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

Revision as of 19:10, 11 July 2020

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

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

$n$	$N^{\circ }$	$F(x)$	Γ-rank	Δ-rank	Aut(dev(G_F))/2²ⁿ	Aut(dev(G_F))/2²ⁿ
$5$	1.1	x³	330	42	4960	4960
	1.2	x⁵	330	42	4960	158720
	2.1	x^-1	496	232	310	310
$6$	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
$7$	1.1	$x^{3}$	3610	198	113792	113792
	1.2	$x^{3}+{\rm {Tr}}(x^{9})$	4026	212	896	896
	2.1	$x^{34}+x^{18}+x^{5}$	4034	210	896	896
	2.2	$x^{3}+x^{17}+x^{33}+x^{34}$	4040	212	896	896
	3.1	$x^{5}$	3708	198	113792	113792
	4.1	$x^{9}$	3610	198	113792	14565376
	5.1	$x^{13}$	4270	338	889	889
	6.1	$x^{57}$	4704	436	889	889
	7.1	$x^{-1}$	8128	4928	1778	1778
	8.1	$x^{65}+x^{10}+x^{3}$	4038	212	896	896
	9.1	$x^{3}+x^{9}+x^{18}+x^{66}$	4044	212	896	896
	10.1	$x^{3}+x^{12}+x^{17}+x^{33}$	4048	210	896	896
	10.2	$x^{3}+x^{17}+x^{20}+x^{34}+x^{66}$	4040	210	896	896
	11.1	$x^{3}+x^{20}+x^{34}+x^{66}$	4048	210	896	896
	12.1	$x^{3}+x^{12}+x^{40}+x^{72}$	4048	210	896	896
	13.1	$x^{3}+x^{5}+x^{10}+x^{33}+x^{34}$	4040	212	896	896
	14.1	$x^{3}+x^{6}+x^{34}+x^{40}+x^{72}$	4048	212	896	896
	14.2	$x^{3}+x^{5}+x^{6}+x^{12}+x^{33}+x^{34}$	4050	210	896	896
	14.3	$u^{2}x^{96}+$ $u^{78}x^{80}+$ $u^{121}x^{72}+$ $u^{49}x^{68}+$ $u^{77}x^{66}+$ $u^{29}x^{65}+$ $u^{119}x^{48}+$ $u^{117}x^{40}+$ $u^{28}x^{36}+$ $u^{107}x^{34}+u^{62}x^{33}+u^{125}x^{24}+u^{76}x^{20}+u^{84}x^{18}+u^{110}x^{17}+u^{49}x^{12}+u^{102}x^{10}+u^{69}x^{9}+$ $u^{14}x^{6}+$ $x^{5}+$ $x^{3}$	4046	212	128	128
$8$	1.1	$x^{3}$	11818	420
	1.2	$x^{9}$	12370	420
	1.3	$x^{3}+{\rm {Tr}}(x^{9})$	13800	432
	1.4	$x^{9}+{\rm {Tr}}(x^{3})$	13804	434
	1.5	$x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}$	13842	436
	1.6	$x^{3}+u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}$	13848	438
	1.7	$u^{188}x^{192}+$ $u^{129}x^{144}+$ $u^{172}x^{132}+$ $u^{138}x^{129}+$ $u^{74}x^{96}+$ $u^{244}x^{72}+$ $u^{22}x^{66}+$ $u^{178}x^{48}+$ $u^{150}x^{36}+$ $u^{146}x^{33}+$ $u^{6}x^{24}+$ $u^{60}x^{18}+$ $u^{80}x^{12}+$ $u^{140}x^{9}+$ $u^{221}x^{6}+$ $u^{19}x^{3}$	14034	438
	1.8	$u^{37}x^{192}+$ $u^{110}x^{144}+$ $u^{40}x^{132}+$ $u^{53}x^{129}+$ $u^{239}x^{96}+$ $u^{235}x^{72}+$ $u^{126}x^{66}+$ $u^{215}x^{48}+$ $u^{96}x^{36}+$ $u^{29}x^{33}+$ $u^{19}x^{24}+$ $u^{14}x^{18}+$ $u^{139}x^{12}+$ $u^{230}x^{9}+$ $u^{234}x^{6}+$ $u^{228}x^{3}$	14032	438
	1.9	$u^{242}x^{192}+$ $u^{100}x^{144}+$ $u^{66}x^{132}+$ $u^{230}x^{129}+$ $u^{202}x^{96}+$ $u^{156}x^{72}+$ $u^{254}x^{66}+$ $u^{18}x^{48}+$ $u^{44}x^{36}+$ $u^{95}x^{33}+$ $u^{100}x^{24}+$ $u^{245}x^{18}+$ $u^{174}x^{12}+$ $u^{175}x^{9}+$ $u^{247}x^{6}+$ $u^{166}x^{3}$	14036	438
	1.10	$u^{100}x^{192}+$ $u^{83}x^{144}+$ $u^{153}x^{132}+$ $u^{65}x^{129}+$ $u^{174}x^{96}+$ $u^{136}x^{72}+$ $u^{46}x^{66}+u^{55}x^{48}+u^{224}x^{36}+u^{180}x^{33}+u^{179}x^{24}+u^{226}x^{18}+u^{54}x^{12}+u^{168}x^{9}+u^{89}x^{6}+u^{56}x^{3}$	14036	438
	1.11	$u^{77}x^{192}+$ $u^{133}x^{144}+$ $u^{47}x^{132}+$ $u^{229}x^{129}+$ $u^{23}x^{96}+$ $u^{242}x^{72}+$ $u^{242}x^{66}+$ $u^{245}x^{48}+$ $u^{212}x^{36}+$ $u^{231}x^{33}+$ $u^{174}x^{24}+$ $u^{216}x^{18}+$ $u^{96}x^{12}+$ $u^{253}x^{9}+$ $u^{154}x^{6}+$ $u^{71}x^{3}$	14032	438
	1.12	$u^{220}x^{192}+$ $u^{94}x^{144}+$ $u^{70}x^{132}+$ $u^{159}x^{129}+$ $u^{145}x^{96}+$ $u^{160}x^{72}+$ $u^{74}x^{66}+$ $u^{184}x^{48}+$ $u^{119}x^{36}+$ $u^{106}x^{33}+$ $u^{253}x^{24}+$ $wx^{18}+$ $u^{90}x^{12}+$ $u^{169}x^{9}+$ $u^{118}x^{6}+$ $u^{187}x^{3}$	14034	438
	1.13	$u^{98}x^{192}+$ $u^{225}x^{144}+$ $u^{111}x^{132}+$ $u^{238}x^{129}+$ $u^{182}x^{96}+$ $u^{125}x^{72}+$ $u^{196}x^{66}+$ $u^{219}x^{48}+$ $u^{189}x^{36}+$ $u^{199}x^{33}+$ $u^{181}x^{24}+$ $u^{110}x^{18}+$ $u^{19}x^{12}+$ $u^{175}x^{9}+$ $u^{133}x^{6}+$ $u^{47}x^{3}$	14030	438
	1.14	$u^{236}x^{192}+$ $u^{212}x^{160}+$ $u^{153}x^{144}+$ $u^{185}x^{136}+$ $u^{3}x^{132}+$ $u^{89}x^{130}+$ $u^{189}x^{129}+$ $u^{182}x^{96}+$ $u^{105}x^{80}+$ $u^{232}x^{72}+$ $u^{219}x^{68}+$ $u^{145}x^{66}+$ $u^{171}x^{65}+$ $u^{107}x^{48}+$ $u^{179}x^{40}+$ $u^{227}x^{36}+$ $u^{236}x^{34}+$ $u^{189}x^{33}+$ $u^{162}x^{24}+$ $u^{216}x^{20}+$ $u^{162}x^{18}+$ $u^{117}x^{17}+$ $u^{56}x^{12}+$ $u^{107}x^{10}+$ $u^{236}x^{9}+$ $u^{253}x^{6}+$ $u^{180}x^{5}+$ $u^{18}x^{3}$	14046	454
	1.15	$u^{27}x^{192}+$ $u^{167}x^{144}+$ $u^{26}x^{132}+$ $u^{231}x^{129}+$ $u^{139}x^{96}+$ $u^{30}x^{72}+$ $u^{139}x^{66}+$ $u^{203}x^{48}+$ $u^{36}x^{36}+$ $u^{210}x^{33}+$ $u^{195}x^{24}+$ $u^{12}x^{18}+$ $u^{43}x^{12}+$ $u^{97}x^{9}+$ $u^{61}x^{6}+$ $u^{39}x^{3}$	14036	454
	1.16	$u^{6}x^{192}+$ $u^{85}x^{144}+$ $u^{251}x^{132}+$ $u^{215}x^{129}+$ $u^{229}x^{96}+$ $u^{195}x^{72}+$ $u^{152}x^{66}+$ $u^{173}x^{48}+$ $u^{209}x^{36}+$ $u^{165}x^{33}+$ $u^{213}x^{24}+$ $u^{214}x^{18}+$ $u^{158}x^{12}+$ $u^{146}x^{9}+$ $x^{6}+$ $u^{50}x^{3}$	14032	438
	1.17	$u^{164}x^{192}+$ $u^{224}x^{144}+$ $u^{59}x^{132}+$ $u^{124}x^{129}+$ $u^{207}x^{96}+$ $u^{211}x^{72}+$ $u^{5}x^{66}+$ $u^{26}x^{48}+$ $u^{20}x^{36}+$ $u^{101}x^{33}+$ $u^{175}x^{24}+$ $u^{241}x^{18}+$ $x^{12}+$ $u^{15}x^{9}+$ $u^{217}x^{6}+$ $u^{212}x^{3}$	14028	438
	2.1	$x^{3}+x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}$	13200	414
	3.1	$x^{3}+u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}$	14024	438
	4.1	$x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}$	14040	454
	5.1	$x^{3}+x^{5}+x^{18}+x^{40}+x^{66}$	14044	446
	6.1	$x^{3}+x^{12}+x^{40}+x^{66}+x^{130}$	14046	438
	7.1	$x^{57}$	15358	960

@@ Line 16: / Line 16: @@
 <td rowspan="3"><math>5</math></td>
 <td>1.1</td>
-<td><math>x^3</math></td>
+<td><span class="htmlMath">x<sup>3</sup></span></td>
 <td>330</td>
 <td>42</td>
@@ Line 24: / Line 24: @@
 <tr>
 <td>1.2</td>
-<td><math>x^5</math></td>
+<td><span class="htmlMath">x<sup>5</sup></span></td>
 <td>330</td>
 <td>42</td>
@@ Line 32: / Line 32: @@
 <tr>
 <td>2.1</td>
-<td><math>x^{-1}</math></td>
+<td><span class="htmlMath">x<sup>-1</sup></span></td>
 <td>496</td>
 <td>232</td>
@@ Line 42: / Line 42: @@
 <td rowspan="14"><math>6</math></td>
 <td>1.1</td>
-<td><math>x^{3}</math></td>
+<td><span class="htmlMath">x<sup>3</sup></span></td>
 <td>1102</td>
 <td>94</td>
@@ Line 50: / Line 50: @@
 <tr>
 <td>1.2</td>
-<td><math>x^{3} + u^{11}x^{6} + ux^{9}</math></td>
+<td><span class="htmlMath">x<sup>3</sup> + u<sup>11</sup>x<sup>6</sup> + ux<sup>9</sup></span></td>
 <td>1146</td>
 <td>94</td>
@@ Line 58: / Line 58: @@
 <tr>
 <td>2.1</td>
-<td><math>ux^{5} + x^{9} + u^{4}x^{17} + ux^{18} + u^{4}x^{20} + ux^{24} + u^{4}x^{34} + ux^{40}</math></td>
+<td><span class="htmlMath">ux<sup>5</sup> + x<sup>9</sup> + u<sup>4</sup>x<sup>17</sup> + ux<sup>18</sup> + u<sup>4</sup>x<sup>20</sup> + ux<sup>24</sup> + u<sup>4</sup>x<sup>34</sup> + ux<sup>40</sup></span></td>
 <td>1158</td>
 <td>96</td>
@@ Line 66: / Line 66: @@
 <tr>
 <td>2.2</td>
-<td><math>u^{7}x^{3} + x^{5} + u^{3}x^{9} + u^{4}x^{10} + x^{17} + u^{6}x^{18}</math></td>
+<td><span class="htmlMath">u<sup>7</sup>x<sup>3</sup> + x<sup>5</sup> + u<sup>3</sup>x<sup>9</sup> + u<sup>4</sup>x<sup>10</sup> + x<sup>17</sup> + u<sup>6</sup>x<sup>18</sup></span></td>
 <td>1166</td>
 <td>94</td>
@@ Line 74: / Line 74: @@
 <tr>
 <td>2.3</td>
-<td><math>x^{3} + ux^{24} + x^{10}</math></td>
+<td><span class="htmlMath">x<sup>3</sup> + ux<sup>24</sup> + x<sup>10</sup></span></td>
 <td>1166</td>
 <td>96</td>
@@ Line 82: / Line 82: @@
 <tr>
 <td>2.4</td>
-<td><math>x^{3} + u^{17}(x^{17} + x^{18} + x^{20} + x^{24})</math></td>
+<td><span class="htmlMath">x<sup>3</sup> + u<sup>17</sup>(x<sup>17</sup> + x<sup>18</sup> + x<sup>20</sup> + x<sup>24</sup>)</span></td>
 <td>1168</td>
 <td>96</td>
@@ Line 90: / Line 90: @@
 <tr>
 <td>2.5</td>
-<td><math>x^{3} + u^{11}x^{5} + u^{13}x^{9} + x^{17} + u^{11}x^{33} + x^{48}</math></td>
+<td><span class="htmlMath">x<sup>3</sup> + u<sup>11</sup>x<sup>5</sup> + u<sup>13</sup>x<sup>9</sup> + x<sup>17</sup> + u<sup>11</sup>x<sup>33</sup> + x<sup>48</sup></span></td>
 <td>1170</td>
 <td>96</td>
@@ Line 98: / Line 98: @@
 <tr>
 <td>2.6</td>
-<td><math>u^{25}x^{5} + x^{9} + u^{38}x^{12} + u^{25}x^{18} + u^{25}x^{36}</math></td>
+<td><span class="htmlMath">u<sup>25</sup>x<sup>5</sup> + x<sup>9</sup> + u<sup>38</sup>x<sup>12</sup> + u<sup>25</sup>x<sup>18</sup> + u<sup>25</sup>x<sup>36</sup></span></td>
 <td>1170</td>
 <td>96</td>
@@ Line 106: / Line 106: @@
 <tr>
 <td>2.7</td>
-<td><math>u^{40}x^{5} + u^{10}x^{6} + u^{62}x^{20} + u^{35}x^{33} + u^{15}x^{34} + u^{29}x^{48}</math></td>
+<td><span class="htmlMath">u<sup>40</sup>x<sup>5</sup> + u<sup>10</sup>x<sup>6</sup> + u<sup>62</sup>x<sup>20</sup> + u<sup>35</sup>x<sup>33</sup> + u<sup>15</sup>x<sup>34</sup> + u<sup>29</sup>x<sup>48</sup></span></td>
 <td>1170</td>
 <td>96</td>
@@ Line 114: / Line 114: @@
 <tr>
 <td>2.8</td>
-<td><math>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}</math></td>
+<td><span class="htmlMath">u<sup>34</sup>x<sup>6</sup> + u<sup>52</sup>x<sup>9</sup> + u<sup>48</sup>x<sup>12</sup> + u<sup>6</sup>x<sup>20</sup> + u<sup>9</sup>x<sup>33</sup> + u<sup>23</sup>x<sup>34</sup> + u<sup>25</sup>x<sup>40</sup></span></td>
 <td>1170</td>
 <td>96</td>
@@ Line 122: / Line 122: @@
 <tr>
 <td>2.9</td>
-<td><math>x^{9} + u^{4}(x^{10} + x^{18}) + u^{9}(x^{12} + x^{20} + x^{40})</math></td>
+<td><span class="htmlMath">x<sup>9</sup> + u<sup>4</sup>(x<sup>10</sup> + x<sup>18</sup>) + u<sup>9</sup>(x<sup>12</sup> + x<sup>20</sup> + x<sup>40</sup>)</span></td>
 <td>1172</td>
 <td>96</td>
@@ Line 130: / Line 130: @@
 <tr>
 <td>2.10</td>
-<td><math>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}</math></td>
+<td><span class="htmlMath">u<sup>52</sup>x<sup>3</sup> + u<sup>47</sup>x<sup>5</sup> + ux<sup>6</sup> + u<sup>9</sup>x<sup>9</sup> + u<sup>44</sup>x<sup>12</sup> + u<sup>47</sup>x<sup>33</sup> + u<sup>10</sup>x<sup>34</sup> + u<sup>33</sup>x<sup>40</sup></span></td>
 <td>1172</td>
 <td>96</td>
@@ Line 138: / Line 138: @@
 <tr>
 <td>2.11</td>
-<td><math>u(x^{6} + x^{10} + x^{24} + x^{33}) + x^{9} + u^{4}x^{17}</math></td>
+<td><span class="htmlMath">u(x<sup>6</sup> + x<sup>10</sup> + x<sup>24</sup> + x<sup>33</sup>) + x<sup>9</sup> + u<sup>4</sup>x<sup>17</sup></span></td>
 <td>1174</td>
 <td>96</td>
@@ Line 146: / Line 146: @@
 <tr>
 <td>2.12</td>
-<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>
+<td><span class="htmlMath">x<sup>3</sup> + u<sup>17</sup>(x<sup>17</sup> + x<sup>18</sup> + x<sup>20</sup> + x<sup>24</sup>) + u<sup>14</sup>((u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>2</sup> + (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>4</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>8</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>16</sup>+ (u<sup>52</sup>x<sup>3</sup> + u<sup>6</sup>x<sup>5</sup> + u<sup>19</sup>x<sup>7</sup> + u<sup>28</sup>x<sup>11</sup> + u<sup>2</sup>x<sup>13</sup>)<sup>32</sup>+ (u<sup>2</sup>x)<sup>9</sup> +(u<sup>2</sup>x)<sup>19</sup> +(u<sup>2</sup>x)<sup>36</sup> + x<sup>21</sup>+x<sup>42</sup></span></td>
 <td>1300</td>
 <td>152</td>

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

Revision as of 19:10, 11 July 2020

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