CCZ-inequivalent representatives from the known APN families for dimensions up to 11: Difference between revisions

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Line 12: Line 12:
<th>Γ-rank</th>
<th>Γ-rank</th>
<th>Δ-rank</th>
<th>Δ-rank</th>
<th>Multiplier group</th>
</tr>
</tr>


Line 22: Line 23:
<td>1102</td>
<td>1102</td>
<td>94</td>
<td>94</td>
<td>24192 = 2<sup>7</sup> * 3<sup>3</sup> * 7</td>
</tr>
</tr>


Line 32: Line 34:
<td>1146</td>
<td>1146</td>
<td>94</td>
<td>94</td>
<td>4032 = 2<sup>6</sup> * 3<sup>2</sup> * 7</td>
</tr>
</tr>


Line 41: Line 44:
<td>1166</td>
<td>1166</td>
<td>96</td>
<td>96</td>
<td>896 = 2<sup>7</sup> * 7</td>
</tr>
</tr>


Line 52: Line 56:
<td>3610</td>
<td>3610</td>
<td>198</td>
<td>198</td>
<td>113792 = 2<sup>7</sup> * 7 * 127 </td>
</tr>
</tr>


Line 62: Line 67:
<td>3708</td>
<td>3708</td>
<td>198</td>
<td>198</td>
<td>113792 = 2<sup>7</sup> * 7 * 127 </td>
</tr>
</tr>


Line 72: Line 78:
<td>3610</td>
<td>3610</td>
<td>198</td>
<td>198</td>
<td>113792 = 2<sup>7</sup> * 7 * 127 </td>
</tr>
</tr>


Line 82: Line 89:
<td>4270</td>
<td>4270</td>
<td>338</td>
<td>338</td>
<td>889 = 7 * 127</td>
</tr>
</tr>


Line 91: Line 99:
<td>4704</td>
<td>4704</td>
<td>436</td>
<td>436</td>
<td>889 = 7 * 127</td>
</tr>
</tr>


Line 101: Line 110:
<td>8128</td>
<td>8128</td>
<td>4928</td>
<td>4928</td>
<td>1778 = 2 * 7 * 127</td>
</tr>
</tr>


Line 112: Line 122:
<td>4026</td>
<td>4026</td>
<td>212</td>
<td>212</td>
<td>896 = 2<sup>7</sup> * 7</td>
</tr>
</tr>


Line 123: Line 134:
<td>11818</td>
<td>11818</td>
<td>420</td>
<td>420</td>
<td>522240 = 2<sup>11</sup> * 3 * 5 * 17</td>
</tr>
</tr>


Line 132: Line 144:
<td>12370</td>
<td>12370</td>
<td>420</td>
<td>420</td>
<td>522240 = 2<sup>11</sup> * 3 * 5 * 17</td>
</tr>
</tr>


Line 142: Line 155:
<td>15358</td>
<td>15358</td>
<td>960</td>
<td>960</td>
<td>2040 = 2<sup>3</sup> * 3 * 5 * 17</td>
</tr>
</tr>


Line 151: Line 165:
<td>13200</td>
<td>13200</td>
<td>414</td>
<td>414</td>
<td>46080 = 2<sup>10</sup> * 3<sup>2</sup> * 5</td>
</tr>
</tr>


Line 160: Line 175:
<td>13200</td>
<td>13200</td>
<td>432</td>
<td>432</td>
<td>6144 = 2<sup>11</sup> * 3</td>
</tr>
</tr>


Line 169: Line 185:
<td>13842</td>
<td>13842</td>
<td>436</td>
<td>436</td>
<td>3072 = 2<sup>10</sup> * 3</td>
</tr>
</tr>


Line 178: Line 195:
<td>13642</td>
<td>13642</td>
<td>436</td>
<td>436</td>
<td>46080 = 2<sup>10</sup> * 3<sup>2</sup> * 5</td>
</tr>
</tr>


Line 188: Line 206:
<td>38470</td>
<td>38470</td>
<td>872</td>
<td>872</td>
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 198: Line 217:
<td>41494</td>
<td>41494</td>
<td>872</td>
<td>872</td>
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 207: Line 227:
<td>38470</td>
<td>38470</td>
<td>872</td>
<td>872</td>
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 216: Line 237:
<td>58676</td>
<td>58676</td>
<td>3086</td>
<td>3086</td>
<td>4599 = 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 225: Line 247:
<td>61726</td>
<td>61726</td>
<td>3482</td>
<td>3482</td>
<td>4599 = 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 234: Line 257:
<td>60894</td>
<td>60894</td>
<td>3956</td>
<td>3956</td>
<td>4599 = 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 243: Line 267:
<td>130816</td>
<td>130816</td>
<td>93024</td>
<td>93024</td>
<td>9198 = 2 * 3<sup>2</sup> * 7 * 73</td>
</tr>
</tr>


Line 252: Line 277:
<td>47890</td>
<td>47890</td>
<td>920</td>
<td>920</td>
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td>
</tr>
</tr>


Line 261: Line 287:
<td>48428</td>
<td>48428</td>
<td>930</td>
<td>930</td>
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td>
</tr>
</tr>


Line 270: Line 297:
<td>48460</td>
<td>48460</td>
<td>944</td>
<td>944</td>
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td>
</tr>
</tr>


Line 279: Line 307:
<td>48596</td>
<td>48596</td>
<td>944</td>
<td>944</td>
<td>10752 = 2<sup>9</sup> * 3 * 7</td>
</tr>
</tr>


Line 289: Line 318:
<td>125042</td>
<td>125042</td>
<td></td>
<td></td>
<td>10475520 = 2<sup>11</sup> * 3 * 5 * 11 * 31</td>
</tr>
</tr>


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<td>136492</td>
<td>136492</td>
<td></td>
<td></td>
<td>10475520 = 2<sup>11</sup> * 3 * 5 * 11 * 31</td>
</tr>
</tr>


Line 307: Line 338:
<td>186416</td>
<td>186416</td>
<td></td>
<td></td>
<td>10230 = 2 * 3 * 5 * 11 * 31</td>
</tr>
</tr>


Line 316: Line 348:
<td>280604</td>
<td>280604</td>
<td></td>
<td></td>
<td>10230 = 2 * 3 * 5 * 11 * 31</td>
</tr>
</tr>


Line 325: Line 358:
<td>151216</td>
<td>151216</td>
<td></td>
<td></td>
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td>
</tr>
</tr>


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<td>153896</td>
<td>153896</td>
<td></td>
<td></td>
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td>
</tr>
</tr>


Line 343: Line 378:
<td>164034</td>
<td>164034</td>
<td></td>
<td></td>
<td>30720 = 2<sup>11</sup> * 3 * 5</td>
</tr>
</tr>


Line 352: Line 388:
<td>164098</td>
<td>164098</td>
<td></td>
<td></td>
<td>15360 = 2<sup>10</sup> * 3 * 5</td>
</tr>
</tr>


Line 361: Line 398:
<td>166068</td>
<td>166068</td>
<td></td>
<td></td>
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td>
</tr>
</tr>


Line 370: Line 408:
<td>166168</td>
<td>166168</td>
<td></td>
<td></td>
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td>
</tr>
</tr>


Line 378: Line 417:
<td><span class="htmlMath">Gold</span></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 387: Line 427:
<td><span class="htmlMath">Gold</span></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 396: Line 437:
<td><span class="htmlMath">Gold</span></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 405: Line 447:
<td><span class="htmlMath">Gold</span></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
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<td><span class="htmlMath">Gold</span></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 423: Line 467:
<td><span class="htmlMath">Kasami</span></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 432: Line 477:
<td><span class="htmlMath">Kasami</span></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 440: Line 486:
<td><span class="htmlMath">Kasami</span></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 448: Line 495:
<td><span class="htmlMath">Kasami</span></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 456: Line 504:
<td><span class="htmlMath">Welch</span></td>
<td><span class="htmlMath">Welch</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 464: Line 513:
<td><span class="htmlMath">Niho</span></td>
<td><span class="htmlMath">Niho</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 472: Line 522:
<td><span class="htmlMath">Inverse</span></td>
<td><span class="htmlMath">Inverse</span></td>
<td>Inverse</td>
<td>Inverse</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
Line 480: Line 531:
<td><span class="htmlMath">C4</span></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>

Revision as of 21:03, 6 January 2020

CCZ-inequivalent APN Functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] from the Known APN Classes for [math]\displaystyle{ 6\leqslant n \leqslant 11 }[/math]

The function families are indexed according to the table of Known infinite families of APN power functions over GF(2^n) in the case of monomials, and according to the table of Known infinite families of quadratic APN polynomials over GF(2^n) in the case of polynomial families.

Dimension N○ Functions Equivalent to Walsh spectrum Γ-rank Δ-rank Multiplier group
6 6.1 x3 Gold Gold 1102 94 24192 = 27 * 33 * 7
6.2 x24+ax17+a8x10+ax9+x3 C3 Gold 1146 94 4032 = 26 * 32 * 7
6.3 ax3+x17+a4x24 C7-C9 Gold 1166 96 896 = 27 * 7
7 7.1 x3 Gold Gold 3610 198 113792 = 27 * 7 * 127
7.2 x5 Gold Gold 3708 198 113792 = 27 * 7 * 127
7.3 x9 Gold Gold 3610 198 113792 = 27 * 7 * 127
7.4 x13 Kasami Gold 4270 338 889 = 7 * 127
7.5 x57 Kasami Gold 4704 436 889 = 7 * 127
7.6 x63 Inverse Inverse 8128 4928 1778 = 2 * 7 * 127
7.7 x3+Tr7(x9) C4 Gold 4026 212 896 = 27 * 7
8 8.1 x3 Gold Gold 11818 420 522240 = 211 * 3 * 5 * 17
8.2 x9 Gold Gold 12370 420 522240 = 211 * 3 * 5 * 17
8.3 x57 Kasami Gold 15358 960 2040 = 23 * 3 * 5 * 17
8.4 x3+x17+p48x18+p3x33+px34+x48 C3 Gold 13200 414 46080 = 210 * 32 * 5
8.5 x3+Tr8(x9) C4 Gold 13200 432 6144 = 211 * 3
8.6 x3+a-1Tr8(a3x9) C4 Gold 13842 436 3072 = 210 * 3
8.7 a(x+x16)(ax+a16x16)+a17(ax+a16x16)12 C10 Gold 13642 436 46080 = 210 * 32 * 5
9 9.1 x3 Gold Gold 38470 872 2354688 = 29 * 32 * 7 * 73
9.2 x5 Gold Gold 41494 872 2354688 = 29 * 32 * 7 * 73
9.3 x17 Gold Gold 38470 872 2354688 = 29 * 32 * 7 * 73
9.4 x13 Kasami Gold 58676 3086 4599 = 32 * 7 * 73
9.5 x241 Kasami Gold 61726 3482 4599 = 32 * 7 * 73
9.6 x19 Welch Gold 60894 3956 4599 = 32 * 7 * 73
9.7 x255 Inverse Inverse 130816 93024 9198 = 2 * 32 * 7 * 73
9.8 x3+Tr9(x9) C4 Gold 47890 920 4608 = 29 * 32
9.9 x3+Tr39(x9+x18) C5 Gold 48428 930 4608 = 29 * 32
9.10 x3+Tr39(x18+x36) C6 Gold 48460 944 4608 = 29 * 32
9.11 x3+a246x10+a47x17+a181x66+a428x129 C11 Gold 48596 944 10752 = 29 * 3 * 7
10 10.1 x3 Gold Gold 125042 10475520 = 211 * 3 * 5 * 11 * 31
10.2 x9 Gold Gold 136492 10475520 = 211 * 3 * 5 * 11 * 31
10.3 x57 Kasami Gold 186416 10230 = 2 * 3 * 5 * 11 * 31
10.4 x339 Dobbertin Dobbertin 280604 10230 = 2 * 3 * 5 * 11 * 31
10.5 x6+x33+p31x192 C3 Gold 151216 476160 = 210 * 3 * 5 * 31
10.6 x33+x72+p31x258 C3 Gold 153896 476160 = 210 * 3 * 5 * 31
10.7 x3+Tr10(x9) C4 Gold 164034 30720 = 211 * 3 * 5
10.8 x3+a-1Tr10(a3x9) C4 Gold 164098 15360 = 210 * 3 * 5
10.9 x3 + p341x9 + p682x96 + x288 C12 Gold 166068 476160 = 210 * 3 * 5 * 31
10.10 x3 + p341x129 + p682x96 + x36 C12 Gold 166168 476160 = 210 * 3 * 5 * 31
11 11.1 x3 Gold Gold
11.2 x5 Gold Gold
11.3 x9 Gold Gold
11.4 x17 Gold Gold
11.5 x33 Gold Gold
11.6 x13 Kasami Gold
11.7 x57 Kasami Gold
11.8 x241 Kasami Gold
11.9 x993 Kasami Gold
11.10 x35 Welch Gold
11.11 x287 Niho Gold
11.12 x1023 Inverse Inverse
11.13 x3+Tr11(x9) C4 Gold
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