x<sup>33</sup>+u<sup>183</sup>x<sup>66</sup>+u<sup>21</sup>x<sup>144</sup></span></td>
x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}
 
</math></td>
 
 
<td>13842</td>
 
<td>13842</td>
 
<td>436</td>
 
<td>436</td>
Line 396: Line 394:
 
<tr>
 
<tr>
 
<td>1.6</td>
 
<td>1.6</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup> + u<sup>65</sup>x<sup>18</sup>+u<sup>120</sup>x<sup>66</sup>+u<sup>135</sup>x<sup>144</sup></span></td>
x^{3} + u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}
 
</math></td>
 
 
<td>13848</td>
 
<td>13848</td>
 
<td>438</td>
 
<td>438</td>
Line 406: Line 402:
 
<tr>
 
<tr>
 
<td>1.7</td>
 
<td>1.7</td>
<td><math>
+
<td><span class="htmlMath">u<sup>188</sup>x<sup>192</sup> + u<sup>129</sup>x<sup>144</sup> + u<sup>172</sup>x<sup>132</sup> + u<sup>138</sup>x<sup>129</sup> + u<sup>74</sup>x<sup>96</sup> + u<sup>244</sup>x<sup>72</sup> + u<sup>22</sup>x<sup>66</sup> + u<sup>178</sup>x<sup>48</sup> + u<sup>150</sup>x<sup>36</sup> + u<sup>146</sup>x<sup>33</sup> + u<sup>6</sup>x<sup>24</sup> + u<sup>60</sup>x<sup>18</sup> + u<sup>80</sup>x<sup>12</sup> + u<sup>140</sup>x<sup>9</sup> + u<sup>221</sup>x<sup>6</sup> + u<sup>19</sup>x<sup>3</sup></span></td>
u^{188}x^{192} + </math> <math>u^{129}x^{144} + </math> <math>u^{172}x^{132} + </math> <math> u^{138}x^{129} + </math> <math>u^{74}x^{96} + </math> <math>u^{244}x^{72} + </math> <math>u^{22}x^{66} + </math> <math> u^{178}x^{48} + </math> <math>u^{150}x^{36} + </math> <math>u^{146}x^{33} + </math> <math>u^{6}x^{24} + </math> <math> u^{60}x^{18} + </math> <math>u^{80}x^{12} + </math> <math>u^{140}x^{9} + </math> <math>u^{221}x^{6} + </math> <math>u^{19}x^{3}
 
</math></td>
 
 
<td>14034</td>
 
<td>14034</td>
 
<td>438</td>
 
<td>438</td>
Line 416: Line 410:
 
<tr>
 
<tr>
 
<td>1.8</td>
 
<td>1.8</td>
<td><math>
+
<td><span class="htmlMath">u<sup>37</sup>x<sup>192</sup> + u<sup>110</sup>x<sup>144</sup> + u<sup>40</sup>x<sup>132</sup> + u<sup>53</sup>x<sup>129</sup> + u<sup>239</sup>x<sup>96</sup> + u<sup>235</sup>x<sup>72</sup> + u<sup>126</sup>x<sup>66</sup> + u<sup>215</sup>x<sup>48</sup> + u<sup>96</sup>x<sup>36</sup> + u<sup>29</sup>x<sup>33</sup> + u<sup>19</sup>x<sup>24</sup> + u<sup>14</sup>x<sup>18</sup> + u<sup>139</sup>x<sup>12</sup> + u<sup>230</sup>x<sup>9</sup> + u<sup>234</sup>x<sup>6</sup> + u<sup>228</sup>x<sup>3</sup></span></td>
u^{37}x^{192} + </math> <math>u^{110}x^{144} + </math> <math>u^{40}x^{132} + </math> <math>u^{53}x^{129}  + </math> <math>u^{239}x^{96} + </math> <math>u^{235}x^{72} + </math> <math>u^{126}x^{66} + </math> <math>u^{215}x^{48} + </math> <math> u^{96}x^{36} + </math> <math>u^{29}x^{33} + </math> <math>u^{19}x^{24} + </math> <math>u^{14}x^{18} + </math> <math> u^{139}x^{12} + </math> <math>u^{230}x^{9} + </math> <math>u^{234}x^{6} + </math> <math>u^{228}x^{3}
 
</math></td>
 
 
<td>14032</td>
 
<td>14032</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.9</td>
 
<td>1.9</td>
<td><math>
+
<td><span class="htmlMath">u<sup>242</sup>x<sup>192</sup> + u<sup>100</sup>x<sup>144</sup> + u<sup>66</sup>x<sup>132</sup> + u<sup>230</sup>x<sup>129</sup> + u<sup>202</sup>x<sup>96</sup> + u<sup>156</sup>x<sup>72</sup> + u<sup>254</sup>x<sup>66</sup> + u<sup>18</sup>x<sup>48</sup> + u<sup>44</sup>x<sup>36</sup> + u<sup>95</sup>x<sup>33</sup> + u<sup>100</sup>x<sup>24</sup> + u<sup>245</sup>x<sup>18</sup> + u<sup>174</sup>x<sup>12</sup> + u<sup>175</sup>x<sup>9</sup> + u<sup>247</sup>x<sup>6</sup> + u<sup>166</sup>x<sup>3</sup></span></td>
u^{242}x^{192} + </math> <math>u^{100}x^{144} + </math> <math>u^{66}x^{132} + </math> <math>u^{230}x^{129} + </math> <math> u^{202}x^{96} + </math> <math>u^{156}x^{72} + </math> <math>u^{254}x^{66} + </math> <math>u^{18}x^{48} + </math> <math> u^{44}x^{36} + </math> <math>u^{95}x^{33} + </math> <math>u^{100}x^{24} + </math> <math>u^{245}x^{18} + </math> <math> u^{174}x^{12} + </math> <math>u^{175}x^{9} + </math> <math>u^{247}x^{6} + </math> <math>u^{166}x^{3}
 
</math></td>
 
 
<td>14036</td>
 
<td>14036</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.10</td>
 
<td>1.10</td>
<td><math>
+
<td><span class="htmlMath">u<sup>100</sup>x<sup>192</sup> + u<sup>83</sup>x<sup>144</sup> + u<sup>153</sup>x<sup>132</sup> + u<sup>65</sup>x<sup>129</sup> + u<sup>174</sup>x<sup>96</sup> + u<sup>136</sup>x<sup>72</sup> + u<sup>46</sup>x<sup>66</sup>+ u<sup>55</sup>x<sup>48</sup>+ u<sup>224</sup>x<sup>36</sup>+ u<sup>180</sup>x<sup>33</sup>+ u<sup>179</sup>x<sup>24</sup>+u<sup>226</sup>x<sup>18</sup>+ u<sup>54</sup>x<sup>12</sup>+ u<sup>168</sup>x<sup>9</sup>+ u<sup>89</sup>x<sup>6</sup>+ u<sup>56</sup>x<sup>3</sup></span></td>
u^{100}x^{192} + </math> <math> u^{83}x^{144} + </math> <math> u^{153}x^{132} + </math> <math> u^{65}x^{129} + </math> <math> u^{174}x^{96} + </math> <math> u^{136}x^{72} + </math> <math>
 
u^{46}x^{66}+ u^{55}x^{48}+ u^{224}x^{36}+ u^{180}x^{33}+ u^{179}x^{24}+u^{226}x^{18}+ u^{54}x^{12}+ u^{168}x^{9}+ u^{89}x^{6}+ u^{56}x^{3}
 
</math></td>
 
 
<td>14036</td>
 
<td>14036</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.11</td>
 
<td>1.11</td>
<td><math>
+
<td><span class="htmlMath">u<sup>77</sup>x<sup>192</sup> + u<sup>133</sup>x<sup>144</sup> + u<sup>47</sup>x<sup>132</sup> + u<sup>229</sup>x<sup>129</sup> + u<sup>23</sup>x<sup>96</sup> + u<sup>242</sup>x<sup>72</sup> + u<sup>242</sup>x<sup>66</sup> + u<sup>245</sup>x<sup>48</sup> + u<sup>212</sup>x<sup>36</sup> + u<sup>231</sup>x<sup>33</sup> + u<sup>174</sup>x<sup>24</sup> + u<sup>216</sup>x<sup>18</sup> + u<sup>96</sup>x<sup>12</sup> + u<sup>253</sup>x<sup>9</sup> + u<sup>154</sup>x<sup>6</sup> + u<sup>71</sup>x<sup>3</sup></span></td>
u^{77}x^{192} + </math> <math> u^{133}x^{144} + </math> <math> u^{47}x^{132} + </math> <math> u^{229}x^{129} + </math> <math> u^{23}x^{96} + </math> <math> u^{242}x^{72} + </math> <math> u^{242}x^{66} + </math> <math> u^{245}x^{48} + </math> <math> u^{212}x^{36} + </math> <math> u^{231}x^{33} + </math> <math> u^{174}x^{24} + </math> <math> u^{216}x^{18} + </math> <math> u^{96}x^{12} + </math> <math> u^{253}x^{9} + </math> <math> u^{154}x^{6} + </math> <math> u^{71}x^{3}
 
</math></td>
 
 
<td>14032</td>
 
<td>14032</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.12</td>
 
<td>1.12</td>
<td><math>
+
<td><span class="htmlMath">u<sup>220</sup>x<sup>192</sup> + u<sup>94</sup>x<sup>144</sup> + u<sup>70</sup>x<sup>132</sup> + u<sup>159</sup>x<sup>129</sup> + u<sup>145</sup>x<sup>96</sup> + u<sup>160</sup>x<sup>72</sup> + u<sup>74</sup>x<sup>66</sup> + u<sup>184</sup>x<sup>48</sup> + u<sup>119</sup>x<sup>36</sup> + u<sup>106</sup>x<sup>33</sup> + u<sup>253</sup>x<sup>24</sup> + wx<sup>18</sup> + u<sup>90</sup>x<sup>12</sup> + u<sup>169</sup>x<sup>9</sup> + u<sup>118</sup>x<sup>6</sup> + u<sup>187</sup>x<sup>3</sup></span></td>
u^{220}x^{192} + </math> <math> u^{94}x^{144} + </math> <math> u^{70}x^{132} + </math> <math> u^{159}x^{129} + </math> <math> u^{145}x^{96} + </math> <math>u^{160}x^{72} + </math> <math> u^{74}x^{66} + </math> <math> u^{184}x^{48} + </math> <math> u^{119}x^{36} + </math> <math> u^{106}x^{33} + </math> <math>u^{253}x^{24} + </math> <math> wx^{18} + </math> <math> u^{90}x^{12} + </math> <math> u^{169}x^{9} + </math> <math> u^{118}x^{6} + </math> <math> u^{187}x^{3}
 
</math></td>
 
 
<td>14034</td>
 
<td>14034</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.13</td>
 
<td>1.13</td>
<td><math>
+
<td><span class="htmlMath">u<sup>98</sup>x<sup>192</sup> + u<sup>225</sup>x<sup>144</sup> + u<sup>111</sup>x<sup>132</sup> + u<sup>238</sup>x<sup>129</sup> + u<sup>182</sup>x<sup>96</sup> + u<sup>125</sup>x<sup>72</sup> + u<sup>196</sup>x<sup>66</sup> + u<sup>219</sup>x<sup>48</sup> + u<sup>189</sup>x<sup>36</sup> + u<sup>199</sup>x<sup>33</sup> + u<sup>181</sup>x<sup>24</sup> + u<sup>110</sup>x<sup>18</sup> + u<sup>19</sup>x<sup>12</sup> + u<sup>175</sup>x<sup>9</sup> + u<sup>133</sup>x<sup>6</sup> + u<sup>47</sup>x<sup>3</sup></span></td>
u^{98}x^{192} + </math> <math> u^{225}x^{144} + </math> <math> u^{111}x^{132} + </math> <math> u^{238}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{125}x^{72} + </math> <math> u^{196}x^{66} + </math> <math> u^{219}x^{48} + </math> <math> u^{189}x^{36} + </math> <math> u^{199}x^{33} + </math> <math> u^{181}x^{24} + </math> <math> u^{110}x^{18} + </math> <math> u^{19}x^{12} + </math> <math> u^{175}x^{9} + </math> <math> u^{133}x^{6} + </math> <math> u^{47}x^{3}
 
</math></td>
 
 
<td>14030</td>
 
<td>14030</td>
 
<td>438</td>
 
<td>438</td>
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<tr>
 
<tr>
 
<td>1.14</td>
 
<td>1.14</td>
<td><math>
+
<td><span class="htmlMath">u<sup>236</sup>x<sup>192</sup> + u<sup>212</sup>x<sup>160</sup> + u<sup>153</sup>x<sup>144</sup> + u<sup>185</sup>x<sup>136</sup> + u<sup>3</sup>x<sup>132</sup> + u<sup>89</sup>x<sup>130</sup> + u<sup>189</sup>x<sup>129</sup> + u<sup>182</sup>x<sup>96</sup> + u<sup>105</sup>x<sup>80</sup> + u<sup>232</sup>x<sup>72</sup> + u<sup>219</sup>x<sup>68</sup> + u<sup>145</sup>x<sup>66</sup> + u<sup>171</sup>x<sup>65</sup> + u<sup>107</sup>x<sup>48</sup> + u<sup>179</sup>x<sup>40</sup> + u<sup>227</sup>x<sup>36</sup> + u<sup>236</sup>x<sup>34</sup> + u<sup>189</sup>x<sup>33</sup> + u<sup>162</sup>x<sup>24</sup> + u<sup>216</sup>x<sup>20</sup> + u<sup>162</sup>x<sup>18</sup> + u<sup>117</sup>x<sup>17</sup> + u<sup>56</sup>x<sup>12</sup> + u<sup>107</sup>x<sup>10</sup> + u<sup>236</sup>x<sup>9</sup> + u<sup>253</sup>x<sup>6</sup> + u<sup>180</sup>x<sup>5</sup> + u<sup>18</sup>x<sup>3</sup></span></td>
u^{236}x^{192} + </math> <math> u^{212}x^{160} + </math> <math> u^{153}x^{144} + </math> <math> u^{185}x^{136} + </math> <math> u^{3}x^{132} + </math> <math>u^{89}x^{130} + </math> <math> u^{189}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{105}x^{80} + </math> <math> u^{232}x^{72} + </math> <math>u^{219}x^{68} + </math> <math> u^{145}x^{66} + </math> <math> u^{171}x^{65} + </math> <math> u^{107}x^{48} + </math> <math> u^{179}x^{40} + </math> <math> u^{227}x^{36} + </math> <math> u^{236}x^{34} + </math> <math> u^{189}x^{33} + </math> <math> u^{162}x^{24} + </math> <math> u^{216}x^{20} + </math> <math>u^{162}x^{18} + </math> <math> u^{117}x^{17} + </math> <math> u^{56}x^{12} + </math> <math> u^{107}x^{10} + </math> <math> u^{236}x^{9} + </math> <math>u^{253}x^{6} + </math> <math> u^{180}x^{5} + </math> <math> u^{18}x^{3}
 
</math></td>
 
 
<td>14046</td>
 
<td>14046</td>
 
<td>454</td>
 
<td>454</td>
Line 487: Line 466:
 
<tr>
 
<tr>
 
<td>1.15</td>
 
<td>1.15</td>
<td><math>
+
<td><span class="htmlMath">u<sup>27</sup>x<sup>192</sup> + u<sup>167</sup>x<sup>144</sup> + u<sup>26</sup>x<sup>132</sup> + u<sup>231</sup>x<sup>129</sup> + u<sup>139</sup>x<sup>96</sup> + u<sup>30</sup>x<sup>72</sup> + u<sup>139</sup>x<sup>66</sup> + u<sup>203</sup>x<sup>48</sup> + u<sup>36</sup>x<sup>36</sup> + u<sup>210</sup>x<sup>33</sup> + u<sup>195</sup>x<sup>24</sup> + u<sup>12</sup>x<sup>18</sup> + u<sup>43</sup>x<sup>12</sup> + u<sup>97</sup>x<sup>9</sup> + u<sup>61</sup>x<sup>6</sup> + u<sup>39</sup>x<sup>3</sup></span></td>
u^{27}x^{192} + </math> <math> u^{167}x^{144} + </math> <math> u^{26}x^{132} + </math> <math>u^{231}x^{129} + </math> <math> u^{139}x^{96} + </math> <math>u^{30}x^{72} + </math> <math> u^{139}x^{66} + </math> <math> u^{203}x^{48} + </math> <math> u^{36}x^{36} + </math> <math> u^{210}x^{33} + </math> <math>u^{195}x^{24} + </math> <math> u^{12}x^{18} + </math> <math> u^{43}x^{12} + </math> <math> u^{97}x^{9} + </math> <math> u^{61}x^{6} + </math> <math>u^{39}x^{3}
 
</math></td>
 
 
<td>14036</td>
 
<td>14036</td>
 
<td>454</td>
 
<td>454</td>
Line 497: Line 474:
 
<tr>
 
<tr>
 
<td>1.16</td>
 
<td>1.16</td>
<td><math>
+
<td><span class="htmlMath">u<sup>6</sup>x<sup>192</sup> + u<sup>85</sup>x<sup>144</sup> + u<sup>251</sup>x<sup>132</sup> + u<sup>215</sup>x<sup>129</sup> + u<sup>229</sup>x<sup>96</sup> + u<sup>195</sup>x<sup>72</sup> + u<sup>152</sup>x<sup>66</sup> + u<sup>173</sup>x<sup>48</sup> + u<sup>209</sup>x<sup>36</sup> + u<sup>165</sup>x<sup>33</sup> + u<sup>213</sup>x<sup>24</sup> + u<sup>214</sup>x<sup>18</sup> + u<sup>158</sup>x<sup>12</sup> + u<sup>146</sup>x<sup>9</sup> + x<sup>6</sup> + u<sup>50</sup>x<sup>3</sup></span></td>
u^{6}x^{192} + </math> <math> u^{85}x^{144} + </math> <math> u^{251}x^{132} + </math> <math> u^{215}x^{129} + </math> <math> u^{229}x^{96} + </math> <math> u^{195}x^{72} + </math> <math> u^{152}x^{66} + </math> <math> u^{173}x^{48} + </math> <math> u^{209}x^{36} + </math> <math> u^{165}x^{33} + </math> <math> u^{213}x^{24} + </math> <math> u^{214}x^{18} + </math> <math> u^{158}x^{12} + </math> <math> u^{146}x^{9} + </math> <math> x^{6} + </math> <math> u^{50}x^{3}
 
</math></td>
 
 
<td>14032</td>
 
<td>14032</td>
 
<td>438</td>
 
<td>438</td>
Line 507: Line 482:
 
<tr>
 
<tr>
 
<td>1.17</td>
 
<td>1.17</td>
<td><math>
+
<td><span class="htmlMath">u<sup>164</sup>x<sup>192</sup> + u<sup>224</sup>x<sup>144</sup> + u<sup>59</sup>x<sup>132</sup> + u<sup>124</sup>x<sup>129</sup> + u<sup>207</sup>x<sup>96</sup> + u<sup>211</sup>x<sup>72</sup> + u<sup>5</sup>x<sup>66</sup> + u<sup>26</sup>x<sup>48</sup> + u<sup>20</sup>x<sup>36</sup> + u<sup>101</sup>x<sup>33</sup> + u<sup>175</sup>x<sup>24</sup> + u<sup>241</sup>x<sup>18</sup> + x<sup>12</sup> + u<sup>15</sup>x<sup>9</sup> + u<sup>217</sup>x<sup>6</sup> + u<sup>212</sup>x<sup>3</sup></span></td>
u^{164}x^{192} + </math> <math> u^{224}x^{144} + </math> <math> u^{59}x^{132} + </math> <math> u^{124}x^{129} + </math> <math> u^{207}x^{96} + </math> <math> u^{211}x^{72} + </math> <math> u^{5}x^{66} + </math> <math> u^{26}x^{48} + </math> <math> u^{20}x^{36} + </math> <math> u^{101}x^{33} + </math> <math> u^{175}x^{24} + </math> <math> u^{241}x^{18} + </math> <math> x^{12} + </math> <math> u^{15}x^{9} + </math> <math> u^{217}x^{6} + </math> <math> u^{212}x^{3}
 
</math></td>
 
 
<td>14028</td>
 
<td>14028</td>
 
<td>438</td>
 
<td>438</td>
Line 517: Line 490:
 
<tr>
 
<tr>
 
<td>2.1</td>
 
<td>2.1</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+ x<sup>17</sup>+u<sup>16</sup>(x<sup>18</sup>+x<sup>33</sup>)+u<sup>15</sup>x<sup>48</sup></span></td>
x^{3}+ x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}
 
</math></td>
 
 
<td>13200</td>
 
<td>13200</td>
 
<td>414</td>
 
<td>414</td>
Line 527: Line 498:
 
<tr>
 
<tr>
 
<td>3.1</td>
 
<td>3.1</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+ u<sup>24</sup>x<sup>6</sup>+u<sup>182</sup>x<sup>132</sup>+u<sup>67</sup>x<sup>192</sup></span></td>
x^{3}+ u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}
 
</math></td>
 
 
<td>14024</td>
 
<td>14024</td>
 
<td>438</td>
 
<td>438</td>
Line 537: Line 506:
 
<tr>
 
<tr>
 
<td>4.1</td>
 
<td>4.1</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+x<sup>6</sup>+x<sup>68</sup>+x<sup>80</sup>+x<sup>132</sup>+x<sup>160</sup></span></td>
x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}
 
</math></td>
 
 
<td>14040</td>
 
<td>14040</td>
 
<td>454</td>
 
<td>454</td>
Line 547: Line 514:
 
<tr>
 
<tr>
 
<td>5.1</td>
 
<td>5.1</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+x<sup>5</sup>+x<sup>18</sup>+x<sup>40</sup>+x<sup>66</sup></span></td>
x^{3}+x^{5}+x^{18}+x^{40}+x^{66}
 
</math></td>
 
 
<td>14044</td>
 
<td>14044</td>
 
<td>446</td>
 
<td>446</td>
Line 557: Line 522:
 
<tr>
 
<tr>
 
<td>6.1</td>
 
<td>6.1</td>
<td><math>
+
<td><span class="htmlMath">x<sup>3</sup>+x<sup>12</sup>+x<sup>40</sup>+x<sup>66</sup>+x<sup>130</sup></span></td>
x^{3}+x^{12}+x^{40}+x^{66}+x^{130}
 
</math></td>
 
 
<td>14046</td>
 
<td>14046</td>
 
<td>438</td>
 
<td>438</td>
Line 567: Line 530:
 
<tr>
 
<tr>
 
<td>7.1</td>
 
<td>7.1</td>
<td><math>
+
<td>
x^{57}
+
<span class="htmlMath">x<sup>57</sup></span>
</math></td>
+
</td>
 
<td>15358</td>
 
<td>15358</td>
 
<td>960</td>
 
<td>960</td>

Revision as of 19:52, 11 July 2020

Known switching classes of APN functions over , , and .

Also available is Magma code generating representatives from the switching classes.

Γ-rank Δ-rank Aut(dev(GF))/22n Aut(dev(GF))/22n
1.1 x3 330 42 4960 4960
1.2 x5 330 42 4960 158720
2.1 x-1 496 232 310 310
1.1 x3 1102 94 24192 48384
1.2 x3 + u11x6 + ux9 1146 94 4032 8064
2.1 ux5 + x9 + u4x17 + ux18 + u4x20 + ux24 + u4x34 + ux40 1158 96 320 320
2.2 u7x3 + x5 + u3x9 + u4x10 + x17 + u6x18 1166 94 448 896
2.3 x3 + ux24 + x10 1166 96 896 896
2.4 x3 + u17(x17 + x18 + x20 + x24) 1168 96 64 64
2.5 x3 + u11x5 + u13x9 + x17 + u11x33 + x48 1170 96 320 320
2.6 u25x5 + x9 + u38x12 + u25x18 + u25x36 1170 96 64 64
2.7 u40x5 + u10x6 + u62x20 + u35x33 + u15x34 + u29x48 1170 96 64 64
2.8 u34x6 + u52x9 + u48x12 + u6x20 + u9x33 + u23x34 + u25x40 1170 96 64 64
2.9 x9 + u4(x10 + x18) + u9(x12 + x20 + x40) 1172 96 64 64
2.10 u52x3 + u47x5 + ux6 + u9x9 + u44x12 + u47x33 + u10x34 + u33x40 1172 96 64 64
2.11 u(x6 + x10 + x24 + x33) + x9 + u4x17 1174 96 64 64
2.12 x3 + u17(x17 + x18 + x20 + x24) + u14((u52x3 + u6x5 + u19x7 + u28x11 + u2x13)+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)2 + (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)4+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)8+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)16+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)32+ (u2x)9 +(u2x)19 +(u2x)36 + x21+x42 1300 152 8 8
1.1

x3

3610 198 113792 113792
1.2

x3 + Tr(x9)

4026 212 896 896
2.1

x34 + x18 + x5

4034 210 896 896
2.2

x3 + x17 + x33 + x34

4040 212 896 896
3.1

x5

3708 198 113792 113792
4.1

x9

3610 198 113792 14565376
5.1

x13

4270 338 889 889
6.1

x57

4704 436 889 889
7.1

x-1

8128 4928 1778 1778
8.1

x65 + x10 + x3

4038 212 896 896
9.1

x3 + x9 + x18 + x66

4044 212 896 896
10.1

x3 + x12 + x17 + x33

4048 210 896 896
10.2

x3 + x17 + x20 + x34 + x66

4040 210 896 896
11.1

x3 + x20 + x34 + x66

4048 210 896 896
12.1

x3 + x12 + x40 + x72

4048 210 896 896
13.1

x3 + x5 + x10 + x33 + x34

4040 212 896 896
14.1

x3 + x6 + x34 + x40 + x72

4048 212 896 896
14.2

x3 + x5 + x6 + x12 + x33 + x34

4050 210 896 896
14.3

u2x96 + u78x80 + u121x72 + u49x68 + u77x66 + u29x65 + u119x48 + u117x40 + u28x36 + u107x34 +u62x33 +u125x24 +u76x20 +u84x18 +u110x17 +u49x12 +u102x10 +u69x9 + u14x6 + x5 + x3

4046 212 128 128
1.1

x3

11818 420
1.2

x9

12370 420
1.3

x3+Tr(x9)

13800 432
1.4

x9+Tr(x3)

13804 434
1.5 x3+u245x33+u183x66+u21x144 13842 436
1.6 x3 + u65x18+u120x66+u135x144 13848 438
1.7 u188x192 + u129x144 + u172x132 + u138x129 + u74x96 + u244x72 + u22x66 + u178x48 + u150x36 + u146x33 + u6x24 + u60x18 + u80x12 + u140x9 + u221x6 + u19x3 14034 438
1.8 u37x192 + u110x144 + u40x132 + u53x129 + u239x96 + u235x72 + u126x66 + u215x48 + u96x36 + u29x33 + u19x24 + u14x18 + u139x12 + u230x9 + u234x6 + u228x3 14032 438
1.9 u242x192 + u100x144 + u66x132 + u230x129 + u202x96 + u156x72 + u254x66 + u18x48 + u44x36 + u95x33 + u100x24 + u245x18 + u174x12 + u175x9 + u247x6 + u166x3 14036 438
1.10 u100x192 + u83x144 + u153x132 + u65x129 + u174x96 + u136x72 + u46x66+ u55x48+ u224x36+ u180x33+ u179x24+u226x18+ u54x12+ u168x9+ u89x6+ u56x3 14036 438
1.11 u77x192 + u133x144 + u47x132 + u229x129 + u23x96 + u242x72 + u242x66 + u245x48 + u212x36 + u231x33 + u174x24 + u216x18 + u96x12 + u253x9 + u154x6 + u71x3 14032 438
1.12 u220x192 + u94x144 + u70x132 + u159x129 + u145x96 + u160x72 + u74x66 + u184x48 + u119x36 + u106x33 + u253x24 + wx18 + u90x12 + u169x9 + u118x6 + u187x3 14034 438
1.13 u98x192 + u225x144 + u111x132 + u238x129 + u182x96 + u125x72 + u196x66 + u219x48 + u189x36 + u199x33 + u181x24 + u110x18 + u19x12 + u175x9 + u133x6 + u47x3 14030 438
1.14 u236x192 + u212x160 + u153x144 + u185x136 + u3x132 + u89x130 + u189x129 + u182x96 + u105x80 + u232x72 + u219x68 + u145x66 + u171x65 + u107x48 + u179x40 + u227x36 + u236x34 + u189x33 + u162x24 + u216x20 + u162x18 + u117x17 + u56x12 + u107x10 + u236x9 + u253x6 + u180x5 + u18x3 14046 454
1.15 u27x192 + u167x144 + u26x132 + u231x129 + u139x96 + u30x72 + u139x66 + u203x48 + u36x36 + u210x33 + u195x24 + u12x18 + u43x12 + u97x9 + u61x6 + u39x3 14036 454
1.16 u6x192 + u85x144 + u251x132 + u215x129 + u229x96 + u195x72 + u152x66 + u173x48 + u209x36 + u165x33 + u213x24 + u214x18 + u158x12 + u146x9 + x6 + u50x3 14032 438
1.17 u164x192 + u224x144 + u59x132 + u124x129 + u207x96 + u211x72 + u5x66 + u26x48 + u20x36 + u101x33 + u175x24 + u241x18 + x12 + u15x9 + u217x6 + u212x3 14028 438
2.1 x3+ x17+u16(x18+x33)+u15x48 13200 414
3.1 x3+ u24x6+u182x132+u67x192 14024 438
4.1 x3+x6+x68+x80+x132+x160 14040 454
5.1 x3+x5+x18+x40+x66 14044 446
6.1 x3+x12+x40+x66+x130 14046 438
7.1

x57

15358 960