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

Revision as of 17:43, 22 January 2019

Known switching classes of APN functions over $\mathbb {F} _{2^{5}}$ , $\mathbb {F} _{2^{6}}$ , $\mathbb {F} _{2^{7}}$ and $\mathbb {F} _{2^{8}}$

$n$	$N^{\circ }$	$F(x)$
$5$	1.1	$x^{3}$
	1.2	$x^{5}$
	2.1	$x^{-1}$
$6$	1.1	$x^{3}$
	1.2	$x^{3}+u^{11}x^{6}+ux^{9}$
	2.1	$ux^{5}+x^{9}+u^{4}x^{17}+ux^{18}+u^{4}x^{20}+ux^{24}+u^{4}x^{34}+ux^{40}$
	2.2	$u^{7}x^{3}+x^{5}+u^{3}x^{9}+u^{4}x^{10}+x^{17}+u^{6}x^{18}$
	2.3	$x^{3}+ux^{24}+x^{10}$
	2.4	$x^{3}+u^{17}(x^{17}+x^{18}+x^{20}+x^{24})$
	2.5	$x^{3}+u^{11}x^{5}+u^{13}x^{9}+x^{17}+u^{11}x^{33}+x^{48}$
	2.6	$u^{25}x^{5}+x^{9}+u^{38}x^{12}+u^{25}x^{18}+u^{25}x^{36}$
	2.7	$u^{40}x^{5}+u^{10}x^{6}+u^{62}x^{20}+u^{35}x^{33}+u^{15}x^{34}+u^{29}x^{48}$
	2.8	$u^{34}x^{6}+u^{52}x^{9}+u^{48}x^{12}+u^{6}x^{20}+u^{9}x^{33}+u^{23}x^{34}+u^{25}x^{40}$
	2.9	$x^{9}+u^{4}(x^{10}+x^{18})+u^{9}(x^{12}+x^{20}+x^{40})$
	2.10	$u^{52}x^{3}+u^{47}x^{5}+ux^{6}+u^{9}x^{9}+u^{44}x^{12}+u^{47}x^{33}+u^{10}x^{34}+u^{33}x^{40}$
	2.11	$u(x^{6}+x^{10}+x^{24}+x^{33})+x^{9}+u^{4}x^{17}$
	2.12	$x^{3}+$ $u^{17}(x^{17}+$ $x^{18}+$ $x^{20}+$ $x^{24})+$ $u^{14}((u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{2}+$ $(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{4}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{8}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{16}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{32}+(u^{2}x)^{9}+(u^{2}x)^{19}+(u^{2}x)^{36}+$ $x^{21}+x^{42}$
$7$	1.1	$x^{3}$
	1.2	$x^{3}+{\rm {Tr}}(x^{9})$
	2.1	$x^{34}+x^{18}+x^{5}$
	2.2	$x^{3}+x^{17}+x^{33}+x^{34}$
	3.1	$x^{5}$
	4.1	$x^{9}$
	5.1	$x^{13}$
	6.1	$x^{57}$
	7.1	$x^{-1}$
	8.1	$x^{65}+x^{10}+x^{3}$
	9.1	$x^{3}+x^{9}+x^{18}+x^{66}$
	10.1	$x^{3}+x^{12}+x^{17}+x^{33}$
	10.2	$x^{3}+x^{17}+x^{20}+x^{34}+x^{66}$
	11.1	$x^{3}+x^{20}+x^{34}+x^{66}$
	12.1	$x^{3}+x^{12}+x^{40}+x^{72}$
	13.1	$x^{3}+x^{5}+x^{10}+x^{33}+x^{34}$
	14.1	$x^{3}+x^{6}+x^{34}+x^{40}+x^{72}$
	14.2	$x^{3}+x^{5}+x^{6}+x^{12}+x^{33}+x^{34}$
	14.3	$u^{2}x^{96}+$ $u^{78}x^{80}+$ $u^{121}x^{72}+$ $u^{49}x^{68}+$ $u^{77}x^{66}+$ $u^{29}x^{65}+$ $u^{119}x^{48}+$ $u^{117}x^{40}+$ $u^{28}x^{36}+$ $u^{107}x^{34}+u^{62}x^{33}+u^{125}x^{24}+u^{76}x^{20}+u^{84}x^{18}+u^{110}x^{17}+u^{49}x^{12}+u^{102}x^{10}+u^{69}x^{9}+$ $u^{14}x^{6}+$ $x^{5}+$ $x^{3}$
8	1.1	$x^{3}$
	1.2	$x^{9}$
	1.3	$x^{3}+{\rm {Tr}}(x^{9})$
	1.4	$x^{9}+{\rm {Tr}}(x^{3})$
	1.5	$x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}$
	1.6	$x^{3}+u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}$
	1.7	$u^{188}x^{192}+$ $u^{129}x^{144}+$ $u^{172}x^{132}+$ $u^{138}x^{129}+$ $u^{74}x^{96}+$ $u^{244}x^{72}+$ $u^{22}x^{66}+$ $u^{178}x^{48}+$ $u^{150}x^{36}+$ $u^{146}x^{33}+$ $u^{6}x^{24}+$ $u^{60}x^{18}+$ $u^{80}x^{12}+$ $u^{140}x^{9}+$ $u^{221}x^{6}+$ $u^{19}x^{3}$
	1.8	$u^{37}x^{192}+$ $u^{110}x^{144}+$ $u^{40}x^{132}+$ $u^{53}x^{129}+$ $u^{239}x^{96}+$ $u^{235}x^{72}+$ $u^{126}x^{66}+$ $u^{215}x^{48}+$ $u^{96}x^{36}+$ $u^{29}x^{33}+$ $u^{19}x^{24}+$ $u^{14}x^{18}+$ $u^{139}x^{12}+$ $u^{230}x^{9}+$ $u^{234}x^{6}+$ $u^{228}x^{3}$
	1.9	$u^{242}x^{192}+$ $u^{100}x^{144}+$ $u^{66}x^{132}+$ $u^{230}x^{129}+$ $u^{202}x^{96}+$ $u^{156}x^{72}+$ $u^{254}x^{66}+$ $u^{18}x^{48}+$ $u^{44}x^{36}+$ $u^{95}x^{33}+$ $u^{100}x^{24}+$ $u^{245}x^{18}+$ $u^{174}x^{12}+$ $u^{175}x^{9}+$ $u^{247}x^{6}+$ $u^{166}x^{3}$
	1.10	$u^{100}x^{192}+$ $u^{83}x^{144}+$ $u^{153}x^{132}+$ $u^{65}x^{129}+$ $u^{174}x^{96}+$ $u^{136}x^{72}+$ $u^{46}x^{66}+u^{55}x^{48}+u^{224}x^{36}+u^{180}x^{33}+u^{179}x^{24}+u^{226}x^{18}+u^{54}x^{12}+u^{168}x^{9}+u^{89}x^{6}+u^{56}x^{3}$
	1.11	$u^{77}x^{192}+$ $u^{133}x^{144}+$ $u^{47}x^{132}+$ $u^{229}x^{129}+$ $u^{23}x^{96}+$ $u^{242}x^{72}+$ $u^{242}x^{66}+$ $u^{245}x^{48}+$ $u^{212}x^{36}+$ $u^{231}x^{33}+$ $u^{174}x^{24}+$ $u^{216}x^{18}+$ $u^{96}x^{12}+$ $u^{253}x^{9}+$ $u^{154}x^{6}+$ $u^{71}x^{3}$
	1.12	$u^{220}x^{192}+$ $u^{94}x^{144}+$ $u^{70}x^{132}+$ $u^{159}x^{129}+$ $u^{145}x^{96}+$ $u^{160}x^{72}+$ $u^{74}x^{66}+$ $u^{184}x^{48}+$ $u^{119}x^{36}+$ $u^{106}x^{33}+$ $u^{253}x^{24}+$ $wx^{18}+$ $u^{90}x^{12}+$ $u^{169}x^{9}+$ $u^{118}x^{6}+$ $u^{187}x^{3}$
	1.13	$u^{98}x^{192}+$ $u^{225}x^{144}+$ $u^{111}x^{132}+$ $u^{238}x^{129}+$ $u^{182}x^{96}+$ $u^{125}x^{72}+$ $u^{196}x^{66}+$ $u^{219}x^{48}+$ $u^{189}x^{36}+$ $u^{199}x^{33}+$ $u^{181}x^{24}+$ $u^{110}x^{18}+$ $u^{19}x^{12}+$ $u^{175}x^{9}+$ $u^{133}x^{6}+$ $u^{47}x^{3}$
	1.14	$u^{236}x^{192}+$ $u^{212}x^{160}+$ $u^{153}x^{144}+$ $u^{185}x^{136}+$ $u^{3}x^{132}+$ $u^{89}x^{130}+$ $u^{189}x^{129}+$ $u^{182}x^{96}+$ $u^{105}x^{80}+$ $u^{232}x^{72}+$ $u^{219}x^{68}+$ $u^{145}x^{66}+$ $u^{171}x^{65}+$ $u^{107}x^{48}+$ $u^{179}x^{40}+$ $u^{227}x^{36}+$ $u^{236}x^{34}+$ $u^{189}x^{33}+$ $u^{162}x^{24}+$ $u^{216}x^{20}+$ $u^{162}x^{18}+$ $u^{117}x^{17}+$ $u^{56}x^{12}+$ $u^{107}x^{10}+$ $u^{236}x^{9}+$ $u^{253}x^{6}+$ $u^{180}x^{5}+$ $u^{18}x^{3}$
	1.15	$u^{27}x^{192}+$ $u^{167}x^{144}+$ $u^{26}x^{132}+$ $u^{231}x^{129}+$ $u^{139}x^{96}+$ $u^{30}x^{72}+$ $u^{139}x^{66}+$ $u^{203}x^{48}+$ $u^{36}x^{36}+$ $u^{210}x^{33}+$ $u^{195}x^{24}+$ $u^{12}x^{18}+$ $u^{43}x^{12}+$ $u^{97}x^{9}+$ $u^{61}x^{6}+$ $u^{39}x^{3}$
	1.16	$u^{6}x^{192}+$ $u^{85}x^{144}+$ $u^{251}x^{132}+$ $u^{215}x^{129}+$ $u^{229}x^{96}+$ $u^{195}x^{72}+$ $u^{152}x^{66}+$ $u^{173}x^{48}+$ $u^{209}x^{36}+$ $u^{165}x^{33}+$ $u^{213}x^{24}+$ $u^{214}x^{18}+$ $u^{158}x^{12}+$ $u^{146}x^{9}+$ $x^{6}+$ $u^{50}x^{3}$
	1.17	$u^{164}x^{192}+$ $u^{224}x^{144}+$ $u^{59}x^{132}+$ $u^{124}x^{129}+$ $u^{207}x^{96}+$ $u^{211}x^{72}+$ $u^{5}x^{66}+$ $u^{26}x^{48}+$ $u^{20}x^{36}+$ $u^{101}x^{33}+$ $u^{175}x^{24}+$ $u^{241}x^{18}+$ $x^{12}+$ $u^{15}x^{9}+$ $u^{217}x^{6}+$ $u^{212}x^{3}$
	2.1	$x^{3}+x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}$
	3.1	$x^{3}+u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}$
	4.1	$x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}$
	5.1	$x^{3}+x^{5}+x^{18}+x^{40}+x^{66}$
	6.1	$x^{3}+x^{12}+x^{40}+x^{66}+x^{130}$
	7.1	$x^{57}$

@@ Line 7: / Line 7: @@
 <th><math>F(x)</math></th>
 </tr>
+<tr>
-<td><math>5</math></td>
+<td rowspan="3"><math>5</math></td>
-<td><math>1.1</math>
+<td>1.1</td>
-<math>1.2</math>
+<td><math>x^3</math></td>
-<math>2.1</math></td>
-<td><math>x^3</math>
-<math>x^5</math>
-<math>x^{-1}</math></td>
 </tr>
-</table>
-<table>
 <tr>
-<th><math>n</math></th>
+<td>1.2</td>
-<th><math>N^\circ</math></th>
+<td><math>x^5</math></td>
-<th><math>F(x)</math></th>
 </tr>
 <tr>
+<td>2.1</td>
+<td><math>x^{-1}</math></td>
+</tr>
+</tr>
+<tr class="strongDivider">
 <td rowspan="14"><math>6</math></td>
 <td>1.1</td>
@@ Line 82: / Line 78: @@
 <td><math>x^{3} + </math> <math>u^{17}(x^{17} + </math> <math>x^{18} + </math> <math>x^{20} + </math> <math>x^{24}) + </math> <math>u^{14}((u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{2} + </math> <math>(u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{4}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{8}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{16}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{32}+ (u^{2}x)^{9} +(u^{2}x)^{19} +(u^{2}x)^{36} + </math> <math>x^{21}+x^{42}</math></td>
 </tr>
-</table>
+<tr class="strongDivider">
-<table>
-<tr>
-<th><math>n</math></th>
-<th><math>N^\circ</math></th>
-<th><math>F(x)</math></th>
-</tr>
-<tr>
 <td rowspan="19"><math>7</math></td>
 <td>1.1</td>
@@ Line 205: / Line 191: @@
 <td><math>
 u^{2}x^{96} + </math> <math>u^{78}x^{80} + </math> <math>u^{121}x^{72} + </math> <math>u^{49}x^{68} + </math> <math>u^{77}x^{66} + </math> <math>u^{29}x^{65} + </math> <math>u^{119}x^{48} + </math> <math>u^{117}x^{40} + </math> <math>u^{28}x^{36} + </math> <math>u^{107}x^{34} +u^{62}x^{33} +u^{125}x^{24} +u^{76}x^{20} +u^{84}x^{18} +u^{110}x^{17} +u^{49}x^{12} +u^{102}x^{10} +u^{69}x^{9} + </math> <math>u^{14}x^{6} + </math> <math>x^{5} + </math> <math>x^{3}
+</math></td>
+</tr>
+<tr class="strongDivider">
+<td rowspan="23">8</td>
+<td>1.1</td>
+<td><math>
+x^{3}
+</math></td>
+</tr>
+<tr>
+<td>1.2</td>
+<td><math>
+x^{9}
+</math></td>
+</tr>
+<tr>
+<td>1.3</td>
+<td><math>
+x^{3}+{\rm Tr}(x^{9})
+</math></td>
+</tr>
+<tr>
+<td>1.4</td>
+<td><math>
+x^{9}+{\rm Tr}(x^{3})
+</math></td>
+</tr>
+<tr>
+<td>1.5</td>
+<td><math>
+x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}
+</math></td>
+</tr>
+<tr>
+<td>1.6</td>
+<td><math>
+x^{3} + u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}
+</math></td>
+</tr>
+<tr>
+<td>1.7</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.8</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.9</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.10</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.11</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.12</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.13</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.14</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.15</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.16</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>1.17</td>
+<td><math>
+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>
+</tr>
+<tr>
+<td>2.1</td>
+<td><math>
+x^{3}+ x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}
+</math></td>
+</tr>
+<tr>
+<td>3.1</td>
+<td><math>
+x^{3}+ u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}
+</math></td>
+</tr>
+<tr>
+<td>4.1</td>
+<td><math>
+x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}
+</math></td>
+</tr>
+<tr>
+<td>5.1</td>
+<td><math>
+x^{3}+x^{5}+x^{18}+x^{40}+x^{66}
+</math></td>
+</tr>
+<tr>
+<td>6.1</td>
+<td><math>
+x^{3}+x^{12}+x^{40}+x^{66}+x^{130}
+</math></td>
+</tr>
+<tr>
+<td>7.1</td>
+<td><math>
+x^{57}
 </math></td>
 </tr>
 </table>

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

Revision as of 17:43, 22 January 2019

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